Texas Instruments TI82 STATS User manual
TI82 STATS
GRAPHING CALCULATOR
GUIDEBOOK
© 1996, 2000, 2005 Texas Instruments Incorporated.
IBM is a registered trademark of International Business Machines Corporation
Macintosh is a registered trademark of Apple Computer, Inc.
82STAT~2.DOC TI83 Intl English, Title Page Bob Fedorisko Revised: 10/28/05 11:55 AM Printed: 10/28/05
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Important
US FCC
Information
Concerning
Radio Frequency
Interference
Texas Instruments makes no warranty, either expressed or implied, including but not limited to any implied warranties of merchantability and fitness for a particular purpose, regarding any programs or book materials and makes such materials available solely on an “asis” basis.
In no event shall Texas Instruments be liable to anyone for special, collateral, incidental, or consequential damages in connection with or arising out of the purchase or use of these materials, and the sole and exclusive liability of Texas Instruments, regardless of the form of action, shall not exceed the purchase price of this equipment. Moreover, Texas
Instruments shall not be liable for any claim of any kind whatsoever against the use of these materials by any other party.
This equipment has been tested and found to comply with the limits for a
Class B digital device, pursuant to Part 15 of the FCC rules. These limits are designed to provide reasonable protection against harmful interference in a residential installation. This equipment generates, uses, and can radiate radio frequency energy and, if not installed and used in accordance with the instructions, may cause harmful interference with radio communications. However, there is no guarantee that interference will not occur in a particular installation.
If this equipment does cause harmful interference to radio or television reception, which can be determined by turning the equipment off and on, you can try to correct the interference by one or more of the following measures:
•
Reorient or relocate the receiving antenna.
•
Increase the separation between the equipment and receiver.
•
Connect the equipment into an outlet on a circuit different from that to which the receiver is connected.
•
Consult the dealer or an experienced radio/television technician for help.
Caution: Any changes or modifications to this equipment not expressly approved by Texas Instruments may void your authority to operate the equipment.
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Table of Contents
This manual describes how to use the TI82 STATS Graphing Calculator. Getting
Started is an overview of TI82 STATS features. Chapter 1 describes how the
TI82 STATS operates. Other chapters describe various interactive features. Chapter
17 shows how to combine these features to solve problems.
Getting Started:
Do This First!
TI82 STATS Keyboard
.....................................................................................
TI82 STATS Menus
............................................................................................
First Steps
....................................................................................................................
Entering a Calculation: The Quadratic Formula
.................................
Converting to a Fraction: The Quadratic Formula
............................
Displaying Complex Results: The Quadratic Formula
...................
Defining a Function: Box with Lid
.............................................................
9
Defining a Table of Values: Box with Lid
.............................................
10
7
8
5
6
2
4
Zooming In on the Table: Box with Lid
..................................................
11
Setting the Viewing Window: Box with Lid
.........................................
12
Displaying and Tracing the Graph: Box with Lid
.............................
13
Zooming In on the Graph: Box with Lid
.................................................
15
Finding the Calculated Maximum: Box with Lid
..............................
16
Other TI82 STATS Features
..........................................................................
17
Chapter 1:
Operating the
TI82 STATS
Turning On and Turning Off the TI82 STATS
.................................
12
Setting the Display Contrast
............................................................................
13
The Display
................................................................................................................
14
Entering Expressions and Instructions
......................................................
16
TI82 STATS Edit Keys
.....................................................................................
18
Setting Modes
...........................................................................................................
19
Using TI82 STATS Variable Names
.......................................................
113
Storing Variable Values
.....................................................................................
114
Recalling Variable Values
................................................................................
115
ENTRY (Last Entry) Storage Area
..............................................................
116
Ans (Last Answer) Storage Area
..................................................................
118
TI82 STATS Menus
............................................................................................
119
VARS and VARS Y.VARS
Menus
..............................................................
121
Equation Operating System (EOSé)
.........................................................
122
Error Conditions
......................................................................................................
124
Introduction iii
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Table of Contents
(continued)
Chapter 2:
Math, Angle, and
Test Operations
Getting Started: Coin Flip
.................................................................................
22
Keyboard Math Operations
..............................................................................
23
MATH Operations
...................................................................................................
25
Using the Equation Solver
................................................................................
28
MATH NUM (Number) Operations
..............................................................
213
Entering and Using Complex Numbers
....................................................
216
MATH CPX
(Complex) Operations
............................................................
218
MATH PRB
(Probability) Operations
........................................................
220
ANGLE
Operations
................................................................................................
223
TEST
(Relational) Operations
........................................................................
225
TEST LOGIC
(Boolean) Operations
..........................................................
226
Chapter 3:
Function
Graphing
Getting Started: Graphing a Circle
..............................................................
32
Defining Graphs
......................................................................................................
33
Setting the Graph Modes
...................................................................................
34
Defining Functions
................................................................................................
35
Selecting and Deselecting Functions
..........................................................
37
Setting Graph Styles for Functions
..............................................................
39
Setting the Viewing Window Variables
...................................................
311
Setting the Graph Format
..................................................................................
313
Displaying Graphs
..................................................................................................
315
Exploring Graphs with the FreeMoving Cursor
................................
317
Exploring Graphs with
TRACE
.....................................................................
318
Exploring Graphs with the
ZOOM
Instructions
..................................
320
Using
ZOOM MEMORY
....................................................................................
323
Using the CALC (Calculate) Operations
..................................................
325
Chapter 4:
Parametric
Graphing
Chapter 5:
Polar Graphing
Getting Started: Path of a Ball
Exploring Parametric Graphs
........................................................................
Defining and Displaying Parametric Graphs
........................................
..........................................................................
42
44
47
Getting Started: Polar Rose
..............................................................................
52
Defining and Displaying Polar Graphs
.....................................................
53
Exploring Polar Graphs
......................................................................................
56
iv Introduction
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Chapter 6:
Sequence
Graphing
Chapter 7:
Tables
Chapter 8:
DRAW
Operations
Chapter 9:
Split Screen
Getting Started: Forest and Trees
.................................................................
62
Defining and Displaying Sequence Graphs
...........................................
63
Selecting Axes Combinations
.........................................................................
68
Exploring Sequence Graphs
.............................................................................
69
Graphing Web Plots
..............................................................................................
611
Using Web Plots to Illustrate Convergence
...........................................
612
Graphing Phase Plots
...........................................................................................
613
Comparing TI82 STATS and TI.82 Sequence Variables
...........
615
Keystroke Differences Between TI82 STATS and TI82
..........
616
Getting Started: Roots of a Function
..........................................................
72
Setting Up the Table
.............................................................................................
73
Defining the Dependent Variables
...............................................................
74
Displaying the Table
.............................................................................................
75
Getting Started: Drawing a Tangent Line
...............................................
82
Using the
DRAW
Menu
......................................................................................
83
Clearing Drawings
.................................................................................................
84
Drawing Line Segments
.....................................................................................
85
Drawing Horizontal and Vertical Lines
...................................................
86
Drawing Tangent Lines
......................................................................................
88
Drawing Functions and Inverses
...................................................................
89
Shading Areas on a Graph
................................................................................
810
Drawing Circles
.......................................................................................................
811
Placing Text on a Graph
.....................................................................................
812
Using Pen to Draw on a Graph
......................................................................
813
Drawing Points on a Graph
..............................................................................
814
Drawing Pixels
.........................................................................................................
816
Storing Graph Pictures ( Pic )
............................................................................
817
Recalling Graph Pictures ( Pic )
.......................................................................
818
Storing Graph Databases ( GDB )
...................................................................
819
Recalling Graph Databases ( GDB )
..............................................................
820
Getting Started: Exploring the Unit Circle
.............................................
92
Using Split Screen
..................................................................................................
93
Horiz (Horizontal) Split Screen
.....................................................................
94
GT (GraphTable) Split Screen
....................................................................
95
TI82 STATS Pixels in Horiz and GT Modes
....................................
96
Introduction v
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Table of Contents
(continued)
Chapter 10:
Matrices
Chapter 11:
Lists
Chapter 12:
Statistics
Chapter 13:
Inferential
Statistics and
Distributions
Getting Started: Systems of Linear Equations
.....................................
102
Defining a Matrix
...................................................................................................
103
Viewing and Editing Matrix Elements
......................................................
104
Using Matrices with Expressions
.................................................................
107
Displaying and Copying Matrices
................................................................
108
Using Math Functions with Matrices
.........................................................
109
Using the
MATRX MATH
Operations
.......................................................
1012
Getting Started: Generating a Sequence
..................................................
112
Naming Lists
..............................................................................................................
113
Storing and Displaying Lists
...........................................................................
114
Entering List Names
.............................................................................................
116
Attaching Formulas to List Names
..............................................................
117
Using Lists in Expressions
................................................................................
119
LIST OPS
Menu
......................................................................................................
1110
LIST MATH
Menu
..................................................................................................
1117
Getting Started: Pendulum Lengths and Periods
................................
122
Setting up Statistical Analyses
.......................................................................
1210
Using the Stat List Editor
..................................................................................
1211
Attaching Formulas to List Names
..............................................................
1214
Detaching Formulas from List Names
......................................................
1216
Switching Stat List Editor Contexts
............................................................
1217
Stat List Editor Contexts
....................................................................................
1218
STAT EDIT
Menu
..................................................................................................
1220
Regression Model Features
..............................................................................
1222
STAT CALC Menu
................................................................................................
1224
Statistical Variables
...............................................................................................
1229
Statistical Analysis in a Program
..................................................................
1230
Statistical Plotting
...................................................................................................
1231
Statistical Plotting in a Program
....................................................................
1237
Getting Started: Mean Height of a Population
.....................................
132
Inferential Stat Editors
.........................................................................................
136
STAT TESTS Menu
.............................................................................................
139
Inferential Statistics Input Descriptions
...................................................
1326
Test and Interval Output Variables
..............................................................
1328
Distribution Functions
.........................................................................................
1329
Distribution Shading
.............................................................................................
1335
vi Introduction
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Chapter 14:
Financial
Functions
Chapter 15:
CATALOG
,
Strings,
Hyperbolic
Functions
Chapter 16:
Programming
Chapter 17:
Applications
Getting Started: Financing a Car
...................................................................
142
Getting Started: Computing Compound Interest
................................
143
Using the TVM Solver
.........................................................................................
144
Using the Financial Functions
........................................................................
145
Calculating Time Value of Money ( TVM )
..............................................
146
Calculating Cash Flows
......................................................................................
148
Calculating Amortization
...................................................................................
149
Calculating Interest Conversion
....................................................................
1412
Finding Days between Dates/Defining Payment Method
.......................
1413
Using the
TVM
Variables
...................................................................................
1414
Browsing the TI82 STATS
CATALOG
..................................................
152
Entering and Using Strings
...............................................................................
153
Storing Strings to String Variables
..............................................................
154
String Functions and Instructions in the
CATALOG
........................
156
Hyperbolic Functions in the
CATALOG
..................................................
1510
Getting Started: Volume of a Cylinder
.....................................................
162
Creating and Deleting Programs
...................................................................
164
Entering Command Lines and Executing Programs
........................
165
Editing Programs
....................................................................................................
166
Copying and Renaming Programs
...............................................................
167
PRGM CTL
(Control) Instructions
..............................................................
168
PRGM I/O
(Input/Output) Instructions
.....................................................
1616
Calling Other Programs as Subroutines
...................................................
1622
Comparing Test Results Using Box Plots
...............................................
172
Graphing Piecewise Functions
.......................................................................
174
Graphing Inequalities
...........................................................................................
175
Solving a System of Nonlinear Equations
..............................................
176
Using a Program to Create the Sierpinski Triangle
..........................
177
Graphing Cobweb Attractors
..........................................................................
178
Using a Program to Guess the Coefficients
...........................................
179
Graphing the Unit Circle and Trigonometric Curves
......................
1710
Finding the Area between Curves
................................................................
1711
Using Parametric Equations: Ferris Wheel Problem
........................
1712
Demonstrating the Fundamental Theorem of Calculus
..................
1714
Computing Areas of Regular NSided Polygons
................................
1716
Computing and Graphing Mortgage Payments
...................................
1718
Introduction vii
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Table of Contents
(continued)
Chapter 18:
Memory
Management
Appendix A:
Tables and
Reference
Information
Appendix B:
General
Information
Checking Available Memory
..........................................................................
182
Deleting Items from Memory
.........................................................................
183
Clearing Entries and List Elements
.............................................................
184
Resetting the TI82 STATS
.............................................................................
185
Chapter 19:
Communication
Link
Getting Started: Sending Variables
.............................................................
192
TI82 STATS
LINK
...............................................................................................
193
Selecting Items to Send
.......................................................................................
194
Receiving Items
.......................................................................................................
195
Transmitting Items
.................................................................................................
196
Transmitting Lists to a TI82
..........................................................................
198
Transmitting from a TI82 to a TI82 STATS
.....................................
199
Backing Up Memory
............................................................................................
1910
Table of Functions and Instructions
Menu Map
Variables
Statistical Formulas
............................................................
...................................................................................................................
.......................................................................................................................
...............................................................................................
A2
A39
A49
A50
Financial Formulas
................................................................................................
A54
Battery Information
...............................................................................................
B2
In Case of Difficulty
.............................................................................................
B4
Error Conditions
......................................................................................................
B5
Accuracy Information
..........................................................................................
B10
Support and Service Information
..................................................................
B12
Warranty Information
..........................................................................................
B13
Index
viii Introduction
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Contents
Getting Started:
Do This First!
TI82 STATS Keyboard
.....................................................................................
TI82 STATS Menus
............................................................................................
First Steps
....................................................................................................................
Entering a Calculation: The Quadratic Formula
.................................
Converting to a Fraction: The Quadratic Formula
............................
Displaying Complex Results: The Quadratic Formula
...................
Defining a Function: Box with Lid
.............................................................
9
Defining a Table of Values: Box with Lid
.............................................
10
7
8
5
6
2
4
Zooming In on the Table: Box with Lid
..................................................
11
Setting the Viewing Window: Box with Lid
.........................................
12
Displaying and Tracing the Graph: Box with Lid
.............................
13
Zooming In on the Graph: Box with Lid
.................................................
15
Finding the Calculated Maximum: Box with Lid
..............................
16
Other TI82 STATS Features
..........................................................................
17
Getting Started 1
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TI82 STATS Keyboard
Generally, the keyboard is divided into these zones: graphing keys, editing keys, advanced function keys, and scientific calculator keys.
Keyboard Zones
Graphing keys access the interactive graphing features.
Editing keys allow you to edit expressions and values.
Advanced function keys display menus that access the advanced functions.
Scientific calculator keys access the capabilities of a standard scientific calculator.
Graphing Keys
Editing Keys
Advanced
Function Keys
Scientific
Calculator Keys
2 Getting Started
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Using the
Color.Coded
Keyboard
The keys on the TI82 STATS are colorcoded to help you easily locate the key you need.
The gray keys are the number keys. The blue keys along the right side of the keyboard are the common math functions. The blue keys across the top set up and display graphs.
The primary function of each key is printed in white on the key.
For example, when you press , the
MATH
menu is displayed.
Using the
y
and
ƒ Keys
The secondary function of each key is printed in yellow above the key. When you press the yellow y key, the character, abbreviation, or word printed in yellow above the other keys becomes active for the next keystroke. For example, when you press y and then , the
TEST
menu is displayed. This guidebook describes this keystroke combination as y [
TEST
].
The alpha function of each key is printed in green above the key. When you press the green ƒ key, the alpha character printed in green above the other keys becomes active for the next keystroke. For example, when you press ƒ and then
, the letter
A
is entered. This guidebook describes this keystroke combination as ƒ [
A
].
The y key accesses the second function printed in yellow above each key.
The
ƒ key accesses the alpha function printed in green above each key.
Getting Started 3
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TI82 STATS Menus
Displaying a Menu
While using your TI82 STATS, you often will need to access items from its menus.
When you press a key that displays a menu, that menu temporarily replaces the screen where you are working. For example, when you press , the
MATH
menu is displayed as a full screen.
After you select an item from a menu, the screen where you are working usually is displayed again.
Moving from One Menu to Another
Some keys access more than one menu. When you press such a key, the names of all accessible menus are displayed on the top line. When you highlight a menu name, the items in that menu are displayed. Press ~ and  to highlight each menu name.
Selecting an Item from a Menu
The number or letter next to the current menu item is highlighted. If the menu continues beyond the screen, a down arrow (
$
) replaces the colon (
:
) in the last displayed item. If you scroll beyond the last displayed item, an up arrow (
#
) replaces the colon in the first item displayed.You can select an item in either of two ways.
¦ Press † or } to move the cursor to the number or letter of the item; press Í.
¦ Press the key or key combination for the number or letter next to the item.
Leaving a Menu without Making a Selection
You can leave a menu without making a selection in any of three ways.
¦ Press ‘ to return to the screen where you were.
¦ Press y [
QUIT
] to return to the home screen.
¦ Press a key for another menu or screen.
4 Getting Started
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First Steps
Before starting the sample problems in this chapter, follow the steps on this page to reset the TI82 STATS to its factory settings and clear all memory. This ensures that the keystrokes in this chapter will produce the illustrated results.
To reset the TI82 STATS, follow these steps.
1. Press É to turn on the calculator.
2. Press and release y, and then press [
MEM
]
(above Ã).
When you press y, you access the operation printed in yellow above the next key that you press. [
MEM
] is the y operation of the Ã key.
The
MEMORY
menu is displayed.
3. Press
5
to select
5:Reset
.
The
RESET
menu is displayed.
4. Press
1
to select
1:All Memory
.
The
RESET MEMORY
menu is displayed.
5. Press
2
to select
2:Reset
.
All memory is cleared, and the calculator is reset to the factory default settings.
When you reset the TI82 STATS, the display contrast is reset.
¦
If the screen is very light or blank, press and release y, and then press and hold } to darken the screen.
¦
If the screen is very dark, press and release y, and then press and hold † to lighten the screen.
Getting Started 5
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Entering a Calculation: The Quadratic Formula
Use the quadratic formula to solve the quadratic equations 3X 2 + 5X + 2 = 0 and 2X 2
N X + 3 = 0. Begin with the equation 3X
2 + 5X + 2 = 0.
1. Press
3
¿ ƒ [
A
] (above ) to store the coefficient of the X 2 term.
2. Press ƒ [
:
] (above Ë). The colon allows you to enter more than one instruction on a line.
3. Press
5
¿ ƒ [
B
] (above ) to store the coefficient of the X term. Press
ƒ [
:
] to enter a new instruction on the same line. Press
2
¿ ƒ [
C
] (above
) to store the constant.
4. Press Í to store the values to the variables
A, B, and C.
The last value you stored is shown on the right side of the display. The cursor moves to the next line, ready for your next entry.
5. Press £ Ì ƒ [
B
] Ã y [
‡
] ƒ [
B
]
¡ ¹
4
ƒ [
A
] ƒ [
C
] ¤ ¤ ¥ £
2
ƒ [
A
] ¤ to enter the expression for one of the solutions for the quadratic formula,
− +
b
2
a ac
6. Press Í to find one solution for the equation 3X 2 + 5X + 2 = 0.
The answer is shown on the right side of the display. The cursor moves to the next line, ready for you to enter the next expression.
6 Getting Started
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Converting to a Fraction: The Quadratic Formula
You can show the solution as a fraction.
1. Press to display the
MATH
menu.
2. Press
1
to select
1:4Frac
from the
MATH menu.
When you press
1
,
Ans4Frac
is displayed on the home screen.
Ans
is a variable that contains the last calculated answer.
3. Press Í to convert the result to a fraction.
To save keystrokes, you can recall the last expression you entered, and then edit it for a new calculation.
4. Press y [
ENTRY
] (above Í) to recall the fraction conversion entry, and then press y
[
ENTRY
] again to recall the quadraticformula expression,
− +
b
2
a ac
5. Press } to move the cursor onto the
+
sign in the formula. Press ¹ to edit the quadraticformula expression to become:
− −
b ac
2
a
6. Press Í to find the other solution for the quadratic equation 3X 2 + 5X + 2 = 0.
Getting Started 7
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Displaying Complex Results: The Quadratic Formula
Now solve the equation 2X 2 N X + 3 = 0. When you set
a+b
i complex number mode, the TI82 STATS displays complex results.
1. Press z † † † † † † (6 times), and then press ~ to position the cursor over
a+b
i.
Press Í to select
a+b
i complexnumber mode.
2. Press y [
QUIT
] (above z) to return to the home screen, and then press ‘ to clear it.
3. Press
2
¿ ƒ [
A
] ƒ [
:
] Ì
1
¿ ƒ [
B
] ƒ [
:
]
3
¿ ƒ
[
C
] Í.
The coefficient of the X 2 term, the coefficient of the X term, and the constant for the new equation are stored to A, B, and C, respectively.
4. Press y [
ENTRY
] to recall the store instruction, and then press y [
ENTRY
] again to recall the quadraticformula expression,
− −
b
2
a ac
5. Press Í to find one solution for the equation 2X
2
N X + 3 = 0.
6. Press y [
ENTRY
] repeatedly until this quadraticformula expression is displayed:
− +
b
2
a ac
7. Press Í to find the other solution for the quadratic equation: 2X
2
N X + 3 = 0.
Note: An alternative for solving equations for real numbers is to use the builtin Equation
Solver (Chapter 2).
8 Getting Started
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Defining a Function: Box with Lid
Take a 20 cm. × 25 cm. sheet of paper and cut X × X squares from two corners. Cut
X × 12.5 cm. rectangles from the other two corners as shown in the diagram below.
Fold the paper into a box with a lid. What value of X would give your box the maximum volume V? Use the table and graphs to determine the solution.
Begin by defining a function that describes the volume of the box.
From the diagram: 2X + A = 20
2X + 2B = 25
V = A B X
Substituting: V = (20 N 2X) (25à 2 N X) X
X
20 A
X B X B
25
1. Press o to display the
Y= editor, which is where you define functions for tables and graphing.
2. Press £
20
¹
2
„ ¤ £
25
¥
2
¹
„ ¤ „ Í to define the volume function as
Y
1
in terms of
X
.
„ lets you enter
X
quickly, without having to press ƒ. The highlighted
=
sign indicates that
Y
1
is selected.
Getting Started 9
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Defining a Table of Values: Box with Lid
The table feature of the TI82 STATS displays numeric information about a function.
You can use a table of values from the function defined on page 9 to estimate an answer to the problem.
1. Press y [
TBLSET
] (above p) to display the
TABLE SETUP
menu.
2. Press Í to accept
TblStart=0
.
3. Press
1
Í to define the table increment
@Tbl=1
. Leave
Indpnt: Auto
and
Depend: Auto
so that the table will be generated automatically.
4. Press y [
TABLE
] (above s) to display the table.
Notice that the maximum value for
Y
1
(box’s volume) occurs when
X
is about
4
, between
3
and
5
.
5. Press and hold † to scroll the table until a negative result for
Y
1
is displayed.
Notice that the maximum length of
X
for this problem occurs where the sign of
Y
1
(box’s volume) changes from positive to negative, between
10
and
11
.
6. Press y [
TBLSET
].
Notice that
TblStart
has changed to
6
to reflect the first line of the table as it was last displayed. (In step 5, the first value of
X
displayed in the table is
6
.)
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Zooming In on the Table: Box with Lid
You can adjust the way a table is displayed to get more information about a defined function. With smaller values for
@Tbl
, you can zoom in on the table.
1. Press
3
Í to set
TblStart
. Press Ë
1
Í to set
@Tbl
.
This adjusts the table setup to get a more accurate estimate of
X
for maximum volume
Y
1
.
2. Press y [
TABLE
].
3. Press † and } to scroll the table.
Notice that the maximum value for
Y
1
is
410.26
, which occurs at
X
=
3.7
. Therefore, the maximum occurs where
3.6
<
X
<
3.8
.
4. Press y [
TBLSET
]. Press
3
Ë
6
Í to set
TblStart
. Press Ë
01
Í to set
@Tbl
.
5. Press y [
TABLE
], and then press † and } to scroll the table.
Four equivalent maximum values are shown,
410.60
at
X
=
3.67
,
3.68
,
3.69
, and
3.70
.
6. Press † and } to move the cursor to
3.67
.
Press ~ to move the cursor into the
Y
1
column.
The value of
Y
1
at
X
=
3.67
is displayed on the bottom line in full precision as
410.261226
.
7. Press † to display the other maximums.
The value of
Y
1
at
X
=
3.68
in full precision is
410.264064
, at
X
=
3.69
is
410.262318
, and at
X
=
3.7
is
410.256
.
The maximum volume of the box would occur at
3.68
if you could measure and cut the paper at
.01cm. increments.
Getting Started 11
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Setting the Viewing Window: Box with Lid
You also can use the graphing features of the TI82 STATS to find the maximum value of a previously defined function. When the graph is activated, the viewing window defines the displayed portion of the coordinate plane. The values of the window variables determine the size of the viewing window.
1. Press p to display the window editor, where you can view and edit the values of the window variables.
The standard window variables define the viewing window as shown.
Xmin
,
Xmax
,
Ymin
, and
Ymax
define the boundaries of the display.
Xscl
and
Yscl
define the distance between tick marks on the
X
and
Y
axes.
Xres
controls resolution.
2. Press
0
Í to define
Xmin
.
3. Press
20
¥
2
to define
Xmax
using an expression.
Xmin
Ymin
Ymax
Xscl
Yscl
Xmax
4. Press Í. The expression is evaluated, and
10
is stored in
Xmax
. Press Í to accept
Xscl
as
1
.
5. Press
0
Í
500
Í
100
Í
1
Í to define the remaining window variables.
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Displaying and Tracing the Graph: Box with Lid
Now that you have defined the function to be graphed and the window in which to graph it, you can display and explore the graph. You can trace along a function using the
TRACE
feature.
1. Press s to graph the selected function in the viewing window.
The graph of
Y
1
=(20N2X)(25à2NX)X
is displayed.
2. Press ~ to activate the freemoving graph cursor.
The
X
and
Y
coordinate values for the position of the graph cursor are displayed on the bottom line.
3. Press , ~, }, and † to move the freemoving cursor to the apparent maximum of the function.
As you move the cursor, the
X
and
Y
coordinate values are updated continually.
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Displaying and Tracing the Graph: Box with Lid
(cont.)
4. Press r. The trace cursor is displayed on the
Y
1
function.
The function that you are tracing is displayed in the topleft corner.
5. Press  and ~ to trace along
Y
1
, one
X
dot at a time, evaluating
Y
1
at each
X
.
You also can enter your estimate for the maximum value of
X
.
6. Press
3
Ë
8
. When you press a number key while in
TRACE
, the
X=
prompt is displayed in the bottomleft corner.
7. Press Í.
The trace cursor jumps to the point on the
Y
1
function evaluated at
X=3.8
.
8. Press  and ~ until you are on the maximum
Y
value.
This is the maximum of
Y
1
(X)
for the
X
pixel values. The actual, precise maximum may lie between pixel values.
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Zooming In on the Graph: Box with Lid
To help identify maximums, minimums, roots, and intersections of functions, you can magnify the viewing window at a specific location using the
ZOOM
instructions.
1. Press q to display the
ZOOM
menu.
This menu is a typical TI82 STATS menu. To select an item, you can either press the number or letter next to the item, or you can press † until the item number or letter is highlighted, and then press Í.
2. Press
2
to select
2:Zoom In
.
The graph is displayed again. The cursor has changed to indicate that you are using a
ZOOM instruction.
3. With the cursor near the maximum value of the function (as in step 8 on page 14), press
Í.
The new viewing window is displayed. Both
Xmax
N
Xmin
and
Ymax
N
Ymin
have been adjusted by factors of 4, the default values for the zoom factors.
4. Press p to display the new window settings.
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Finding the Calculated Maximum: Box with Lid
You can use a
CALCULATE
menu operation to calculate a local maximum of a function.
1. Press y [
CALC
] (above r) to display the
CALCULATE
menu. Press
4
to select
4:maximum
.
The graph is displayed again with a
Left Bound?
prompt.
2. Press  to trace along the curve to a point to the left of the maximum, and then press
Í.
A
4
at the top of the screen indicates the selected bound.
A
Right Bound?
prompt is displayed.
3. Press ~ to trace along the curve to a point to the right of the maximum, and then press
Í.
A
3
at the top of the screen indicates the selected bound.
A
Guess?
prompt is displayed.
4. Press  to trace to a point near the maximum, and then press Í.
Or, press
3
Ë
8
, and then press Í to enter a guess for the maximum.
When you press a number key in
TRACE
, the
X=
prompt is displayed in the bottomleft corner.
Notice how the values for the calculated maximum compare with the maximums found with the freemoving cursor, the trace cursor, and the table.
Note: In steps 2 and 3 above, you can enter values directly for Left Bound and Right Bound, in the same way as described in step 4.
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Other TI82 STATS Features
Getting Started has introduced you to basic TI82 STATS operation. This guidebook describes in detail the features you used in Getting Started. It also covers the other features and capabilities of the TI82 STATS.
Graphing
You can store, graph, and analyze up to 10 functions (Chapter
3), up to six parametric functions (Chapter 4), up to six polar functions (Chapter 5), and up to three sequences (Chapter 6).
You can use
DRAW
operations to annotate graphs (Chapter 8).
Sequences
Tables
You can generate sequences and graph them over time. Or, you can graph them as web plots or as phase plots (Chapter 6).
You can create function evaluation tables to analyze many functions simultaneously (Chapter 7).
Split Screen
Matrices
Lists
Statistics
You can split the screen horizontally to display both a graph and a related editor (such as the
Y=
editor), the table, the stat list editor, or the home screen. Also, you can split the screen vertically to display a graph and its table simultaneously
(Chapter 9).
You can enter and save up to 10 matrices and perform standard matrix operations on them (Chapter 10).
You can enter and save as many lists as memory allows for use in statistical analyses. You can attach formulas to lists for automatic computation. You can use lists to evaluate expressions at multiple values simultaneously and to graph a family of curves (Chapter 11).
You can perform one and twovariable, listbased statistical analyses, including logistic and sine regression analysis. You can plot the data as a histogram, xyLine, scatter plot, modified or regular boxandwhisker plot, or normal probability plot. You can define and store up to three stat plot definitions (Chapter
12).
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Other TI82 STATS Features (
continued
)
Inferential
Statistics
Financial
Functions
CATALOG
Programming
Linking to a PC or Macintoshë
You can perform 16 hypothesis tests and confidence intervals and 15 distribution functions. You can display hypothesis test results graphically or numerically (Chapter 13).
You can use timevalueofmoney (
TVM
) functions to analyze financial instruments such as annuities, loans, mortgages, leases, and savings. You can analyze the value of money over equal time periods using cash flow functions. You can amortize loans with the amortization functions (Chapter 14).
The
CATALOG
is a convenient, alphabetical list of all functions and instructions on the TI82 STATS. You can paste any function or instruction from the
CATALOG
to the current cursor location (Chapter 15).
You can enter and store programs that include extensive control and input/output instructions (Chapter 16).
You can connect your TI82 STATS to a personal computer using TI Connect™ software and a TI Connectivity cable. The software is included on the CD in the TI82 STATS package.
When you connect to the TI Connect™ software, the TI82
STATS calculator will be identified by TI Connect™ as a TI83 calculator. Everything else should function as expected.
For more information, consult the TI Connect™ Help.
The TI82 STATS has a port to connect and communicate with another TI82 STATS, a TI.82, the CalculatorBased
Laboratoryé (CBLé) System, a CalculatorBased Rangeré
(CBRé), or a personal computer. The unittounit link cable is included with the TI82 STATS (Chapter 19).
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Contents
1
Operating the TI82 STATS
Turning On and Turning Off the TI82 STATS
.................................
Setting the Display Contrast
............................................................................
The Display
................................................................................................................
Entering Expressions and Instructions
......................................................
TI82 STATS Edit Keys
.....................................................................................
Setting Modes
...........................................................................................................
Using TI82 STATS Variable Names
.......................................................
13
Storing Variable Values
.....................................................................................
14
8
9
4
6
2
3
Recalling Variable Values
................................................................................
15
ENTRY
(Last Entry) Storage Area
..............................................................
16
Ans
(Last Answer) Storage Area
.................................................................
18
TI82 STATS Menus
............................................................................................
19
VARS
and
VARS Y.VARS
Menus
..............................................................
21
Equation Operating System (EOSé)
.........................................................
22
Error Conditions
......................................................................................................
24
Operating the TI82 STATS 11
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Turning On and Turning Off the TI82 STATS
Turning On the
Calculator
Turning Off the
Calculator
Batteries
To turn on the TI82 STATS, press É.
•
If you previously had turned off the calculator by pressing y [
OFF
], the TI82 STATS displays the home screen as it was when you last used it and clears any error.
•
If Automatic Power Down™ (APDé) had previously turned off the calculator, the TI82 STATS will return exactly as you left it, including the display, cursor, and any error.
To prolong the life of the batteries, APD turns off the
TI82 STATS automatically after about five minutes without any activity.
To turn off the TI82 STATS manually, press y [
OFF
].
•
All settings and memory contents are retained by Constant
Memoryé.
•
Any error condition is cleared.
The TI82 STATS uses four AAA alkaline batteries and has a userreplaceable backup lithium battery (CR1616 or CR1620).
To replace batteries without losing any information stored in memory, follow the steps in Appendix B.
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Setting the Display Contrast
Adjusting the
Display Contrast
You can adjust the display contrast to suit your viewing angle and lighting conditions. As you change the contrast setting, a number from
0
(lightest) to
9
(darkest) in the topright corner indicates the current level. You may not be able to see the number if contrast is too light or too dark.
Note: The TI82 STATS has 40 contrast settings, so each number
0
through 9 represents four settings.
The TI82 STATS retains the contrast setting in memory when it is turned off.
To adjust the contrast, follow these steps.
1. Press and release the y key.
2. Press and hold † or }, which are below and above the contrast symbol (yellow, halfshaded circle).
•
† lightens the screen.
•
} darkens the screen.
Note: If you adjust the contrast setting to
0, the display may become completely blank. To restore the screen, press and release y, and then press and hold
} until the display reappears.
When to Replace
Batteries
When the batteries are low, a lowbattery message is displayed when you turn on the calculator.
To replace the batteries without losing any information in memory, follow the steps in Appendix B.
Generally, the calculator will continue to operate for one or two weeks after the lowbattery message is first displayed. After this period, the TI82 STATS will turn off automatically and the unit will not operate. Batteries must be replaced. All memory is retained.
Note: The operating period following the first lowbattery message could be longer than two weeks if you use the calculator infrequently.
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The Display
Types of
Displays
Home Screen
Displaying
Entries and
Answers
The TI82 STATS displays both text and graphs. Chapter 3 describes graphs. Chapter 9 describes how the TI82 STATS can display a horizontally or vertically split screen to show graphs and text simultaneously.
The home screen is the primary screen of the TI82 STATS. On this screen, enter instructions to execute and expressions to evaluate. The answers are displayed on the same screen.
When text is displayed, the TI82 STATS screen can display a maximum of eight lines with a maximum of 16 characters per line. If all lines of the display are full, text scrolls off the top of the display. If an expression on the home screen, the
Y=
editor
(Chapter 3), or the program editor (Chapter 16) is longer than one line, it wraps to the beginning of the next line. In numeric editors such as the window screen (Chapter 3), a long expression scrolls to the right and left.
When an entry is executed on the home screen, the answer is displayed on the right side of the next line.
Entry
Answer
The mode settings control the way the TI82 STATS interprets expressions and displays answers (page 1.9).
If an answer, such as a list or matrix, is too long to display entirely on one line, an ellipsis (
...
) is displayed to the right or left. Press ~ and  to scroll the answer.
Entry
Answer
Returning to the
Home Screen
To return to the home screen from any other screen, press y
[
QUIT
].
Busy Indicator
When the TI82 STATS is calculating or graphing, a vertical moving line is displayed as a busy indicator in the topright corner of the screen. When you pause a graph or a program, the busy indicator becomes a vertical moving dotted line.
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Display Cursors
In most cases, the appearance of the cursor indicates what will happen when you press the next key or select the next menu item to be pasted as a character.
Cursor Appearance Effect of Next Keystroke
Entry Solid rectangle
$
A character is entered at the cursor; any existing character is overwritten
Insert Underline
__
Second Reverse arrow
Þ
A character is inserted in front of the cursor location
A 2nd character (yellow on the keyboard) is entered or a 2nd operation is executed
Alpha Reverse A
Ø
Full Checkerboard rectangle
#
An alpha character (green on the keyboard) is entered or
SOLVE
is executed
No entry; the maximum characters are entered at a prompt or memory is full
If you press ƒ during an insertion, the cursor becomes an underlined
A
(
A
) If you press y during an insertion, the underline cursor becomes an underlined # ( # ).
Graphs and editors sometimes display additional cursors, which are described in other chapters.
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Entering Expressions and Instructions
What Is an
Expression?
An expression is a group of numbers, variables, functions and their arguments, or a combination of these elements. An expression evaluates to a single answer. On the TI82 STATS, you enter an expression in the same order as you would write it on paper. For example, pR 2 is an expression.
You can use an expression on the home screen to calculate an answer. In most places where a value is required, you can use an expression to enter a value.
Entering an
Expression
Multiple Entries on a Line
To create an expression, you enter numbers, variables, and functions from the keyboard and menus. An expression is completed when you press Í, regardless of the cursor location. The entire expression is evaluated according to
Equation Operating System (EOSé) rules (page 1.22), and the answer is displayed.
Most TI82 STATS functions and operations are symbols comprising several characters. You must enter the symbol from the keyboard or a menu; do not spell it out. For example, to calculate the log of 45, you must press «
45
. Do not enter the letters
L
,
O
, and
G
. If you enter
LOG
, the TI82 STATS interprets the entry as implied multiplication of the variables
L
,
O
, and
G
.
Calculate 3.76 ÷ (L7.9 + ‡5) + 2 log 45.
3
Ë
76
¥ £ Ì
7
Ë
9
Ã y [
‡
Í
]
5
¤ ¤
Ã
2
«
45
¤
To enter two or more expressions or instructions on a line, separate them with colons (ƒ [
:
]). All instructions are stored together in last entry (
ENTRY
; page 1.16).
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Entering a
Number in
Scientific
Notation
To enter a number in scientific notation, follow these steps.
1. Enter the part of the number that precedes the exponent. This value can be an expression.
2. Press y [
EE
]. åååå is pasted to the cursor location.
3. If the exponent is negative, press Ì, and then enter the exponent, which can be one or two digits.
Functions
Instructions
Interrupting a
Calculation
When you enter a number in scientific notation, the
TI82 STATS does not automatically display answers in scientific or engineering notation. The mode settings (page 1.9) and the size of the number determine the display format.
A function returns a value. For example,
÷
,
L
,
+
,
‡(
, and
log(
are the functions in the example on page 1.6. In general, the first letter of each function is lowercase on the TI82 STATS. Most functions take at least one argument, as indicated by an open parenthesis (
(
) following the name. For example,
sin(
requires one argument,
sin(
value
)
.
An instruction initiates an action. For example,
ClrDraw
is an instruction that clears any drawn elements from a graph.
Instructions cannot be used in expressions. In general, the first letter of each instruction name is uppercase. Some instructions take more than one argument, as indicated by an open parenthesis (
(
) at the end of the name. For example,
Circle(
requires three arguments,
Circle(
X
,
Y
,
radius
)
.
To interrupt a calculation or graph in progress, which would be indicated by the busy indicator, press É.
When you interrupt a calculation, the menu is displayed.
•
To return to the home screen, select
1:Quit
.
•
To go to the location of the interruption, select
2:Goto
.
When you interrupt a graph, a partial graph is displayed.
•
To return to the home screen, press ‘ or any nongraphing key.
•
To restart graphing, press a graphing key or select a graphing instruction.
Operating the TI82 STATS 17
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TI82 STATS Edit Keys
Keystrokes Result
~ or 
Moves the cursor within an expression; these keys repeat.
} or †
Moves the cursor from line to line within an expression that occupies more than one line; these keys repeat.
On the top line of an expression on the home screen, } moves the cursor to the beginning of the expression.
On the bottom line of an expression on the home screen, † moves the cursor to the end of the expression.
y  y ~
Í
‘
Moves the cursor to the beginning of an expression.
Moves the cursor to the end of an expression.
Evaluates an expression or executes an instruction.
On a line with text on the home screen, clears the current line.
On a blank line on the home screen, clears everything on the home screen.
In an editor, clears the expression or value where the cursor is located; it does not store a zero.
{ y [
INS
]
Deletes a character at the cursor; this key repeats.
Changes the cursor to
__
; inserts characters in front of the underline cursor; to end insertion, press y [
INS
] or press , }, ~, or †.
y
Changes the cursor to Þ; the next keystroke performs a
2nd operation
(an operation in yellow above a key and to the left); to cancel
2nd
, press y again.
ƒ
Changes the cursor to Ø; the next keystroke pastes an alpha character
(a character in green above a key and to the right) or executes
SOLVE
(Chapters 10 and 11); to cancel ƒ, press ƒ or press , },
~, or †.
y [
A .
LOCK
] Changes the cursor to Ø; sets alphalock; subsequent keystrokes (on an alpha key) paste alpha characters; to cancel alphalock, press ƒ; name prompts set alphalock automatically.
„
Pastes an
Seq
X
in
Func
mode, a
T
mode with one keystroke.
in
Par
mode, a
q
in
Pol
mode, or an
n
in
18 Operating the TI82 STATS
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Setting Modes
Checking Mode
Settings
Changing Mode
Settings
Mode settings control how the TI82 STATS displays and interprets numbers and graphs. Mode settings are retained by the
Constant Memory feature when the TI82 STATS is turned off.
All numbers, including elements of matrices and lists, are displayed according to the current mode settings.
To display the mode settings, press z. The current settings are highlighted. Defaults are highlighted below. The following pages describe the mode settings in detail.
Normal Sci Eng
Float 0123456789
Radian Degree
Func Par Pol Seq
Connected
Sequential
Dot
Simul
Real a+bi re^qi
Full Horiz GT
Numeric notation
Number of decimal places
Unit of angle measure
Type of graphing
Whether to connect graph points
Whether to plot simultaneously
Real, rectangular cplx, or polar cplx
Full screen, two splitscreen modes
To change mode settings, follow these steps.
1. Press † or } to move the cursor to the line of the setting that you want to change.
2. Press ~ or  to move the cursor to the setting you want.
3. Press Í.
Setting a Mode from a Program
You can set a mode from a program by entering the name of the mode as an instruction; for example,
Func
or
Float
. From a blank command line, select the mode setting from the mode screen; the instruction is pasted to the cursor location.
Operating the TI82 STATS 19
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Setting Modes
(continued)
Normal, Sci, Eng
Notation modes only affect the way an answer is displayed on the home screen. Numeric answers can be displayed with up to
10 digits and a twodigit exponent. You can enter a number in any format.
Normal
notation mode is the usual way we express numbers, with digits to the left and right of the decimal, as in
12345.67
.
Sci
(scientific) notation mode expresses numbers in two parts.
The significant digits display with one digit to the left of the decimal. The appropriate power of 10 displays to the right of
E
, as in
1.234567
E
4
.
Eng
(engineering) notation mode is similar to scientific notation. However, the number can have one, two, or three digits before the decimal; and the powerof10 exponent is a multiple of three, as in
12.34567
E
3
.
Note: If you select
Normal notation, but the answer cannot display in
10 digits (or the absolute value is less than .001), the TI82 STATS expresses the answer in scientific notation.
Float,
0123456789
Float
(floating) decimal mode displays up to 10 digits, plus the sign and decimal.
0123456789
(fixed) decimal mode specifies the number of digits
(
0
through
9
) to display to the right of the decimal. Place the cursor on the desired number of decimal digits, and then press
Í.
The decimal setting applies to
Normal
,
Sci
, and
Eng
notation modes.
The decimal setting applies to these numbers:
•
An answer displayed on the home screen
•
Coordinates on a graph (Chapters 3, 4, 5, and 6)
•
The
Tangent(
DRAW
instruction equation of the line,
x
, and
dy/dx
values (Chapter 8)
•
Results of
CALCULATE
operations (Chapters 3, 4, 5, and 6)
•
The regression equation stored after the execution of a regression model (Chapter 12)
110 Operating the TI82 STATS
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Radian, Degree
Func, Par, Pol,
Seq
Connected, Dot
Angle modes control how the TI82 STATS interprets angle values in trigonometric functions and polar/rectangular conversions.
Radian
mode interprets angle values as radians. Answers display in radians.
Degree
mode interprets angle values as degrees. Answers display in degrees.
Graphing modes define the graphing parameters. Chapters 3, 4,
5, and 6 describe these modes in detail.
Func
(function) graphing mode plots functions, where
Y
is a function of
X
(Chapter 3).
Par
(parametric) graphing mode plots relations, where
X
and
Y
are functions of
T
(Chapter 4).
Pol
(polar) graphing mode plots functions, where
r
is a function of
q
(Chapter 5).
Seq
(sequence) graphing mode plots sequences (Chapter 6).
Connected
plotting mode draws a line connecting each point calculated for the selected functions.
Dot
plotting mode plots only the calculated points of the selected functions.
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Setting Modes
(continued)
Sequential, Simul Sequential
graphingorder mode evaluates and plots one function completely before the next function is evaluated and plotted.
Simul
(simultaneous) graphingorder mode evaluates and plots all selected functions for a single value of
X
and then evaluates and plots them for the next value of
X
.
Note: Regardless of which graphing mode is selected, the
TI82 STATS will sequentially graph all stat plots before it graphs any functions.
Real, a+bi, re^qi
Real
mode does not display complex results unless complex numbers are entered as input.
Two complex modes display complex results.
•
a+b
i (rectangular complex mode) displays complex numbers in the form a+bi.
•
re^q
i (polar complex mode) displays complex numbers in the form re^qi.
Full, Horiz, G.T
Full
screen mode uses the entire screen to display a graph or edit screen.
Each splitscreen mode displays two screens simultaneously.
•
Horiz
(horizontal) mode displays the current graph on the top half of the screen; it displays the home screen or an editor on the bottom half (Chapter 9).
•
G.T
(graphtable) mode displays the current graph on the left half of the screen; it displays the table screen on the right half (Chapter 9).
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Using TI82 STATS Variable Names
Variables and
Defined Items
Notes about
Variables
On the TI82 STATS you can enter and use several types of data, including real and complex numbers, matrices, lists, functions, stat plots, graph databases, graph pictures, and strings.
The TI82 STATS uses assigned names for variables and other items saved in memory. For lists, you also can create your own fivecharacter names.
Variable Type
Real numbers
Complex numbers
Matrices
Lists
Functions
Parametric equations
Polar functions
Sequence functions
Stat plots
Graph databases
Graph pictures
Strings
System variables
Names
A
,
B
, . . . ,
Z
,
q
A
,
B
, . . . ,
Z
,
q
ã
A
ä
,
ã
B
ä
,
ã
C
ä
, . . . ,
ã
J
ä
L
1
,
L
2
,
L
3
,
L
4
,
L
5
,
L
6
, and userdefined names
Y
1
,
Y
2
, . . . ,
Y
9
,
Y
0
X
1T
and
Y
1T
, . . . ,
X
6T
and
Y
6T r
1
,
r
2
,
r
3
,
r
4
,
r
5
,
r
6 u
,
v
,
w
Plot1, Plot2, Plot3
GDB1
,
GDB2
, . . . ,
GDB9
,
GDB0
Pic1
,
Pic2
, . . . ,
Pic9
,
Pic0
Str1
,
Str2
, . . . ,
Str9
,
Str0
Xmin
,
Xmax
, and others
•
You can create as many list names as memory will allow
(Chapter 11).
•
Programs have userdefined names and share memory with variables (Chapter 16).
•
From the home screen or from a program, you can store to matrices (Chapter 10), lists (Chapter 11), strings (Chapter
15), system variables such as
Xmax
(Chapter 1),
TblStart
(Chapter 7), and all
Y=
functions (Chapters 3, 4, 5, and 6).
•
From an editor, you can store to matrices, lists, and
Y= functions (Chapter 3).
•
From the home screen, a program, or an editor, you can store a value to a matrix element or a list element.
•
You can use
DRAW STO
menu items to store and recall graph databases and pictures (Chapter 8).
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Storing Variable Values
Storing Values in a Variable
Values are stored to and recalled from memory using variable names. When an expression containing the name of a variable is evaluated, the value of the variable at that time is used.
To store a value to a variable from the home screen or a program using the ¿ key, begin on a blank line and follow these steps.
1. Enter the value you want to store. The value can be an expression.
2. Press ¿. ! is copied to the cursor location.
3. Press ƒ and then the letter of the variable to which you want to store the value.
4. Press Í. If you entered an expression, it is evaluated.
The value is stored to the variable.
Displaying a
Variable Value
To display the value of a variable, enter the name on a blank line on the home screen, and then press Í.
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Recalling Variable Values
Using Recall
(RCL)
To recall and copy variable contents to the current cursor location, follow these steps. To leave
RCL
, press ‘.
1. Press y ã
RCL
ä.
Rcl
and the edit cursor are displayed on the bottom line of the screen.
2. Enter the name of the variable in any of five ways.
•
Press ƒ and then the letter of the variable.
•
Press y ã
LIST
ä, and then select the name of the list, or press y [
L
n].
•
Press , and then select the name of the matrix.
•
Press to display the
VARS
menu or ~ to display the
VARS Y.VARS
menu; then select the type and then the name of the variable or function.
•
Press , and then select the name of the program
(in the program editor only).
The variable name you selected is displayed on the bottom line and the cursor disappears.
3. Press Í. The variable contents are inserted where the cursor was located before you began these steps.
Note: You can edit the characters pasted to the expression without affecting the value in memory.
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ENTRY (Last Entry) Storage Area
Using ENTRY
(Last Entry)
Accessing a
Previous Entry
When you press Í on the home screen to evaluate an expression or execute an instruction, the expression or instruction is placed in a storage area called
ENTRY
(last entry).
When you turn off the TI82 STATS,
ENTRY
is retained in memory.
To recall
ENTRY
, press y [
ENTRY
]. The last entry is pasted to the current cursor location, where you can edit and execute it.
On the home screen or in an editor, the current line is cleared and the last entry is pasted to the line.
Because the TI82 STATS updates
ENTRY
only when you press
Í, you can recall the previous entry even if you have begun to enter the next expression.
5
Ã
7
Í y [
ENTRY
]
The TI82 STATS retains as many previous entries as possible in
ENTRY
, up to a capacity of 128 bytes. To scroll those entries, press y [
ENTRY
] repeatedly. If a single entry is more than 128 bytes, it is retained for
ENTRY
, but it cannot be placed in the
ENTRY
storage area.
1
¿ ƒ
A
Í
2
¿ ƒ
B
Í y [
ENTRY
]
If you press y [
ENTRY
] after displaying the oldest stored entry, the newest stored entry is displayed again, then the nextnewest entry, and so on.
y [
ENTRY
]
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Reexecuting the
Previous Entry
After you have pasted the last entry to the home screen and edited it (if you chose to edit it), you can execute the entry. To execute the last entry, press Í.
To reexecute the displayed entry, press Í again. Each reexecution displays an answer on the right side of the next line; the entry itself is not redisplayed.
0
¿ ƒ
N
Í
ƒ
N
Ã
1
¿ ƒ
N
ƒ ã:ä ƒ
N
¡ Í
Í
Í
Multiple Entry
Values on a Line
To store to
ENTRY
two or more expressions or instructions, separate each expression or instruction with a colon, then press
Í. All expressions and instructions separated by colons are stored in
ENTRY
.
When you press y [
ENTRY
], all the expressions and instructions separated by colons are pasted to the current cursor location. You can edit any of the entries, and then execute all of them when you press Í.
For the equation A=pr
2
, use trial and error to find the radius of a circle that covers 200 square centimeters. Use 8 as your first guess.
8
¿ ƒ
R
ƒ
[
:
] y [ p
] ƒ
R
¡ Í y [
ENTRY
] y 
7
y [
INS
] Ë
95
Í
Continue until the answer is as accurate as you want.
Clearing ENTRY Clear Entries
(Chapter 18) clears all data that the TI82 STATS is holding in the
ENTRY
storage area.
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Ans (Last Answer) Storage Area
Using Ans in an
Expression
Continuing an
Expression
When an expression is evaluated successfully from the home screen or from a program, the TI82 STATS stores the answer to a storage area called
Ans
(last answer).
Ans
may be a real or complex number, a list, a matrix, or a string. When you turn off the TI82 STATS, the value in
Ans
is retained in memory.
You can use the variable
Ans
to represent the last answer in most places. Press y [
ANS
] to copy the variable name
Ans
to the cursor location. When the expression is evaluated, the
TI82 STATS uses the value of
Ans
in the calculation.
Calculate the area of a garden plot 1.7 meters by 4.2 meters.
Then calculate the yield per square meter if the plot produces a total of 147 tomatoes.
1
Ë
7
¯
4
Ë
2
Í
147
¥ y [
Í
ANS
]
You can use
Ans
as the first entry in the next expression without entering the value again or pressing y [
ANS
]. On a blank line on the home screen, enter the function. The TI82 STATS pastes the variable name
Ans
to the screen, then the function.
5
¥
2
Í
¯
9
Ë
9
Í
Storing Answers
To store an answer, store
Ans
to a variable before you evaluate another expression.
Calculate the area of a circle of radius 5 meters. Next, calculate the volume of a cylinder of radius 5 meters and height 3.3 meters, and then store the result in the variable V.
y [ p
]
5
¡
Í
¯
3
Ë
3
Í
¿ ƒ
V
Í
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TI82 STATS Menus
Using a
TI82 STATS
Menu
You can access most TI82 STATS operations using menus.
When you press a key or key combination to display a menu, one or more menu names appear on the top line of the screen.
•
The menu name on the left side of the top line is highlighted.
Up to seven items in that menu are displayed, beginning with item
1
, which also is highlighted.
•
A number or letter identifies each menu item’s place in the menu. The order is
1
through
9
, then
0
, then
A
,
B
,
C
, and so on. The
LIST NAMES
,
PRGM EXEC
, and
PRGM EDIT
menus only label items
1
through
9
and
0
.
•
When the menu continues beyond the displayed items, a down arrow ( $ ) replaces the colon next to the last displayed item.
•
When a menu item ends in an ellipsis, the item displays a secondary menu or editor when you select it.
To display any other menu listed on the top line, press ~ or  until that menu name is highlighted. The cursor location within the initial menu is irrelevant. The menu is displayed with the cursor on the first item.
Note: The Menu Map in Appendix A shows each menu, each operation under each menu, and the key or key combination you press to display each menu.
Scrolling a Menu
To scroll down the menu items, press †. To scroll up the menu items, press }.
To page down six menu items at a time, press ƒ †. To page up six menu items at a time, press ƒ }. The green arrows on the calculator, between † and }, are the pagedown and pageup symbols.
To wrap to the last menu item directly from the first menu item, press }. To wrap to the first menu item directly from the last menu item, press †.
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TI82 STATS Menus
(continued)
Selecting an Item from a Menu
You can select an item from a menu in either of two ways.
•
Press the number or letter of the item you want to select. The cursor can be anywhere on the menu, and the item you select need not be displayed on the screen.
•
Press † or } to move the cursor to the item you want, and then press Í.
After you select an item from a menu, the TI82 STATS typically displays the previous screen.
Note: On the LIST NAMES, PRGM EXEC, and PRGM EDIT menus, only items
1 through 9 and 0 are labeled in such a way that you can select them by pressing the appropriate number key. To move the cursor to the first item beginning with any alpha character or q, press the key combination for that alpha character or q. If no items begin with that character, then the cursor moves beyond it to the next item.
Calculate 3
‡27.
† † † Í
27
¤ Í
Leaving a Menu without Making a
Selection
You can leave a menu without making a selection in any of four ways.
•
Press y [
QUIT
] to return to the home screen.
•
Press ‘ to return to the previous screen.
•
Press a key or key combination for a different menu, such as
or y [
LIST
].
•
Press a key or key combination for a different screen, such as o or y [
TABLE
].
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VARS and VARS Y.VARS Menus
VARS Menu
You can enter the names of functions and system variables in an expression or store to them directly.
To display the
VARS
menu, press . All
VARS
menu items display secondary menus, which show the names of the system variables.
1:Window
,
2:Zoom
, and
5:Statistics
each access more than one secondary menu.
VARS YVARS
1: Window...
2: Zoom...
3: GDB...
4: Picture...
5: Statistics...
6: Table...
7: String...
X/Y
,
T/q
, and
U/V/W variables
ZX/ZY
Graph database
Picture
XY
,
ZT/Zq
, and
ZU variables variables variables
,
G
,
EQ
,
TEST
, and
PTS variables
TABLE variables
String variables
Selecting a
Variable from the
VARS Menu or
VARS Y.VARS
Menu
To display the
VARS Y.VARS
menu, press ~.
1:Function
,
2:Parametric
, and
3:Polar
display secondary menus of the
Y=
function variables.
VARS YVARS
1: Function...
2: Parametric...
3: Polar...
4: On/Off...
Y
n functions
X
n
T
,
Y
n
T
functions
r
n functions
Lets you select/deselect functions
Note: The sequence variables (
u, v, w) are located on the keyboard as the second functions of
¬, −, and ®.
To select a variable from the
VARS
or
VARS Y.VARS
menu, follow these steps.
1. Display the
VARS
or
VARS Y.VARS
menu.
•
Press to display the
VARS
menu.
•
Press ~ to display the
VARS Y.VARS
menu.
2. Select the type of variable, such as
2:Zoom
from the
VARS menu or
3:Polar
from the
VARS Y.VARS
menu. A secondary menu is displayed.
3. If you selected
1:Window
,
2:Zoom
, or
5:Statistics
from the
VARS
menu, you can press ~ or  to display other secondary menus.
4. Select a variable name from the menu. It is pasted to the cursor location.
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Equation Operating System (EOSé)
Order of
Evaluation
The Equation Operating System (EOSé) defines the order in which functions in expressions are entered and evaluated on the
TI82 STATS. EOS lets you enter numbers and functions in a simple, straightforward sequence.
EOS evaluates the functions in an expression in this order:
1 Singleargument functions that precede the argument, such as
‡(
,
sin(
, or
log(
2 Functions that are entered after the argument, such as
2
,
M1
,
!
,
¡
,
r
, and conversions
3 Powers and roots, such as
2^5
or
5 x
‡32
4 Permutations (
nPr
) and combinations (
nCr
)
5 Multiplication, implied multiplication, and division
6 Addition and subtraction
7 Relational functions, such as
>
or
8 Logic operator
and
9 Logic operators
or
and
xor
Within a priority level, EOS evaluates functions from left to right.
Calculations within parentheses are evaluated first.
Multiargument functions, such as
nDeriv(A
as they are encountered.
2
,A,6)
, are evaluated
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Implied
Multiplication
The TI82 STATS recognizes implied multiplication, so you need not press ¯ to express multiplication in all cases. For example, the TI82 STATS interprets
2p
,
4sin(46)
,
5(1+2)
, and
(2
ääää5)7 as implied multiplication.
Note: TI82 STATS implied multiplication rules differ from those of the
äääX,
Parentheses
All calculations inside a pair of parentheses are completed first.
For example, in the expression
4(1+2)
, EOS first evaluates the portion inside the parentheses,
1+2
, and then multiplies the answer,
3
, by
4
.
Negation
You can omit the close parenthesis (
)
) at the end of an expression. All open parenthetical elements are closed automatically at the end of an expression. This is also true for open parenthetical elements that precede the store or displayconversion instructions.
Note: An open parenthesis following a list name, matrix name, or Y= function name does not indicate implied multiplication. It specifies elements in the list (Chapter 11) or matrix (Chapter 10) and specifies a value for which to solve the
Y= function.
To enter a negative number, use the negation key. Press Ì and then enter the number. On the TI82 STATS, negation is in the third level in the EOS hierarchy. Functions in the first level, such as squaring, are evaluated before negation.
For example,
MX
2
, evaluates to a negative number (or 0). Use parentheses to square a negative number.
Note: Use the
¹ key for subtraction and the Ì key for negation. If you press
¹ to enter a negative number, as in 9 ¯ ¹ 7, or if you press
Ì to indicate subtraction, as in 9 Ì 7, an error occurs. If you press
ƒ A Ì ƒ B, it is interpreted as implied multiplication
(
A
ääääMB).
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Error Conditions
Diagnosing an
Error
The TI82 STATS detects errors while performing these tasks.
•
Evaluating an expression
•
Executing an instruction
•
Plotting a graph
•
Storing a value
When the TI82 STATS detects an error, it returns an error message as a menu title, such as
ERR:SYNTAX
or
ERR:DOMAIN
. Appendix B describes each error type and possible reasons for the error.
Correcting an
Error
•
If you select
1:Quit
(or press y [
QUIT
] or ‘), then the home screen is displayed.
•
If you select
2:Goto
, then the previous screen is displayed with the cursor at or near the error location.
Note: If a syntax error occurs in the contents of a Y= function during program execution, then the Goto option returns to the Y= editor, not to the program.
To correct an error, follow these steps.
1. Note the error type (
ERR:
error type).
2. Select
2:Goto
, if it is available. The previous screen is displayed with the cursor at or near the error location.
3. Determine the error. If you cannot recognize the error, refer to Appendix B.
4. Correct the expression.
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Contents
2
Math, Angle, and Test
Operations
Getting Started: Coin Flip
.................................................................................
Keyboard Math Operations
..............................................................................
MATH
Operations
...................................................................................................
Using the Equation Solver
................................................................................
MATH NUM
(Number) Operations
..............................................................
13
5
8
2
3
Entering and Using Complex Numbers
....................................................
16
MATH CPX
(Complex) Operations
............................................................
18
MATH PRB
(Probability) Operations
........................................................
20
ANGLE
Operations
................................................................................................
23
TEST
(Relational) Operations
........................................................................
24
TEST LOGIC
(Boolean) Operations
..........................................................
26
Math, Angle, and Test Operations 2.1
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Getting Started: Coin Flip
Getting Started is a fastpaced introduction. Read the chapter for details.
Suppose you want to model flipping a fair coin 10 times. You want to track how many of those 10 coin flips result in heads. You want to perform this simulation 40 times. With a fair coin, the probability of a coin flip resulting in heads is 0.5 and the probability of a coin flip resulting in tails is 0.5.
1. Begin on the home screen. Press  to display the
MATH PRB
menu. Press
7
to select
7:randBin(
(random Binomial).
randBin(
is pasted to the home screen. Press
10
to enter the number of coin flips. Press ¢. Press Ë
5
to enter the probability of heads. Press ¢. Press
40
to enter the number of simulations. Press ¤.
2. Press Í to evaluate the expression. A list of
40 elements is displayed. The list contains the count of heads resulting from each set of 10 coin flips. The list has 40 elements because this simulation was performed 40 times. In this example, the coin came up heads five times in the first set of 10 coin flips, five times in the second set of 10 coin flips, and so on.
3. Press ¿ y ã
L1
ä Í to store the data to the list name
L
1
. You then can use the data for another activity, such as plotting a histogram
(Chapter 12).
4. Press ~ or  to view the additional counts in the list. Ellipses (
...
) indicate that the list continues beyond the screen.
Note: Since randBin( generates random numbers, your list elements may differ from those in the example.
2.2 Math, Angle, and Test Operations
Keyboard Math Operations
Using Lists with
Math Operations
Math operations that are valid for lists return a list calculated element by element. If you use two lists in the same expression, they must be the same length.
+ (Addition),
N (Subtraction),
ääää (Multiplication),
à (Division)
You can use
+
(addition, Ã),
N
(subtraction, ¹), ääää
(multiplication, ¯), and
à
(division, ¥) with real and complex numbers, expressions, lists, and matrices. You cannot use
à
with matrices.
valueA
+
valueB valueA
ääää
valueB
valueA
N
valueB valueA
à
valueB
Trigonometric
Functions
You can use the trigonometric (trig) functions (sine, ˜; cosine, ™; and tangent, š) with real numbers, expressions, and lists. The current angle mode setting affects interpretation.
For example,
sin(30)
in
Radian
mode returns
L.9880316241
; in
Degree
mode it returns
.5
.
sin(
value
) cos(
value
) tan(
value
)
You can use the inverse trig functions (arcsine, y [
SIN
L1
]; arccosine, y [
COS
L1
]; and arctangent, y [
TAN
L1
]) with real numbers, expressions, and lists. The current angle mode setting affects interpretation.
sin
L1
(
value
) cos
L1
(
value
) tan
L1
(
Note: The trig functions do not operate on complex numbers.
value
)
^ (Power),
2
(Square),
‡( (Square Root)
You can use
^
(power, ›),
2
(square, ¡), and
‡(
(square root, y [
‡
]) with real and complex numbers, expressions, lists, and matrices. You cannot use
‡(
with matrices.
value
^
power value
2
‡(
value
)
L1
(Inverse)
You can use
L1
(inverse, —) with real and complex numbers, expressions, lists, and matrices. The multiplicative inverse is equivalent to the reciprocal, 1àx.
value
L1
Math, Angle, and Test Operations 2.3
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Keyboard Math Operations
(continued) log(,
10^(, ln(
You can use
log(
(logarithm, «),
10^(
(power of 10, y
[
10
x
]), and
ln(
(natural log, µ) with real or complex numbers, expressions, and lists.
log(
value
) 10^(
power
) ln(
value
) e^( (Exponential) e^(
(exponential, y ã e
x
]) returns the constant
e
raised to a power. You can use
e^(
with real or complex numbers, expressions, and lists.
e^(
power
) e (Constant) e
(constant, y [ e
]) is stored as a constant on the TI82 STATS
. Press y [ e
] to copy
e
to the cursor location. In calculations, the TI82 STATS uses 2.718281828459 for
e
.
L (Negation) M
(negation, Ì) returns the negative of value. You can use
M
with real or complex numbers, expressions, lists, and matrices.
M
value
EOS rules (Chapter 1) determine when negation is evaluated.
For example,
LA
2
returns a negative number, because squaring is evaluated before negation. Use parentheses to square a negated number, as in
(LA)
2
.
p (Pi)
Note: On the TI82 STATS, the negation symbol (M) is shorter and higher than the subtraction sign (N), which is displayed when you press
¹.
p
(Pi, y [ p
]) is stored as a constant in the TI82 STATS. In calculations, the TI82 STATS uses 3.1415926535898 for
p
.
2.4 Math, Angle, and Test Operations
MATH Operations
MATH Menu
4Frac,
4Dec
To display the
MATH
menu, press .
MAT
H
NUM CPX PRB
1: 4Frac
2: 4Dec
3:
3
4:
5:
3
‡( x
‡
6: fMin(
7: fMax(
8: nDeriv(
9: fnInt(
0: Solver...
Displays the answer as a fraction.
Displays the answer as a decimal.
Calculates the cube.
Calculates the cube root.
Calculates the x
th
root.
Finds the minimum of a function.
Finds the maximum of a function.
Computes the numerical derivative.
Computes the function integral.
Displays the equation solver.
4Frac
(display as a fraction) displays an answer as its rational equivalent. You can use
4Frac
with real or complex numbers, expressions, lists, and matrices. If the answer cannot be simplified or the resulting denominator is more than three digits, the decimal equivalent is returned. You can only use
4Frac
following value.
value
4Frac
4Dec
(display as a decimal) displays an answer in decimal form.
You can use
4Dec
with real or complex numbers, expressions, lists, and matrices. You can only use
4Dec
following value.
value
4Dec
Math, Angle, and Test Operations 2.5
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MATH Operations
(continued)
3
(Cube),
3
‡( (Cube Root)
3
(cube) returns the cube of value. You can use
3
with real or complex numbers, expressions, lists, and square matrices.
value
3
3
‡(
(cube root) returns the cube root of value. You can use
3
‡(
with real or complex numbers, expressions, and lists.
3
‡(
value
) x
‡ (Root) fMin(, fMax( x
‡
(x
th
root) returns the x
th
root of value. You can use
x
‡
with real or complex numbers, expressions, and lists.
x th root
x
‡
value
fMin(
(function minimum) and
fMax(
(function maximum) return the value at which the local minimum or local maximum value of expression with respect to variable occurs, between lower and upper values for variable.
fMin(
and
fMax(
are not valid in
expression. The accuracy is controlled by tolerance (if not specified, the default is 1â
L
5).
fMin(
expression
,
variable
,
lower
,
upper[
,
tolerance]
) fMax(
expression
,
variable
,
lower
,
upper[
,
tolerance]
)
Note: In this guidebook, optional arguments and the commas that accompany them are enclosed in brackets ([ ]).
2.6 Math, Angle, and Test Operations
nDeriv( nDeriv(
(numerical derivative) returns an approximate derivative of expression with respect to variable, given the value at which to calculate the derivative and H (if not specified, the default is
1â
L
3).
nDeriv(
is valid only for real numbers.
nDeriv(
expression
,
variable
,
value[
,
H]
) nDeriv(
uses the symmetric difference quotient method, which approximates the numerical derivative value as the slope of the secant line through these points.
f¢( x
) = f( x
+H)Nf( x NH)
2H
As H becomes smaller, the approximation usually becomes more accurate.
fnInt(
You can use
nDeriv(
once in expression. Because of the method used to calculate
nDeriv(
, the TI82 STATS can return a false derivative value at a nondifferentiable point.
fnInt(
(function integral) returns the numerical integral (Gauss
Kronrod method) of expression with respect to variable, given
lower limit, upper limit, and a tolerance (if not specified, the default is 1â
L
5).
fnInt(
is valid only for real numbers.
fnInt(
expression
,
variable
,
lower
,
upper[
,
tolerance]
)
Tip: To speed the drawing of integration graphs (when
fnInt( is used in a Y= equation), increase the value of the Xres window variable before you press s.
Math, Angle, and Test Operations 2.7
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PM Page 7 of 26
Using the Equation Solver
Solver Solver
displays the equation solver, in which you can solve for any variable in an equation. The equation is assumed to be equal to zero.
Solver
is valid only for real numbers.
When you select
Solver
, one of two screens is displayed.
•
The equation editor (see step 1 picture below) is displayed when the equation variable
eqn
is empty.
•
The interactive solver editor (see step 3 picture on page 2.9) is displayed when an equation is stored in
eqn
.
Entering an
Expression in the
Equation Solver
To enter an expression in the equation solver, assuming that the variable
eqn
is empty, follow these steps.
1. Select
0:Solver
from the
MATH
menu to display the equation editor.
2. Enter the expression in any of three ways.
•
Enter the expression directly into the equation solver.
•
Paste a
Y=
variable name from the
VARS Y.VARS
menu to the equation solver.
•
Press y [
RCL
], paste a
Y=
variable name from the
VARS Y.VARS
menu, and press Í. The expression is pasted to the equation solver.
The expression is stored to the variable
eqn
as you enter it.
2.8 Math, Angle, and Test Operations
Entering an
Expression in the
Equation Solver
(continued)
3. Press Í or †. The interactive solver editor is displayed.
•
The equation stored in
eqn
is set equal to zero and displayed on the top line.
•
Variables in the equation are listed in the order in which they appear in the equation. Any values stored to the listed variables also are displayed.
•
The default lower and upper bounds appear in the last line of the editor (
bound={L1
åååå
99,1
åååå
99}
).
•
A
$
is displayed in the first column of the bottom line if the editor continues beyond the screen.
Tip: To use the solver to solve an equation such as
K=.5MV
2 eqn:0=KN.5MV
2
in the equation editor.
, enter
Entering and
Editing Variable
Values
When you enter or edit a value for a variable in the interactive solver editor, the new value is stored in memory to that variable.
You can enter an expression for a variable value. It is evaluated when you move to the next variable. Expressions must resolve to real numbers at each step during the iteration.
You can store equations to any
VARS Y.VARS
variables, such as
Y
1
or
r
6
, and then reference the variables in the equation. The interactive solver editor displays all variables of all
Y=
functions referenced in the equation.
Math, Angle, and Test Operations 2.9
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PM Page 9 of 26
Using the Equation Solver
(continued)
Solving for a
Variable in the
Equation Solver
To solve for a variable using the equation solver after an equation has been stored to
eqn
, follow these steps.
1. Select
0:Solver
from the
MATH
menu to display the interactive solver editor, if not already displayed.
2. Enter or edit the value of each known variable. All variables, except the unknown variable, must contain a value. To move the cursor to the next variable, press Í or †.
3. Enter an initial guess for the variable for which you are solving. This is optional, but it may help find the solution more quickly. Also, for equations with multiple roots, the
TI82 STATS will attempt to display the solution that is closest to your guess.
The default guess is calculated as
(upper + lower)
2
.
2.10 Math, Angle, and Test Operations
Solving for a
Variable in the
Equation Solver
(continued)
4. Edit
bound={
lower
,
upper
}
. lower and upper are the bounds between which the TI82 STATS searches for a solution. This is optional, but it may help find the solution more quickly. The default is
bound={L1
åååå
99,1
åååå
99}
.
5. Move the cursor to the variable for which you want to solve and press ƒ [
SOLVE
] (above the Í key).
•
The solution is displayed next to the variable for which you solved. A solid square in the first column marks the variable for which you solved and indicates that the equation is balanced. An ellipsis shows that the value continues beyond the screen.
Note: When a number continues beyond the screen, be sure to press
~ to scroll to the end of the number to see whether it ends with a negative or positive exponent. A very small number may appear to be a large number until you scroll right to see the exponent.
•
The values of the variables are updated in memory.
•
leftNrt=
diff is displayed in the last line of the editor. diff is the difference between the left and right sides of the equation. A solid square in the first column next to
leftNrt=
indicates that the equation has been evaluated at the new value of the variable for which you solved.
Math, Angle, and Test Operations 2.11
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PM Page 11 of 26
Using the Equation Solver
(continued)
Editing an
Equation Stored to eqn
To edit or replace an equation stored to
eqn
when the interactive equation solver is displayed, press } until the equation editor is displayed. Then edit the equation.
Equations with
Multiple Roots
Some equations have more than one solution. You can enter a new initial guess (page 2.10) or new bounds (page 2.11) to look for additional solutions.
Further Solutions
After you solve for a variable, you can continue to explore solutions from the interactive solver editor. Edit the values of one or more variables. When you edit any variable value, the solid squares next to the previous solution and
leftNrt=
diff
disappear. Move the cursor to the variable for which you now want to solve and press ƒ [
SOLVE
].
Controlling the
Solution for
Solver or solve(
The TI82 STATS solves equations through an iterative process.
To control that process, enter bounds that are relatively close to the solution and enter an initial guess within those bounds. This will help to find a solution more quickly. Also, it will define which solution you want for equations with multiple solutions.
Using solve( on the Home Screen or from a
Program
The function
solve(
is available only from
CATALOG
or from within a program. It returns a solution (root) of expression for
variable, given an initial guess, and lower and upper bounds within which the solution is sought. The default for lower is
L1â99. The default for upper is 1â99.
solve(
is valid only for real numbers.
solve(
expression
,
variable
,
guess[
,{
lower
,
upper
}
]
)
expression is assumed equal to zero. The value of variable will not be updated in memory. guess may be a value or a list of two values. Values must be stored for every variable in expression, except variable, before expression is evaluated. lower and upper must be entered in list format.
2.12 Math, Angle, and Test Operations
MATH NUM (Number) Operations
MATH NUM Menu
To display the
MATH NUM
menu, press ~.
MATH NU
M
1: abs(
2: round(
3: iPart(
4: fPart(
5: int(
6: min(
7: max(
8: lcm(
9: gcd(
CPX PRB
Absolute value
Round
Integer part
Fractional part
Greatest integer
Minimum value
Maximum value
Least common multiple
Greatest common divisor
abs( abs(
(absolute value) returns the absolute value of real or complex (modulus) numbers, expressions, lists, and matrices.
abs(
value
) round(
Note:
abs( is also available on the MATH CPX menu.
round(
returns a number, expression, list, or matrix rounded to
#decimals (9). If #decimals is omitted, value is rounded to the digits that are displayed, up to 10 digits.
round(
value[
,
#decimals]
)
Math, Angle, and Test Operations 2.13
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PM Page 13 of 26
MATH NUM (Number) Operations
(continued) iPart(, fPart( iPart(
(integer part) returns the integer part or parts of real or complex numbers, expressions, lists, and matrices.
iPart(
value
) fPart(
(fractional part) returns the fractional part or parts of real or complex numbers, expressions, lists, and matrices.
fPart(
value
) int( int(
(greatest integer) returns the largest integer real or complex numbers, expressions, lists, and matrices.
int(
value
)
Note: For a given value, the result of
int( is the same as the result of
iPart( for nonnegative numbers and negative integers, but one integer less than the result of
iPart( for negative noninteger numbers.
2.14 Math, Angle, and Test Operations
min(, max( min(
(minimum value) returns the smaller of valueA and valueB or the smallest element in list. If listA and listB are compared,
min(
returns a list of the smaller of each pair of elements. If list and value are compared,
min(
compares each element in list with value.
max(
(maximum value) returns the larger of valueA and valueB or the largest element in list. If listA and listB are compared,
max(
returns a list of the larger of each pair of elements. If list and value are compared,
max(
compares each element in list with value.
min(
valueA
,
valueB
) min(
list
) min(
listA
,
listB
) min(
list
,
value
) max(
valueA
,
valueB
) max(
list
) max(
listA
,
listB
) max(
list
,
value
) lcm(, gcd(
Note:
min( and max( also are available on the LIST MATH menu.
lcm(
returns the least common multiple of valueA and valueB, both of which must be nonnegative integers. When listA and
listB are specified,
lcm(
returns a list of the lcm of each pair of elements. If list and value are specified,
lcm(
finds the lcm of each element in list and value.
gcd(
returns the greatest common divisor of valueA and valueB, both of which must be nonnegative integers. When listA and
listB are specified,
gcd(
returns a list of the gcd of each pair of elements. If list and value are specified,
gcd(
finds the gcd of each element in list and value.
lcm(
valueA
,
valueB
) lcm(
listA
,
listB
) lcm(
list
,
value
) gcd(
valueA
,
valueB
) gcd(
listA
,
listB
) gcd(
list
,
value
)
Math, Angle, and Test Operations 2.15
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PM Page 15 of 26
Entering and Using Complex Numbers
ComplexNumber
Modes
The TI82 STATS displays complex numbers in rectangular form and polar form. To select a complexnumber mode, press z, and then select either of the two modes.
•
a+b
i (rectangularcomplex mode)
•
re^q
i (polarcomplex mode)
On the TI82 STATS, complex numbers can be stored to variables. Also, complex numbers are valid list elements.
In
Real
mode, complexnumber results return an error, unless you entered a complex number as input. For example, in
Real
mode
ln(L1)
returns an error; in
a+b
i mode
ln(L1)
returns an answer.
Real
mode
a+b
i mode
$ $
Entering
Complex
Numbers
Note about
Radian versus
Degree Mode
Complex numbers are stored in rectangular form, but you can enter a complex number in rectangular form or polar form, regardless of the mode setting. The components of complex numbers can be real numbers or expressions that evaluate to real numbers; expressions are evaluated when the command is executed.
Radian mode is recommended for complex number calculations.
Internally, the TI82 STATS converts all entered trig values to radians, but it does not convert values for exponential, logarithmic, or hyperbolic functions.
In degree mode, complex identities such as e^(iq) = cos(q) + i sin(q) are not generally true because the values for cos and sin are converted to radians, while those for e^( ) are not. For example, e^(i45) = cos(45) + i sin(45) is treated internally as
e^(i45) = cos(p/4) + i sin(p/4). Complex identities are always true in radian mode.
2.16 Math, Angle, and Test Operations
Interpreting
Complex Results
Complex numbers in results, including list elements, are displayed in either rectangular or polar form, as specified by the mode setting or by a display conversion instruction (page 2.19).
In the example below,
re^q
i and
Radian
modes are set.
Rectangular
Complex Mode
Rectangularcomplex mode recognizes and displays a complex number in the form a+b
i, where a
is the real component, b
is the imaginary component, and i is a constant equal to
1
.
To enter a complex number in rectangular form, enter the value of a (real component), press Ã or ¹, enter the value of b
(imaginary component), and press y [i] (constant).
real component(
+
or
N
)imaginary componenti
PolarComplex
Mode
Polarcomplex mode recognizes and displays a complex number in the form re^ log, q q
i, where r is the magnitude, e is the base of the natural
is the angle, and i is a constant equal to
1
.
To enter a complex number in polar form, enter the value of r
(magnitude), press y [ e value of q
x
] (exponential function), enter the
(angle), press y [i] (constant), and then press ¤.
magnitude
e^(
anglei
)
Math, Angle, and Test Operations 2.17
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PM Page 17 of 26
MATH CPX (Complex) Operations
MATH CPX Menu
To display the
MATH CPX
menu, press ~ ~.
MATH NU
M
1: conj(
2: real(
3: imag(
4: angle(
5: abs(
6: 4Rect
7: 4Polar
CPX PRB
Returns the complex conjugate.
Returns the real part.
Returns the imaginary part.
Returns the polar angle.
Returns the magnitude (modulus).
Displays the result in rectangular form.
Displays the result in polar form.
conj( conj(
(conjugate) returns the complex conjugate of a complex number or list of complex numbers.
conj(
a
+
bi
)
returns aNbi in
a+b
i mode.
conj(
r
e^(
q
i
))
returns r
e^(
Lq
i
)
in
re^q
i mode.
real( imag( real(
(real part) returns the real part of a complex number or list of complex numbers.
real(
a
+
bi
)
returns a.
real(
r
e^(
q
i
))
returns r
ääää
cos( q
).
imag(
(imaginary part) returns the imaginary (nonreal) part of a complex number or list of complex numbers.
imag(
a
+
bi
)
returns b.
imag(
r
e^(
q
i
))
returns r ääää
sin(
q
).
2.18 Math, Angle, and Test Operations
angle( abs(
4Rect
4Polar angle(
returns the polar angle of a complex number or list of complex numbers, calculated as tan
L1
(b/a), where b is the imaginary part and a is the real part. The calculation is adjusted by +p in the second quadrant or Np in the third quadrant.
angle(
a
+
bi
)
returns tan L
1
(b/a).
angle(
r
e^(
q
i
))
returns q
, where Lp< q
<p.
abs(
(absolute value) returns the magnitude (modulus),
(real2+imag2) , of a complex number or list of complex numbers.
abs(
a
+
bi
)
returns (a2+b2) .
abs(
r
e^(
q
i
))
returns r (magnitude).
4Rect
(display as rectangular) displays a complex result in rectangular form. It is valid only at the end of an expression. It is not valid if the result is real.
complex result
8Rect
returns a+bi.
4Polar
(display as polar) displays a complex result in polar form.
It is valid only at the end of an expression. It is not valid if the result is real.
complex result
8Polar
returns r
e^(
q
i
)
.
Math, Angle, and Test Operations 2.19
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PM Page 19 of 26
MATH PRB (Probability) Operations
MATH PRB Menu
To display the
MATH PRB
menu, press .
MATH NUM CPXPRB
1: rand
2: nPr
3: nCr
4: !
5: randInt(
6: randNorm(
7: randBin(
Randomnumber generator
Number of permutations
Number of combinations
Factorial
Randominteger generator
Random # from Normal distribution
Random # from Binomial distribution
rand rand
(random number) generates and returns one or more random numbers > 0 and < 1. To generate a list of randomnumbers, specify an integer > 1 for numtrials (number of trials).
The default for numtrials is 1.
rand
[
(
numtrials
)
]
Tip: To generate random numbers beyond the range of 0 to 1, you can include
rand in an expression. For example, rand
ääää5 generates a random number > 0 and < 5.
With each
rand
execution, the TI82 STATS generates the same randomnumber sequence for a given seed value. The
TI82 STATS factoryset seed value for
rand
is
0
. To generate a different randomnumber sequence, store any nonzero seed value to
rand
. To restore the factoryset seed value, store
0
to
rand
or reset the defaults (Chapter 18).
Note: The seed value also affects randInt(, randNorm(, and
randBin( instructions (page 2.22).
2.20 Math, Angle, and Test Operations
nPr, nCr nPr
(number of permutations) returns the number of permutations of items taken number at a time. items and number must be nonnegative integers. Both items and number can be lists.
items
nPr
number
nCr
(number of combinations) returns the number of combinations of items taken number at a time. items and number must be nonnegative integers. Both items and number can be lists.
items
nCr
number
! (Factorial)
!
(factorial) returns the factorial of either an integer or a multiple of .5. For a list, it returns factorials for each integer or multiple of .5. value must be ‚L.5 and 69.
value
!
Note: The factorial is computed recursively using the relationship
(n+1)! = n
än!, until n is reduced to either 0 or L1/2. At that point, the definition 0!=1 or the definition (L1à2)!=‡p is used to complete the calculation. Hence: n!=n
ä(nN1)ä(nN2)ä ... ä2ä1, if n is an integer ‚0 n!= n
ä(nN1)ä(nN2)ä ... ä1à2ä‡p, if n+1à2 is an integer ‚0 n! is an error, if neither n nor n+1à2 is an integer ‚0.
(The variable n equals value in the syntax description above.)
Math, Angle, and Test Operations 2.21
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PM Page 21 of 26
MATH PRB (Probability) Operations
(continued) randInt( randInt(
(random integer) generates and displays a random integer within a range specified by lower and upper integer bounds. To generate a list of random numbers, specify an integer >1 for numtrials (number of trials); if not specified, the default is 1.
randInt(
lower
,
upper[
,
numtrials]
) randNorm( randNorm(
(random Normal) generates and displays a random real number from a specified Normal distribution. Each generated value could be any real number, but most will be within the interval [mN3(s), m+3(s)]. To generate a list of random numbers, specify an integer > 1 for numtrials (number of trials); if not specified, the default is 1.
randNorm(
m
,
s [
,
numtrials]
) randBin( randBin(
(random Binomial) generates and displays a random integer from a specified Binomial distribution. numtrials
(number of trials) must be ‚ 1. prob (probability of success) must be ‚ 0 and 1. To generate a list of random numbers, specify an integer > 1 for numsimulations (number of simulations); if not specified, the default is 1.
randBin(
numtrials
,
prob[
,
numsimulations]
)
Note: The seed value stored to
rand also affects randInt(,
randNorm(, and randBin( instructions (page 220).
2.22 Math, Angle, and Test Operations
ANGLE Operations
ANGLE Menu
DMS Entry
Notation
To display the
ANGLE
menu, press y [
ANGLE
]. The
ANGLE menu displays angle indicators and instructions. The
Radian
/
Degree
mode setting affects the TI82 STATS interpretation of
ANGLE
menu entries.
ANGLE
1: ¡
2: '
3: r
4: 8DMS
5: R8Pr(
6: R8Pq(
7: P8Rx(
8: P8Ry(
Degree notation
DMS minute notation
Radian notation
Displays as degree/minute/second
Returns
Returns
Returns
Returns r q x y
, given
, given
, given
, given
X
X
R
R and and and and
Y
Y q q
DMS (degrees/minutes/seconds) entry notation comprises the degree symbol (
¡
), the minute symbol (
'
), and the second symbol
(
"
). degrees must be a real number; minutes and seconds must be real numbers ‚ 0.
degrees
¡
minutes
'
seconds
"
For example, enter for 30 degrees, 1 minute, 23 seconds. If the angle mode is not set to
Degree
, you must use
¡
so that the
TI82 STATS can interpret the argument as degrees, minutes, and seconds.
Degree
mode
Radian
mode
¡ (Degree)
¡
(degree) designates an angle or list of angles as degrees, regardless of the current angle mode setting. In
Radian
mode, you can use
¡
to convert degrees to radians.
value
¡
{
value1
,
value2
,
value3
,
value4
,
...
,
value n
}¡
¡
also designates degrees (D) in DMS format.
'
(minutes) designates minutes (M) in DMS format.
"
(seconds) designates seconds (S) in DMS format.
Note: " is not on the ANGLE menu. To enter ", press ƒ [
ã
].
Math, Angle, and Test Operations 2.23
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ANGLE Operations
(continued) r
(Radians) r
(radians) designates an angle or list of angles as radians, regardless of the current angle mode setting. In
Degree
mode, you can use
r
to convert radians to degrees.
value
r
Degree
mode
8DMS
8DMS
(degree/minute/second) displays answer in DMS format
(page 2.23). The mode setting must be
Degree
for answer to be interpreted as degrees, minutes, and seconds.
8DMS
is valid only at the end of a line.
answer
8DMS
R8Pr (,
R8Pq ( ,
P8Rx(,
P8Ry(
R8Pr(
converts rectangular coordinates to polar coordinates and returns
r
.
R8Pq(
converts rectangular coordinates to polar coordinates and returns
q
. x and y can be lists.
R8Pr(
x
,
y
), R8Pq(
x
,
y
)
Note: Radian mode is set.
P8Rx(
converts polar coordinates to rectangular coordinates and returns
x
.
P8Ry(
converts polar coordinates to rectangular coordinates and returns
y
. r and q
can be lists.
P8Rx(
r
,
q
), P8Ry(
r
,
q
)
Note: Radian mode is set.
2.24 Math, Angle, and Test Operations
TEST (Relational) Operations
TEST Menu
=, ƒ,
>, ‚,
<,
To display the
TEST
menu, press y [
TEST
].
This operator...
TEST LOGIC
1: =
2: ƒ
3: >
4: ‚
5: <
6:
Returns 1 (true) if...
Equal
Not equal to
Greater than
Greater than or equal to
Less than
Less than or equal to
Relational operators compare valueA and valueB and return
1
if the test is true or
0
if the test is false. valueA and valueB can be real numbers, expressions, or lists. For
=
and
ƒ
only, valueA and
valueB also can be matrices or complex numbers. If valueA and
valueB are matrices, both must have the same dimensions.
Relational operators are often used in programs to control program flow and in graphing to control the graph of a function over specific values.
valueA
=
valueB valueA
>
valueB valueA
<
valueB valueA
ƒ
valueB valueA
‚
valueB valueA
valueB
Using Tests
Relational operators are evaluated after mathematical functions according to EOS rules (Chapter 1).
•
The expression
2+2=2+3
returns
0
. The TI82 STATS performs the addition first because of EOS rules, and then it compares 4 to 5.
•
The expression
2+(2=2)+3
returns
6
. The TI82 STATS performs the relational test first because it is in parentheses, and then it adds 2, 1, and 3.
Math, Angle, and Test Operations 2.25
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TEST LOGIC (Boolean) Operations
TEST LOGIC
Menu
Boolean
Operators and, or, xor not(
Using Boolean
Operations
To display the
TEST LOGIC
menu, press y ã
TEST
ä ~.
This operator...
TEST LOGIC
1: and
2: or
3: xor
4: not(
Returns a 1 (true) if...
Both values are nonzero (true).
At least one value is nonzero (true).
Only one value is zero (false).
The value is zero (false).
Boolean operators are often used in programs to control program flow and in graphing to control the graph of the function over specific values. Values are interpreted as zero
(false) or nonzero (true).
and
,
or
, and
xor
(exclusive or) return a value of
1
if an expression is true or
0
if an expression is false, according to the table below. valueA and valueB can be real numbers, expressions, or lists.
valueA
and
valueB valueA
or
valueB valueA
xor
valueB
valueA valueB
ƒ0
ƒ0
0
0
ƒ0
0
ƒ0
0 returns returns returns returns
and
1
0
0
0 or
1
1
1
0 xor
0
1
1
0 not(
returns
1
if value (which can be an expression) is
0
.
not(
value
)
Boolean logic is often used with relational tests. In the following program, the instructions store
4
into
C
.
2.26 Math, Angle, and Test Operations
Contents
3
Function
Graphing
Getting Started: Graphing a Circle
..............................................................
Defining Graphs
......................................................................................................
Setting the Graph Modes
...................................................................................
Defining Functions
................................................................................................
Selecting and Deselecting Functions
..........................................................
Setting Graph Styles for Functions
..............................................................
Setting the Viewing Window Variables
...................................................
11
Setting the Graph Format
..................................................................................
13
7
9
4
5
2
3
Displaying Graphs
..................................................................................................
15
Exploring Graphs with the FreeMoving Cursor
................................
17
Exploring Graphs with
TRACE
.....................................................................
18
Exploring Graphs with the
ZOOM
Instructions
..................................
20
Using
ZOOM MEMORY
....................................................................................
23
Using the
CALC
(Calculate) Operations
..................................................
25
Function Graphing 3.1
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Getting Started: Graphing a Circle
Getting Started is a fastpaced introduction. Read the chapter for details.
Graph a circle of radius 10, centered on the origin in the standard viewing window.
To graph this circle, you must enter separate formulas for the upper and lower portions of the circle. Then use
ZSquare
(zoom square) to adjust the display and make the functions appear as a circle.
1. In
Func
mode, press o to display the
Y= editor. Press y ã
‡
ä
100
¹ „ ¡ ¤
Í to enter the expression Y=‡(100NX
2
), which defines the top half of the circle.
The expression Y=L‡(100NX
2
) defines the bottom half of the circle. On the TI82 STATS, you can define one function in terms of another.
To define
Y
2
=LY
1
, press Ì to enter the negation sign. Press ~ to display the
VARS Y.VARS
menu. Then press Í to select
1:Function
. The
FUNCTION secondary menu is displayed. Press
1
to select
1:Y
1
.
2. Press q
6
to select
6:ZStandard
. This is a quick way to reset the window variables to the standard values. It also graphs the functions; you do not need to press s.
Notice that the functions appear as an ellipse in the standard viewing window.
3. To adjust the display so that each pixel represents an equal width and height, press q
5
to select
5:ZSquare
. The functions are replotted and now appear as a circle on the display.
4. To see the
ZSquare
window variables, press p and notice the new values for
Xmin
,
Xmax
,
Ymin
, and
Ymax
.
3.2 Function Graphing
Defining Graphs
TI82 STATS—
Graphing Mode
Similarities
Chapter 3 specifically describes function graphing, but the steps shown here are similar for each TI82 STATS graphing mode.
Chapters 4, 5, and 6 describe aspects that are unique to parametric graphing, polar graphing, and sequence graphing.
Defining a Graph
To define a graph in any graphing mode, follow these steps.
Some steps are not always necessary.
1. Press z and set the appropriate graph mode (page 3.4).
2. Press o and enter, edit, or select one or more functions in the
Y=
editor (page 3.5 and 3.7).
3. Deselect stat plots, if necessary (page 3.7).
4. Set the graph style for each function (page 3.9).
5. Press p and define the viewing window variables
(page 3.11).
6. Press y [
FORMAT
] and select the graph format settings
(page 3.13).
Displaying and
Exploring a
Graph
Saving a Graph for Later Use
After you have defined a graph, press s to display it.
Explore the behavior of the function or functions using the
TI82 STATS tools described in this chapter.
You can store the elements that define the current graph to any of 10 graph database variables (
GDB1
through
GDB9
, and
GDB0
; Chapter 8). To recreate the current graph later, simply recall the graph database to which you stored the original graph.
These types of information are stored in a
GDB
.
•
Y=
functions
•
Graph style settings
•
Window settings
•
Format settings
You can store a picture of the current graph display to any of 10 graph picture variables (
Pic1
through
Pic9
, and
Pic0
; Chapter
8). Then you can superimpose one or more stored pictures onto the current graph.
Function Graphing 3.3
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Setting the Graph Modes
Checking and
Changing the
Graphing Mode
To display the mode screen, press z. The default settings are highlighted below. To graph functions, you must select
Func
mode before you enter values for the window variables and before you enter the functions.
Setting Modes from a Program
The TI82 STATS has four graphing modes.
•
Func
(function graphing)
•
Par
(parametric graphing; Chapter 4)
•
Pol
(polar graphing; Chapter 5)
•
Seq
(sequence graphing; Chapter 6)
Other mode settings affect graphing results. Chapter 1 describes each mode setting.
•
Float
or
0123456789
(fixed) decimal mode affects displayed graph coordinates.
•
Radian
or
Degree
angle mode affects interpretation of some functions.
•
Connected
or
Dot
plotting mode affects plotting of selected functions.
•
Sequential
or
Simul
graphingorder mode affects function plotting when more than one function is selected.
To set the graphing mode and other modes from a program, begin on a blank line in the program editor and follow these steps.
1. Press z to display the mode settings.
2. Press †, ~, , and } to place the cursor on the mode that you want to select.
3. Press Í to paste the mode name to the cursor location.
The mode is changed when the program is executed.
3.4 Function Graphing
Defining Functions
Displaying
Functions in the
Y= Editor
To display the
Y=
editor, press o. You can store up to 10 functions to the function variables
Y
1
through
Y
9
, and
Y
0
. You can graph one or more defined functions at once. In this example, functions
Y
1
and
Y
2
are defined and selected.
Defining or
Editing a
Function
To define or edit a function, follow these steps.
1. Press o to display the
Y=
editor.
2. Press † to move the cursor to the function you want to define or edit. To erase a function, press ‘.
3. Enter or edit the expression to define the function.
•
You may use functions and variables (including matrices and lists) in the expression. When the expression evaluates to a nonreal number, the value is not plotted; no error is returned.
•
The independent variable in the function is
X
.
Func
mode defines „ as
X
. To enter
X
, press „ or press
ƒ [
X
].
•
When you enter the first character, the
=
is highlighted, indicating that the function is selected.
As you enter the expression, it is stored to the variable
Yn
as a userdefined function in the
Y=
editor.
4. Press Í or † to move the cursor to the next function.
Function Graphing 3.5
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Defining Functions
(continued)
Defining a
Function from the Home Screen or a Program
To define a function from the home screen or a program, begin on a blank line and follow these steps.
1. Press ƒ [
ã
], enter the expression, and then press ƒ
[
ã
] again.
2. Press ¿.
3. Press ~
1
to select
1:Function
from the
VARS Y.VARS
menu.
4. Select the function name, which pastes the name to the cursor location on the home screen or program editor.
5. Press Í to complete the instruction.
"
expression
"
!
n
Evaluating Y=
Functions in
Expressions
When the instruction is executed, the TI82 STATS stores the expression to the designated variable
Y
n, selects the function, and displays the message
Done
.
You can calculate the value of a
Y=
function
Y
n at a specified
value of
X
. A list of values returns a list.
Y
n
(
value
)
Y
n
({
value1
,
value2
,
value3
,
. . .
,
value n
})
3.6 Function Graphing
Selecting and Deselecting Functions
Selecting and
Deselecting a
Function
You can select and deselect (turn on and turn off) a function in the
Y=
editor. A function is selected when the
=
sign is highlighted. The TI82 STATS graphs only the selected functions. You can select any or all functions
Y
1
through
Y
9
, and
Y
0
.
To select or deselect a function in the
Y=
editor, follow these steps.
1. Press o to display the
Y=
editor.
2. Move the cursor to the function you want to select or deselect.
3. Press  to place the cursor on the function’s
=
sign.
4. Press Í to change the selection status.
When you enter or edit a function, it is selected automatically.
When you clear a function, it is deselected.
Turning On or
Turning Off a Stat
Plot in the Y=
Editor
To view and change the on/off status of a stat plot in the
Y=
editor, use
Plot1 Plot2 Plot3
(the top line of the
Y=
editor).
When a plot is on, its name is highlighted on this line.
To change the on/off status of a stat plot from the
Y= editor, press } and ~ to place the cursor on
Plot1
,
Plot2
, or
Plot3
, and then press Í.
Plot1
is turned on.
Plot2
and
Plot3
are turned off.
Function Graphing 3.7
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Selecting and Deselecting Functions
(continued)
Selecting and
Deselecting
Functions from the Home Screen or a Program
To select or deselect a function from the home screen or a program, begin on a blank line and follow these steps.
1. Press ~ to display the
VARS Y.VARS
menu.
2. Select
4:On/Off
to display the
ON/OFF
secondary menu.
3. Select
1:FnOn
to turn on one or more functions or
2:FnOff
to turn off one or more functions. The instruction you select is copied to the cursor location.
4. Enter the number (
1
through
9
, or
0
; not the variable
Y
n) of each function you want to turn on or turn off.
•
If you enter two or more numbers, separate them with commas.
•
To turn on or turn off all functions, do not enter a number after
FnOn
or
FnOff
.
FnOn
[function#
,
function#
,
. . .
,
function n]
FnOff
[function#
,
function#
,
. . .
,
function n]
5. Press Í. When the instruction is executed, the status of each function in the current mode is set and
Done
is displayed.
For example, in
Func
mode,
FnOff :FnOn 1,3
turns off all functions in the
Y=
editor, and then turns on
Y
1
and
Y
3
.
3.8 Function Graphing
Setting Graph Styles for Functions
Graph Style
Icons in the Y=
Editor
This table describes the graph styles available for function graphing. Use the styles to visually differentiate functions to be graphed together. For example, you can set
Y
1
as a solid line,
Y
2
as a dotted line, and
Y
3
as a thick line.
Icon Style
ì
ç
è
é
ê
ë
í
Line
Thick
Above
Below
Path
Description
A solid line connects plotted points; this is the default in
Connected
mode
A thick solid line connects plotted points
Shading covers the area a*bove the graph
Shading covers the area below the graph
A circular cursor traces the leading edge of the graph and draws a path
Animate A circular cursor traces the leading edge of the graph without drawing a path
Dot A small dot represents each plotted point; this is the default in
Dot
mode
Note: Some graph styles are not available in all graphing modes.
Chapters 4, 5, and 6 list the styles for Par, Pol, and Seq modes.
Setting the Graph
Style
To set the graph style for a function, follow these steps.
1. Press o to display the
Y=
editor.
2. Press † and } to move the cursor to the function.
3. Press   to move the cursor left, past the
=
sign, to the graph style icon in the first column. The insert cursor is displayed. (Steps 2 and 3 are interchangeable.)
4. Press Í repeatedly to rotate through the graph styles.
The seven styles rotate in the same order in which they are listed in the table above.
5. Press ~, }, or † when you have selected a style.
Function Graphing 3.9
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Setting Graph Styles for Functions
(continued)
Shading Above and Below
When you select é or ê for two or more functions, the
TI82 STATS rotates through four shading patterns.
•
Vertical lines shade the first function with a é or ê graph style.
•
Horizontal lines shade the second.
•
Negatively sloping diagonal lines shade the third.
•
Positively sloping diagonal lines shade the fourth.
•
The rotation returns to vertical lines for the fifth é or ê function, repeating the order described above.
When shaded areas intersect, the patterns overlap.
Setting a Graph
Style from a
Program
Note: When
é or ê is selected for a Y= function that graphs a family of curves, such as
Y1={1,2,3}X, the four shading patterns rotate for each member of the family of curves.
To set the graph style from a program, select
H:GraphStyle(
from the
PRGM CTL
menu. To display this menu, press while in the program editor. function# is the number of the
Y= function name in the current graphing mode. graphstyle# is an integer from
1
to
7
that corresponds to the graph style, as shown below.
1
= ç (line)
4
= ê (below)
2
= è (thick)
5
= ë (path)
3
= é (above)
6
= ì (animate)
GraphStyle(
function#
,
graphstyle#
)
For example, when this program is executed in
Func
mode,
GraphStyle(1,3)
sets
Y
1
to é (above).
7
= í (dot)
3.10 Function Graphing
Setting the Viewing Window Variables
The TI82 STATS
Viewing Window
The viewing window is the portion of the coordinate plane defined by
Xmin
,
Xmax
,
Ymin
, and
Ymax
.
Xscl
(X scale) defines the distance between tick marks on the xaxis.
Yscl
(Y scale) defines the distance between tick marks on the yaxis. To turn off tick marks, set
Xscl=0
and
Yscl=0
.
Ymax
Xmin
Xscl
Yscl
Xmax
Ymin
Displaying the
Window
Variables
To display the current window variable values, press p.
The window editor above and to the right shows the default values in
Func
graphing mode and
Radian
angle mode. The window variables differ from one graphing mode to another.
Xres
sets pixel resolution (
1
through
8
) for function graphs only.
The default is
1
.
•
At
Xres=1
, functions are evaluated and graphed at each pixel on the xaxis.
•
At
Xres=8
, functions are evaluated and graphed at every eighth pixel along the xaxis.
Tip: Small Xres values improve graph resolution but may cause the
TI82 STATS to draw graphs more slowly.
Changing a
Window Variable
Value
To change a window variable value from the window editor, follow these steps.
1. Press † or } to move the cursor to the window variable you want to change.
2. Edit the value, which can be an expression.
•
Enter a new value, which clears the original value.
•
Move the cursor to a specific digit, and then edit it.
3. Press Í, †, or }. If you entered an expression, the
TI82 STATS evaluates it. The new value is stored.
Note:
Xmin<Xmax and Ymin<Ymax must be true in order to graph.
Function Graphing 3.11
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Setting the Viewing Window Variables
(continued)
Storing to a
Window Variable from the Home
Screen or a
Program
To store a value, which can be an expression, to a window variable, begin on a blank line and follow these steps.
1. Enter the value you want to store.
2. Press ¿.
3. Press to display the
VARS
menu.
4. Select
1:Window
to display the
Func
window variables (
X/Y secondary menu).
•
Press ~ to display the
Par
and
Pol
window variables (
T/q secondary menu).
•
Press ~ ~ to display the
Seq
window variables (
U/V/W secondary menu).
5. Select the window variable to which you want to store a value. The name of the variable is pasted to the current cursor location.
6. Press Í to complete the instruction.
When the instruction is executed, the TI82 STATS stores the value to the window variable and displays the value.
@X and @Y
The variables
@X
and
@Y
(items
8
and
9
on the
VARS
(
1:Window
)
X/Y
secondary menu) define the distance from the center of one pixel to the center of any adjacent pixel on a graph
(graphing accuracy).
@
X
and
@
Y
are calculated from
Xmin
,
Xmax
,
Ymin
, and
Ymax
when you display a graph.
@X
=
(Xmax N Xmin)
94
@Y
=
(Ymax N Ymin)
62
You can store values to
@X
and
@Y
. If you do,
Xmax
and
Ymax
are calculated from
@X
,
Xmin
,
@Y
, and
Ymin
.
3.12 Function Graphing
Setting the Graph Format
Displaying the
Format Settings
To display the format settings, press y [
FORMAT
]. The default settings are highlighted below.
RectGC PolarGC
CoordOn CoordOff
GridOff GridOn
AxesOn AxesOff
LabelOff LabelOn
ExprOn ExprOff
Sets cursor coordinates.
Sets coordinates display on or off.
Sets grid off or on.
Sets axes on or off.
Sets axes label off or on.
Sets expression display on or off.
Format settings define a graph’s appearance on the display.
Format settings apply to all graphing modes.
Seq
graphing mode has an additional mode setting (Chapter 6).
Changing a
Format Setting
To change a format setting, follow these steps.
1. Press †, ~, }, and  as necessary to move the cursor to the setting you want to select.
2. Press Í to select the highlighted setting.
RectGC, PolarGC RectGC
(rectangular graphing coordinates) displays the cursor location as rectangular coordinates
X
and
Y
.
PolarGC
(polar graphing coordinates) displays the cursor location as polar coordinates
R
and
q
.
The
RectGC
/
PolarGC
setting determines which variables are updated when you plot the graph, move the freemoving cursor, or trace.
•
RectGC
updates
X
and
Y
; if
CoordOn
format is selected,
X
and
Y
are displayed.
•
PolarGC
updates
X
,
Y
,
R
, and
q
; if
CoordOn
format is selected,
R
and
q
are displayed.
Function Graphing 3.13
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Setting the Graph Format
(continued)
CoordOn,
CoordOff
CoordOn
(coordinates on) displays the cursor coordinates at the bottom of the graph. If
ExprOff
format is selected, the function number is displayed in the topright corner.
CoordOff
(coordinates off) does not display the function number or coordinates.
GridOff, GridOn
Grid points cover the viewing window in rows that correspond to the tick marks (page 3.11) on each axis.
GridOff
does not display grid points.
GridOn
displays grid points.
AxesOn, AxesOff
AxesOn
displays the axes.
AxesOff
does not display the axes.
This overrides the
LabelOff
/
LabelOn
format setting.
LabelOff,
LabelOn
LabelOff
and
LabelOn
determine whether to display labels for the axes (
X
and
Y
), if
AxesOn
format is also selected.
ExprOn, ExprOff
ExprOn
and
ExprOff
determine whether to display the
Y=
expression when the trace cursor is active. This format setting also applies to stat plots.
When
ExprOn
is selected, the expression is displayed in the topleft corner of the graph screen.
When
ExprOff
and
CoordOn
both are selected, the number in the topright corner specifies which function is being traced.
3.14 Function Graphing
Displaying Graphs
Displaying a New
Graph
To display the graph of the selected function or functions, press s.
TRACE
,
ZOOM
instructions, and
CALC
operations display the graph automatically. As the TI82 STATS plots the graph, the busy indicator is on. As the graph is plotted,
X
and
Y
are updated.
Pausing or
Stopping a Graph
While plotting a graph, you can pause or stop graphing.
•
Press Í to pause; then press Í to resume.
•
Press É to stop; then press s to redraw.
Smart Graph
Smart Graph is a TI82 STATS feature that redisplays the last graph immediately when you press s, but only if all graphing factors that would cause replotting have remained the same since the graph was last displayed.
If you performed any of these actions since the graph was last displayed, the TI82 STATS will replot the graph based on new values when you press s.
•
Changed a mode setting that affects graphs
•
Changed a function in the current picture
•
Selected or deselected a function or stat plot
•
Changed the value of a variable in a selected function
•
Changed a window variable or graph format setting
•
Cleared drawings by selecting
ClrDraw
•
Changed a stat plot definition
Function Graphing 3.15
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Displaying Graphs
(continued)
Overlaying
Functions on a
Graph
On the TI82 STATS, you can graph one or more new functions without replotting existing functions. For example, store
sin(X)
to
Y
1
in the
Y=
editor and press s. Then store
cos(X)
to
Y
2
and press s again. The function
Y
2
is graphed on top of
Y
1
, the original function.
Graphing a
Family of Curves
If you enter a list (Chapter 11) as an element in an expression, the TI82 STATS plots the function for each value in the list, thereby graphing a family of curves. In
Simul
graphingorder mode, it graphs all functions sequentially for the first element in each list, and then for the second, and so on.
{2,4,6}sin(X)
graphs three functions:
2 sin(X)
,
4 sin(X)
, and
6 sin(X)
.
{2,4,6}sin({1,2,3}X)
graphs
2 sin(X)
,
4 sin(2X)
, and
6 sin(3X)
.
Note: When using more than one list, the lists must have the same dimensions.
3.16 Function Graphing
Exploring Graphs with the FreeMoving Cursor
FreeMoving
Cursor
Graphing
Accuracy
When a graph is displayed, press , ~, }, or † to move the cursor around the graph. When you first display the graph, no cursor is visible. When you press , ~, }, or †, the cursor moves from the center of the viewing window.
As you move the cursor around the graph, the coordinate values of the cursor location are displayed at the bottom of the screen if
CoordOn
format is selected. The
Float
/
Fix
decimal mode setting determines the number of decimal digits displayed for the coordinate values.
To display the graph with no cursor and no coordinate values, press ‘ or Í. When you press , ~, }, or †, the cursor moves from the same position.
The freemoving cursor moves from pixel to pixel on the screen.
When you move the cursor to a pixel that appears to be on the function, the cursor may be near, but not actually on, the function. The coordinate value displayed at the bottom of the screen actually may not be a point on the function. To move the cursor along a function, use r (page 3.18).
The coordinate values displayed as you move the cursor approximate actual math coordinates, *accurate to within the width and height of the pixel. As
Xmin
,
Xmax
,
Ymin
, and
Ymax
get closer together (as in a
ZoomIn
) graphing accuracy increases, and the coordinate values more closely approximate the math coordinates.
Freemoving cursor “on” the curve
Function Graphing 3.17
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Exploring Graphs with TRACE
Beginning a
Trace
Use
TRACE
to move the cursor from one plotted point to the next along a function. To begin a trace, press r. If the graph is not displayed already, press r to display it. The trace cursor is on the first selected function in the
Y= editor, at the middle
X
value on the screen. The cursor coordinates are displayed at the bottom of the screen if
CoordOn
format is selected. The
Y= expression is displayed in the topleft corner of the screen, if
ExprOn
format is selected.
Moving the Trace
Cursor
To move the TRACE cursor . . .
do this:
. . . to the previous or next plotted point, press  or ~.
. . . five plotted points on a function (
Xres
affects this), press y  or y
~.
. . . to any valid
X
value on a function, enter a value, and then press Í.
. . . from one function to another, press } or †.
When the trace cursor moves along a function, the
Y
value is calculated from the
X
value; that is,
Y
=
Y
n
(X)
. If the function is undefined at an
X
value, the
Y
value is blank.
Trace cursor on the curve
If you move the trace cursor beyond the top or bottom of the screen, the coordinate values at the bottom of the screen continue to change appropriately.
Moving the Trace
Cursor from
Function to
Function
To move the trace cursor from function to function, press † and
}. The cursor follows the order of the selected functions in the
Y=
editor. The trace cursor moves to each function at the same
X
value. If
ExprOn
format is selected, the expression is updated.
3.18 Function Graphing
Moving the Trace
Cursor to Any
Valid X Value
To move the trace cursor to any valid
X
value on the current function, enter the value. When you enter the first digit, an
X=
prompt and the number you entered are displayed in the bottomleft corner of the screen. You can enter an expression at the
X=
prompt. The value must be valid for the current viewing window. When you have completed the entry, press Í to move the cursor.
Panning to the
Left or Right
Note: This feature does not apply to stat plots.
If you trace a function beyond the left or right side of the screen, the viewing window automatically pans to the left or right.
Xmin
and
Xmax
are updated to correspond to the new viewing window.
Quick Zoom
Leaving and
Returning to
TRACE
While tracing, you can press Í to adjust the viewing window so that the cursor location becomes the center of the new viewing window, even if the cursor is above or below the display. This allows panning up and down. After Quick Zoom, the cursor remains in
TRACE
.
When you leave and return to
TRACE
, the trace cursor is displayed in the same location it was in when you left
TRACE unless Smart Graph has replotted the graph (page 3.15).
,
Using TRACE in a Program
On a blank line in the program editor, press r. The instruction
Trace
is pasted to the cursor location. When the instruction is encountered during program execution, the graph is displayed with the trace cursor on the first selected function.
As you trace, the cursor coordinate values are updated. When you finish tracing the functions, press Í to resume program execution.
Function Graphing 3.19
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Exploring Graphs with the ZOOM Instructions
ZOOM Menu
Zoom Cursor
ZBox
To display the
ZOOM
menu, press q. You can adjust the viewing window of the graph quickly in several ways. All
ZOOM
instructions are accessible from programs.
ZOO
M
MEMORY
1: ZBox
2: Zoom In
3: Zoom Out
4: ZDecimal
5: ZSquare
6: ZStandard
7: ZTrig
8: ZInteger
9: ZoomStat
0: ZoomFit
Draws a box to define the viewing window.
Magnifies the graph around the cursor.
Views more of a graph around the cursor.
Sets
@
X
and
@
Y
to 0.1.
Sets equalsize pixels on the
X
and
Y
axes.
Sets the standard window variables.
Sets the builtin trig window variables.
Sets integer values on the
X
and
Y
axes.
Sets the values for current stat lists.
Fits
YMin
and
YMax
between
XMin
and
XMax
.
When you select
1:ZBox
,
2:Zoom In
, or
3:Zoom Out
, the cursor on the graph becomes the zoom cursor (
+
), a smaller version of the freemoving cursor (
+
).
To define a new viewing window using
ZBox
, follow these steps.
1. Select
1:ZBox
from the
ZOOM
menu. The zoom cursor is displayed at the center of the screen.
2. Move the zoom cursor to any spot you want to define as a corner of the box, and then press Í. When you move the cursor away from the first defined corner, a small, square dot indicates the spot.
3. Press , }, ~, or †. As you move the cursor, the sides of the box lengthen or shorten proportionately on the screen.
Note: To cancel ZBox before you press Í, press ‘.
4. When you have defined the box, press Í to replot the graph.
To use
ZBox
to define another box within the new graph, repeat steps 2 through 4. To cancel
ZBox
, press ‘.
3.20 Function Graphing
Zoom In,
Zoom Out
ZDecimal
ZSquare
Zoom In
magnifies the part of the graph that surrounds the cursor location.
Zoom Out
displays a greater portion of the graph, centered on the cursor location. The
XFact
and
YFact
settings determine the extent of the zoom.
To zoom in on a graph, follow these steps.
1. Check
XFact
and
YFact
(page 3.24); change as needed.
2. Select
2:Zoom In
from the
ZOOM
menu. The zoom cursor is displayed.
3. Move the zoom cursor to the point that is to be the center of the new viewing window.
4. Press Í. The TI82 STATS adjusts the viewing window by
XFact
and
YFact
; updates the window variables; and replots the selected functions, centered on the cursor location.
5. Zoom in on the graph again in either of two ways.
•
To zoom in at the same point, press Í.
•
To zoom in at a new point, move the cursor to the point that you want as the center of the new viewing window, and then press Í.
To zoom out on a graph, select
3:Zoom Out
and repeat steps 3 through 5.
To cancel
Zoom In
or
Zoom Out
, press ‘.
ZDecimal
replots the functions immediately. It updates the window variables to preset values, as shown below. These values set
@
X
and
@
Y
equal to
0.1
and set the
X
and
Y
value of each pixel to one decimal place.
Xmin=L4.7
Xmax=4.7
Xscl=1
Ymin=L3.1
Ymax=3.1
Yscl=1
ZSquare
replots the functions immediately. It redefines the viewing window based on the current values of the window variables. It adjusts in only one direction so that
, which makes the graph of a circle look like a circle.
Xscl
and
Yscl
remain unchanged. The midpoint of the current graph (not the intersection of the axes) becomes the midpoint of the new graph.
Function Graphing 3.21
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Exploring Graphs with the ZOOM Instructions
(cont.)
ZStandard
ZTrig
ZInteger
ZoomStat
ZoomFit
ZStandard
replots the functions immediately. It updates the window variables to the standard values shown below.
Xmin=L10
Xmax=10
Xscl=1
Ymin=L10
Ymax=10
Yscl=1
Xres=1
ZTrig
replots the functions immediately. It updates the window variables to preset values that are appropriate for plotting trig functions. Those preset values in
Radian
mode are shown below.
Xmin=L(47à24)p
Xmax=(47à24)p
Xscl=p/2
Ymin=L4
Ymax=4
Yscl=1
ZInteger
redefines the viewing window to the dimensions shown below. To use
ZInteger
, move the cursor to the point that you want to be the center of the new window, and then press
Í;
ZInteger
replots the functions.
@X=1
@Y=1
Xscl=10
Yscl=10
ZoomStat
redefines the viewing window so that all statistical data points are displayed. For regular and modified box plots, only
Xmin
and
Xmax
are adjusted.
ZoomFit
replots the functions immediately.
ZoomFit
recalculates
YMin
and
YMax
to include the minimum and maximum
Y
values of the selected functions between the current
XMin
and
XMax
.
XMin
and
XMax
are not changed.
3.22 Function Graphing
Using ZOOM MEMORY
ZOOM MEMORY
Menu
To display the
ZOOM MEMORY
menu, press q ~.
ZOOMMEMOR
Y
1: ZPrevious
2: ZoomSto
3: ZoomRcl
4: SetFactors...
Uses the previous viewing window.
Stores the userdefined window.
Recalls the userdefined window.
Changes
Zoom In
and
Zoom Out
factors.
ZPrevious
ZoomSto
ZoomRcl
ZPrevious
replots the graph using the window variables of the graph that was displayed before you executed the last
ZOOM instruction.
ZoomSto
immediately stores the current viewing window. The graph is displayed, and the values of the current window variables are stored in the userdefined
ZOOM
variables
ZXmin
,
ZXmax
,
ZXscl
,
ZYmin
,
ZYmax
,
ZYscl
, and
ZXres
.
These variables apply to all graphing modes. For example, changing the value of
ZXmin
in
Func
mode also changes it in
Par
mode.
ZoomRcl
graphs the selected functions in a userdefined viewing window. The userdefined viewing window is determined by the values stored with the
ZoomSto
instruction.
The window variables are updated with the userdefined values, and the graph is plotted.
Function Graphing 3.23
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Using ZOOM MEMORY
(continued)
ZOOM FACTORS
The zoom factors,
XFact
and
YFact
, are positive numbers (not necessarily integers) greater than or equal to 1. They define the magnification or reduction factor used to
Zoom In
or
Zoom Out
around a point.
Checking XFact and YFact
To display the
ZOOM FACTORS
screen, where you can review the current values for
XFact
and
YFact
, select
4:SetFactors
from the
ZOOM MEMORY
menu. The values shown are the defaults.
Changing XFact and YFact
Using ZOOM
MEMORY Menu
Items from the
Home Screen or a Program
You can change
XFact
and
YFact
in either of two ways.
•
Enter a new value. The original value is cleared automatically when you enter the first digit.
•
Place the cursor on the digit you want to change, and then enter a value or press { to delete it.
From the home screen or a program, you can store directly to any of the userdefined
ZOOM
variables.
From a program, you can select the
ZoomSto
and
ZoomRcl
instructions from the
ZOOM MEMORY
menu.
3.24 Function Graphing
Using the CALC (Calculate) Operations
CALCULATE
Menu value
To display the
CALCULATE
menu, press y ã
CALC
ä. Use the items on this menu to analyze the current graph functions.
CALCULAT
E
1: value
2: zero
3: minimum
4: maximum
5: intersect
6: dy/dx
7: ‰f(x)dx
Calculates a function
Y
value for a given
Finds a zero (xintercept) of a function.
Finds a minimum of a function.
Finds a maximum of a function.
Finds an intersection of two functions.
Finds a numeric derivative of a function.
Finds a numeric integral of a function.
X
.
value
evaluates one or more currently selected functions for a specified value of
X
.
Note: When a value is displayed for
X, press ‘ to clear the value. When no value is displayed, press
‘ to cancel the value operation.
To evaluate a selected function at
X
, follow these steps.
1. Select
1:value
from the
CALCULATE
menu. The graph is displayed with
X=
in the bottomleft corner.
2. Enter a real value, which can be an expression, for
X
between
Xmin
and
Xmax
.
3. Press Í.
The cursor is on the first selected function in the
Y= editor at the
X
value you entered, and the coordinates are displayed, even if
CoordOff
format is selected.
To move the cursor from function to function at the entered
X
value, press } or †. To restore the freemoving cursor, press
 or ~.
Function Graphing 3.25
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Using the CALC (Calculate) Operations
(continued) zero zero
finds a zero (xintercept or root) of a function using
solve(
.
Functions can have more than one xintercept value;
zero
finds the zero closest to your guess.
The time
zero
spends to find the correct zero value depends on the accuracy of the values you specify for the left and right bounds and the accuracy of your guess.
To find a zero of a function, follow these steps.
1. Select
2:zero
from the
CALCULATE
menu. The current graph is displayed with
Left Bound?
in the bottomleft corner.
2. Press } or † to move the cursor onto the function for which you want to find a zero.
3. Press  or ~ (or enter a value) to select the xvalue for the left bound of the interval, and then press Í. A
4
indicator on the graph screen shows the left bound.
Right
Bound?
is displayed in the bottomleft corner. Press  or ~
(or enter a value) to select the xvalue for the right bound, and then press Í. A
3
indicator on the graph screen shows the right bound.
Guess?
is then displayed in the bottomleft corner.
4. Press  or ~ (or enter a value) to select a point near the zero of the function, between the bounds, and then press
Í.
The cursor is on the solution and the coordinates are displayed, even if
CoordOff
format is selected. To move to the same xvalue for other selected functions, press } or †. To restore the freemoving cursor, press  or ~.
3.26 Function Graphing
minimum, maximum intersect minimum
and
maximum
find a minimum or maximum of a function within a specified interval to a tolerance of 1âL5.
To find a minimum or maximum, follow these steps.
1. Select
3:minimum
or
4:maximum
from the
CALCULATE menu. The current graph is displayed.
2. Select the function and set left bound, right bound, and guess as described for
zero
(steps 2 through 4; page 3.26).
The cursor is on the solution, and the coordinates are displayed, even if you have selected
CoordOff
format;
Minimum
or
Maximum
is displayed in the bottomleft corner.
To move to the same xvalue for other selected functions, press
} or †. To restore the freemoving cursor, press  or ~.
intersect
finds the coordinates of a point at which two or more functions intersect using
solve(
. The intersection must appear on the display to use
intersect
.
To find an intersection, follow these steps.
1. Select
5:intersect
from the
CALCULATE
menu. The current graph is displayed with
First curve?
in the bottomleft corner.
2. Press † or }, if necessary, to move the cursor to the first function, and then press Í.
Second curve?
is displayed in the bottomleft corner.
3. Press † or }, if necessary, to move the cursor to the second function, and then press Í.
4. Press ~ or  to move the cursor to the point that is your guess as to location of the intersection, and then press Í.
The cursor is on the solution and the coordinates are displayed, even if
CoordOff
format is selected.
Intersection
is displayed in the bottomleft corner. To restore the freemoving cursor, press
, }, ~, or †.
Function Graphing 3.27
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Using the CALC (Calculate) Operations
(continued) dy/dx
‰f(x)dx dy/dx
(numerical derivative) finds the numerical derivative
(slope) of a function at a point, with H=1âL3.
To find a function’s slope at a point, follow these steps.
1. Select
6:dy/dx
from the
CALCULATE
menu. The current graph is displayed.
2. Press } or † to select the function for which you want to find the numerical derivative.
3. Press  or ~ (or enter a value) to select the
X
value at which to calculate the derivative, and then press Í.
The cursor is on the solution and the numerical derivative is displayed.
To move to the same xvalue for other selected functions, press
} or †. To restore the freemoving cursor, press  or ~.
‰f(x)dx
(numerical integral) finds the numerical integral of a function in a specified interval. It uses the
fnInt(
function, with a tolerance of H=1âL3.
To find the numerical derivative of a function, follow these steps.
1. Select
7:‰f(x)dx
from the
CALCULATE
menu. The current graph is displayed with
Lower Limit?
in the bottomleft corner.
2. Press } or † to move the cursor to the function for which you want to calculate the integral.
3. Set lower and upper limits as you would set left and right bounds for
zero
(step 3; page 3.26). The integral value is displayed, and the integrated area is shaded.
Note: The shaded area is a drawing. Use ClrDraw (Chapter 8) or any action that invokes Smart Graph to clear the shaded area.
3.28 Function Graphing
Contents
4
Parametric
Graphing
Getting Started: Path of a Ball
........................................................................
42
Defining and Displaying Parametric Graphs
........................................
44
Exploring Parametric Graphs
..........................................................................
47
Parametric Graphing 41
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Getting Started: Path of a Ball
Getting Started is a fastpaced introduction. Read the chapter for details.
Graph the parametric equation that describes the path of a ball hit at an initial speed of 30 meters per second, at an initial angle of 25 degrees with the horizontal from ground level. How far does the ball travel? When does it hit the ground? How high does it go? Ignore all forces except gravity.
For initial velocity v
0
and angle q, the position of the ball as a function of time has horizontal and vertical components.
Horizontal: X1(t)=tv
Vertical: Y1(t)=tv
0
0 cos(q) sin(q)N
1
2
gt 2
The vertical and horizontal vectors of the ball’s motion also will be graphed.
Vertical vector: X2(t)=0
Horizontal vector: X3(t)=X1(t)
Gravity constant: g=9.8 m/sec 2
Y2(t)=Y1(t)
Y3(t)=0
1. Press z. Press † † † ~ Í to select
Par
mode. Press † † ~ Í to select
Simul
for simultaneous graphing of all three parametric equations in this example.
2. Press o. Press
30
„ ™
25
y
[
ANGLE
]
1
(to select ¡) ¤ Í to define
X
1T
in terms of
T
.
3. Press
30
„ ˜
25
y [
ANGLE
]
1
¤ ¹
9.8
¥
2
„ ¡ Í to define
Y
1T
.
The vertical component vector is defined by
X
2T
and
Y
2T
.
4. Press
0
Í to define
X
2T
.
5. Press ~ to display the
VARS Y.VARS
menu. Press
2
to display the
PARAMETRIC secondary menu. Press
2
Í to define
Y
2T
.
42 Parametric Graphing
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The horizontal component vector is defined by
X
3T
and
Y
3T
.
6. Press ~
2
, and then press
1
Í to define
X
3T
. Press
0
Í to define
Y
3T
.
7. Press   } Í to change the graph style to è for
X
3T
and
Y
3T
. Press } Í
Í to change the graph style to ë for
X
2T
and
Y
2T
. Press } Í Í to change the graph style to ë for
X
1T
and
Y
1T
. (These keystrokes assume that all graph styles were set to ç originally.)
8. Press p. Enter these values for the window variables.
Tmin=0
Tmax=5
Tstep=.1
Xmin=L10
Xmax=100
Xscl=50
Ymin=L5
Ymax=15
Yscl=10
9. Press y [
FORMAT
] † † † ~ Í to set
AxesOff
, which turns off the axes.
10. Press s. The plotting action simultaneously shows the ball in flight and the vertical and horizontal component vectors of the motion.
Tip: To simulate the ball flying through the air, set graph style to
ì (animate) for X
1T
and
Y
1T
.
11. Press r to obtain numerical results and answer the questions at the beginning of this section.
Tracing begins at
Tmin
on the first parametric equation (
X
1T
and
Y
1T
). As you press ~ to trace the curve, the cursor follows the path of the ball over time. The values for
X
(distance),
Y
(height), and
T
(time) are displayed at the bottom of the screen.
Parametric Graphing 43
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Defining and Displaying Parametric Graphs
TI82 STATS
Graphing Mode
Similarities
Setting
Parametric
Graphing Mode
Displaying the
Parametric Y=
Editor
The steps for defining a parametric graph are similar to the steps for defining a function graph. Chapter 4 assumes that you are familiar with Chapter 3: Function Graphing. Chapter 4 details aspects of parametric graphing that differ from function graphing.
To display the mode screen, press z. To graph parametric equations, you must select
Par
graphing mode before you enter window variables and before you enter the components of parametric equations.
After selecting
Par
graphing mode, press o to display the parametric
Y=
editor.
Selecting a
Graph Style
In this editor, you can display and enter both the
X
and
Y
components of up to six equations,
X
1T
and
Y
1T
through
X
6T
and
Y
6T
. Each is defined in terms of the independent variable
T
. A common application of parametric graphs is graphing equations over time.
The icons to the left of
X
1T
through
X
6T
represent the graph style of each parametric equation (Chapter 3). The default in
Par
mode is ç (line), which connects plotted points. Line, è (thick),
ë (path), ì (animate), and í (dot) styles are available for parametric graphing.
44 Parametric Graphing
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Defining and
Editing
Parametric
Equations
Selecting and
Deselecting
Parametric
Equations
To define or edit a parametric equation, follow the steps in
Chapter 3 for defining a function or editing a function. The independent variable in a parametric equation is
T
. In
Par
graphing mode, you can enter the parametric variable
T
in either of two ways.
•
Press „.
•
Press ƒ ã
T
ä.
Two components,
X
and
Y
, define a single parametric equation.
You must define both of them.
The TI82 STATS graphs only the selected parametric equations. In the
Y=
editor, a parametric equation is selected when the
=
signs of both the
X
and
Y
components are highlighted. You may select any or all of the equations
X
1T
and
Y
1T
through
X
6T
and
Y
6T
.
To change the selection status, move the cursor onto the = sign of either the
X
or
Y
component and press Í. The status of both the
X
and
Y
components is changed.
Setting Window
Variables
To display the window variable values, press p. These variables define the viewing window. The values below are defaults for
Par
graphing in
Radian
angle mode.
Tmin=0
Tmax=6.2831853...
Tstep=.1308996...
Xmin=L10
Xmax=10
Xscl=1
Ymin=L10
Ymax=10
Yscl=1
Smallest
T
value to evaluate
Largest
T
value to evaluate (2p)
T
value increment (pà24)
Smallest
X
value to be displayed
Largest
X
value to be displayed
Spacing between the
X
tick marks
Smallest
Y
value to be displayed
Largest
Y
value to be displayed
Spacing between the
Y
tick marks
Note: To ensure that sufficient points are plotted, you may want to change the
T window variables.
Parametric Graphing 45
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Defining and Displaying Parametric Graphs
(continued)
Setting the Graph
Format
To display the current graph format settings, press y
[
FORMAT
]. Chapter 3 describes the format settings in detail. The other graphing modes share these format settings;
Seq
graphing mode has an additional axes format setting.
Displaying a
Graph
When you press s, the TI82 STATS plots the selected parametric equations. It evaluates the
X
and
Y
components for each value of
T
(from
Tmin
to
Tmax
in intervals of
Tstep
), and then plots each point defined by
X
and
Y
. The window variables define the viewing window.
As the graph is plotted,
X
,
Y
, and
T
are updated.
Smart Graph applies to parametric graphs (Chapter 3).
Window
Variables and
Y.VARS Menus
You can perform these actions from the home screen or a program.
•
Access functions by using the name of the
X
or
Y
component of the equation as a variable.
•
Store parametric equations.
•
Select or deselect parametric equations.
•
Store values directly to window variables.
46 Parametric Graphing
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Exploring Parametric Graphs
FreeMoving
Cursor
TRACE
The freemoving cursor in
Par
graphing works the same as in
Func
graphing.
In
RectGC
format, moving the cursor updates the values of
X
and
Y
; if
CoordOn
format is selected,
X
and
Y
are displayed.
In
PolarGC
format,
X
,
Y
,
R
, and
q
are updated; if
CoordOn
format is selected,
R
and
q
are displayed.
To activate
TRACE
, press r. When
TRACE
is active, you can move the trace cursor along the graph of the equation one
Tstep
at a time. When you begin a trace, the trace cursor is on the first selected function at
Tmin
. If
ExprOn
is selected, then the function is displayed.
In
RectGC
format,
TRACE
updates and displays the values of
X
,
Y
, and
T
if
CoordOn
format is on.
In
PolarGC
format,
X
,
Y
,
R
,
q
and
T
are updated; if
CoordOn
format is selected,
R
,
q
, and
T
are displayed. The
X
and
Y
(or
R
and
q
) values are calculated from
T
.
To move five plotted points at a time on a function, press y
 or y ~. If you move the cursor beyond the top or bottom of the screen, the coordinate values at the bottom of the screen continue to change appropriately.
Quick Zoom is available in
Par
graphing; panning is not
(Chapter 3).
Parametric Graphing 47
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Exploring Parametric Graphs
(continued)
Moving the Trace
Cursor to Any
Valid T Value
To move the trace cursor to any valid
T
value on the current function, enter the number. When you enter the first digit, a
T=
prompt and the number you entered are displayed in the bottomleft corner of the screen. You can enter an expression at the
T=
prompt. The value must be valid for the current viewing window. When you have completed the entry, press Í to move the cursor.
ZOOM
CALC
ZOOM
operations in
Par
graphing work the same as in
Func
graphing. Only the
X
(
Xmin
,
Xmax
, and
Xscl
) and
Y
(
Ymin
,
Ymax
, and
Yscl
) window variables are affected.
The
T
window variables (
Tmin
,
Tmax
, and
Tstep
) are only affected when you select
ZStandard
. The
VARS ZOOM secondary menu
ZT/Zq
items
1:ZTmin
,
2:ZTmax
, and
3:ZTstep
are the zoom memory variables for
Par
graphing.
CALC
operations in
Par
graphing work the same as in
Func
graphing. The
CALCULATE
menu items available in
Par
graphing are
1:value
,
2:dy/dx
,
3:dy/dt
, and
4:dx/dt
.
48 Parametric Graphing
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Contents
5
Polar
Graphing
Getting Started: Polar Rose
..............................................................................
Defining and Displaying Polar Graphs
.....................................................
Exploring Polar Graphs
......................................................................................
2
3
6
Polar Graphing 5–1
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Getting Started: Polar Rose
Getting Started is a fastpaced introduction. Read the chapter for details.
The polar equation R=Asin(Bq) graphs a rose. Graph the rose for A=8 and B=2.5, and then explore the appearance of the rose for other values of A and B.
1. Press z to display the mode screen. Press
† † † ~ ~ Í to select
Pol
graphing mode. Select the defaults (the options on the left) for the other mode settings.
2. Press o to display the polar
Y= editor. Press
8
˜
2.5
„ ¤ Í to define
r
1
.
3. Press q
6
to select
6:ZStandard
and graph the equation in the standard viewing window.
The graph shows only five petals of the rose, and the rose does not appear to be symmetrical. This is because the standard window sets
qmax=2p
and defines the window, rather than the pixels, as square.
4. Press p to display the window variables. Press †
4
y [ p
] to increase the value of
qmax
to 4p.
5. Press q
5
to select
5:ZSquare
and plot the graph.
6. Repeat steps 2 through 5 with new values for the variables
A
and
B
in the polar equation
r
1
=Asin(Bq)
. Observe how the new values affect the graph.
5–2 Polar Graphing
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Defining and Displaying Polar Graphs
TI82 STATS
Graphing Mode
Similarities
Setting Polar
Graphing Mode
Displaying the
Polar Y= Editor
The steps for defining a polar graph are similar to the steps for defining a function graph. Chapter 5 assumes that you are familiar with Chapter 3: Function Graphing. Chapter 5 details aspects of polar graphing that differ from function graphing.
To display the mode screen, press z. To graph polar equations, you must select
Pol
graphing mode before you enter values for the window variables and before you enter polar equations.
After selecting
Pol
graphing mode, press o to display the polar
Y=
editor.
In this editor, you can enter and display up to six polar equations,
r
1
through
r
6
. Each is defined in terms of the independent variable
q
(page 5.4).
Selecting Graph
Styles
The icons to the left of
r
1
through
r
6
represent the graph style of each polar equation (Chapter 3). The default in
Pol
graphing mode is ç (line), which connects plotted points. Line, è (thick),
ë (path), ì (animate), and í (dot) styles are available for polar graphing.
Polar Graphing 5–3
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PM Page 3 of 6
Defining and Displaying Polar Graphs
(continued)
Defining and
Editing Polar
Equations
To define or edit a polar equation, follow the steps in Chapter 3 for defining a function or editing a function. The independent variable in a polar equation is
q
. In
Pol
graphing mode, you can enter the polar variable
q
in either of two ways.
•
Press „.
•
Press ƒ ãqä.
Selecting and
Deselecting Polar
Equations
The TI82 STATS graphs only the selected polar equations. In the
Y=
editor, a polar equation is selected when the
=
sign is highlighted. You may select any or all of the equations.
To change the selection status, move the cursor onto the
=
sign, and then press Í.
Setting Window
Variables
To display the window variable values, press p. These variables define the viewing window. The values below are defaults for
Pol
graphing in
Radian
angle mode.
qmin=0 qmax=6.2831853... qstep=.1308996...
Xmin=L10
Xmax=10
Xscl=1
Ymin=L10
Ymax=10
Yscl=1
Smallest
q
value to evaluate
Largest
q
value to evaluate (2p)
Increment between
q
values (pà24)
Smallest
X
value to be displayed
Largest
X
value to be displayed
Spacing between the
X
tick marks
Smallest
Y
value to be displayed
Largest
Y
value to be displayed
Spacing between the
Y
tick marks
Note: To ensure that sufficient points are plotted, you may want to change the q window variables.
5–4 Polar Graphing
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Setting the Graph
Format
To display the current graph format settings, press y
[
FORMAT
]. Chapter 3 describes the format settings in detail. The other graphing modes share these format settings.
Displaying a
Graph
Window
Variables and
Y.VARS Menus
When you press s, the TI82 STATS plots the selected polar equations. It evaluates
R
for each value of
q
(from
qmin
to
qmax
in intervals of
qstep
) and then plots each point. The window variables define the viewing window.
As the graph is plotted,
X
,
Y
,
R
, and
q
are updated.
Smart Graph applies to polar graphs (Chapter 3).
You can perform these actions from the home screen or a program.
•
Access functions by using the name of the equation as a variable.
•
Store polar equations.
•
Select or deselect polar equations.
•
Store values directly to window variables.
Polar Graphing 5–5
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Exploring Polar Graphs
FreeMoving
Cursor
TRACE
The freemoving cursor in
Pol
graphing works the same as in
Func
graphing. In
RectGC
format, moving the cursor updates the values of
X
and
Y
; if
CoordOn
format is selected,
X
and
Y
are displayed. In
PolarGC
format,
X
,
Y
,
R
, and
q
are updated; if
CoordOn
format is selected,
R
and
q
are displayed.
To activate
TRACE
, press r. When
TRACE
is active, you can move the trace cursor along the graph of the equation one
qstep
at a time. When you begin a trace, the trace cursor is on the first selected function at
qmin
. If
ExprOn
format is selected, then the equation is displayed.
In
RectGC
format,
TRACE
updates the values of
X
,
Y
, and
q
; if
CoordOn
format is selected,
X
,
Y
, and
q
are displayed. In
PolarGC
format,
TRACE
updates
X
,
Y
,
R
, and
q
; if
CoordOn
format is selected,
R
and
q
are displayed.
To move five plotted points at a time on a function, press y
 or y ~. If you move the trace cursor beyond the top or bottom of the screen, the coordinate values at the bottom of the screen continue to change appropriately.
Quick Zoom is available in
Pol
graphing mode; panning is not
(Chapter 3).
Moving the Trace
Cursor to Any
Valid q Value
To move the trace cursor to any valid
q
value on the current function, enter the number. When you enter the first digit, a
q=
prompt and the number you entered are displayed in the bottomleft corner of the screen. You can enter an expression at the
q=
prompt. The value must be valid for the current viewing window. When you complete the entry, press Í to move the cursor.
ZOOM
CALC
ZOOM
operations in
Pol
graphing work the same as in
Func
graphing. Only the
X
(
Xmin
,
Xmax
, and
Xscl
) and
Y
(
Ymin
,
Ymax
, and
Yscl
) window variables are affected.
The
q
window variables (
qmin
,
qmax
, and
qstep
) are not affected, except when you select
ZStandard
. The
VARS ZOOM
secondary menu
ZT/Zq
items
4:Zqmin
,
5:Zqmax
, and
6:Zqstep
are zoom memory variables for
Pol
graphing.
CALC
operations in
Pol
graphing work the same as in
Func
graphing. The
CALCULATE
menu items available in
Pol
graphing are
1:value
,
2:dy/dx
, and
3:dr/dq
.
5–6 Polar Graphing
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Contents
6
Sequence
Graphing
Getting Started: Forest and Trees
.................................................................
Defining and Displaying Sequence Graphs
...........................................
Selecting Axes Combinations
.........................................................................
Exploring Sequence Graphs
.............................................................................
Graphing Web Plots
..............................................................................................
11
Using Web Plots to Illustrate Convergence
...........................................
12
Graphing Phase Plots
...........................................................................................
13
Comparing TI82 STATS and TI.82 Sequence Variables
...........
15
Keystroke Differences Between TI82 STATS and TI82
..........
16
8
9
2
3
Sequence Graphing 6–1
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Getting Started: Forest and Trees
Getting Started is a fastpaced introduction. Read the chapter for details.
A small forest of 4,000 trees is under a new forestry plan. Each year 20 percent of the trees will be harvested and 1,000 new trees will be planted. Will the forest eventually disappear? Will the forest size stabilize? If so, in how many years and with how many trees?
1. Press z. Press † † † ~ ~ ~ Í to select
Seq
graphing mode.
2. Press y [
FORMAT
] and select
Time
axes format and
ExprOn
format if necessary.
3. Press o. If the graphstyle icon is not
íííí
(dot), press  , press Í until
íííí is displayed, and then press ~ ~.
4. Press ~
3
to select
iPart(
(integer part) because only whole trees are harvested. After each annual harvest, 80 percent (.80) of the trees remain. Press Ë
8
y [ u
] £ „ ¹
1
¤ to define the number of trees after each harvest. Press Ã
1000
¤ to define the new trees. Press †
4000
to define the number of trees at the beginning of the program.
5. Press p
0
to set
nMin=0
. Press †
50
to set
nMax=50
.
nMin
and
nMax
evaluate forest size over 50 years. Set the other window variables.
PlotStart=1
PlotStep=1
Xmin=0
Xmax=50
Xscl=10
Ymin=0
Ymax=6000
Yscl=1000
6. Press r. Tracing begins at
nMin
(the start of the forestry plan). Press ~ to trace the sequence year by year. The sequence is displayed at the top of the screen. The values for
n
(number of years),
X
(
X=n
, because
n
is plotted on the xaxis), and
Y
(tree count) are displayed at the bottom. When will the forest stabilize? With how many trees?
6–2 Sequence Graphing
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Defining and Displaying Sequence Graphs
TI82 STATS
Graphing Mode
Similarities
TI82 STATS
Sequence
Functions u, v, and w
The steps for defining a sequence graph are similar to the steps for defining a function graph. Chapter 6 assumes that you are familiar with Chapter 3: Function Graphing. Chapter 6 details aspects of sequence graphing that differ from function graphing.
Setting Sequence
Graphing Mode
To display the mode screen, press z. To graph sequence functions, you must select
Seq
graphing mode before you enter window variables and before you enter sequence functions.
Sequence graphs automatically plot in
Simul
mode, regardless of the current plottingorder mode setting.
The TI82 STATS has three sequence functions that you can enter from the keyboard:
u
,
v
, and
w
. They are above the ¬, −, and ® keys.
You can define sequence functions in terms of:
•
The independent variable
n
•
The previous term in the sequence function, such as
u(nN1)
•
The term that precedes the previous term in the sequence function, such as
u(nN2)
•
The previous term or the term that precedes the previous term in another sequence function, such as
u(nN1)
or
u(nN2)
referenced in the sequence
v(n)
.
Note: Statements in this chapter about u(n) are also true for v(n) and
w(n); statements about
u(nN1) are also true for v(nN1) and w(nN1); statements about u(nN2) are also true for v(nN2) and w(nN2).
Sequence Graphing 6–3
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Defining and Displaying Sequence Graphs
(continued)
Displaying the
Sequence Y=
Editor
After selecting
Seq
mode, press o to display the sequence
Y=
editor.
In this editor, you can display and enter sequences for
u(n)
,
v(n)
, and
w(n)
. Also, you can edit the value for
nMin
, which is the sequence window variable that defines the minimum
n
value to evaluate.
The sequence
Y=
editor displays the
nMin
value because of its relevance to
u(nMin)
,
v(nMin)
, and
w(nMin)
, which are the initial values for the sequence equations
u(n)
,
v(n)
, and
w(n)
, respectively.
nMin
in the
Y=
editor is the same as
nMin
in the window editor.
If you enter a new value for
nMin
in one editor, the new value for
nMin
is updated in both editors.
Note: Use
u(nMin), v(nMin), or w(nMin) only with a recursive sequence, which requires an initial value.
Selecting Graph
Styles
The icons to the left of
u(n)
,
v(n)
, and
w(n)
represent the graph style of each sequence (Chapter 3). The default in
Seq
mode is
í (dot), which shows discrete values. Dot, ç (line), and è (thick) styles are available for sequence graphing. Graph styles are ignored in
Web
format.
Selecting and
Deselecting
Sequence
Functions
The TI82 STATS graphs only the selected sequence functions.
In the
Y=
editor, a sequence function is selected when the
=
signs of both
u(n)=
and
u(nMin)=
are highlighted.
To change the selection status of a sequence function, move the cursor onto the
=
sign of the function name, and then press
Í. The status is changed for both the sequence function
u(n)
and its initial value
u(nMin)
.
6–4 Sequence Graphing
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Defining and
Editing a
Sequence
Function
Nonrecursive
Sequences
To define or edit a sequence function, follow the steps in
Chapter 3 for defining a function. The independent variable in a sequence is
n
.
In
Seq
graphing mode, you can enter the sequence variable in either of two ways.
•
Press „.
•
Press y [
CATALOG
] [
N
].
You can enter the function name from the keyboard.
•
To enter the function name
u
, press y [ u
] (above ¬).
•
To enter the function name
v
, press y [ v
] (above −).
•
To enter the function name
w
, press y [ w
] (above ®).
Generally, sequences are either nonrecursive or recursive.
Sequences are evaluated only at consecutive integer values.
n
is always a series of consecutive integers, starting at zero or any positive integer.
In a nonrecursive sequence, the
n
th term is a function of the independent variable
n
. Each term is independent of all other terms.
For example, in the nonrecursive sequence below, you can calculate
u(5)
directly, without first calculating
u(1)
or any previous term.
The sequence equation above returns the sequence
2
,
4
,
6
,
8
,
10
, . . . for
n
=
1
,
2
,
3
,
4
,
5
,
. . . .
Note: You may leave blank the initial value u(nMin) when calculating nonrecursive sequences.
Sequence Graphing 6–5
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Defining and Displaying Sequence Graphs
(continued)
Recursive
Sequences
In a recursive sequence, the
n
th term in the sequence is defined in relation to the previous term or the term that precedes the previous term, represented by
u(nN1)
and
u(nN2)
. A recursive sequence may also be defined in relation to
n
, as in
u(n)=u(nN1)+n.
For example, in the sequence below you cannot calculate
u(5)
without first calculating
u(1)
,
u(2)
,
u(3)
, and
u(4)
.
Using an initial value
u(nMin) = 1
, the sequence above returns
1
,
2
,
4
,
8
,
16
, . . .
Tip: On the TI82 STATS, you must type each character of the terms.
For example, to enter
u(nN1), press y [ u
]
£ „ ¹ À ¤.
Recursive sequences require an initial value or values, since they reference undefined terms.
•
If each term in the sequence is defined in relation to the previous term, as in
u(nN1)
, you must specify an initial value for the first term.
•
If each term in the sequence is defined in relation to the term that precedes the previous term, as in
u(nN2)
, you must specify initial values for the first two terms. Enter the initial values as a list enclosed in braces ({ }) with commas separating the values.
The value of the first term is 0 and the value of the second term is 1 for the sequence
u(n)
.
6–6 Sequence Graphing
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Setting Window
Variables
To display the window variables, press p. These variables define the viewing window. The values below are defaults for
Seq
graphing in both
Radian
and
Degree
angle modes.
nMin=1
nMax=10
PlotStart=1
PlotStep=1
Xmin=L10
Xmax=10
Xscl=1
Ymin=L10
Ymax=10
Yscl=1
Smallest
n
value to evaluate
Largest
n
value to evaluate
First term number to be plotted
Incremental
n
value (for graphing only)
Smallest
X
value to be displayed
Largest
X
value to be displayed
Spacing between the
X
tick marks
Smallest
Y
value to be displayed
Largest
Y
value to be displayed
Spacing between the
Y
tick marks
nMin
must be an integer ‚ 0.
nMax
,
PlotStart
, and
PlotStep
must be integers ‚ 1.
nMin
is the smallest
n
value to evaluate.
nMin
also is displayed in the sequence
Y=
editor.
nMax
is the largest
n
value to evaluate. Sequences are evaluated at
u(nMin)
,
u(nMin+1)
,
u(nMin+2)
, . . . ,
u(nMax)
.
PlotStart
is the first term to be plotted.
PlotStart=1
begins plotting on the first term in the sequence. If you want plotting to begin with the fifth term in a sequence, for example, set
PlotStart=5
. The first four terms are evaluated but are not plotted on the graph.
PlotStep
is the incremental
n
value for graphing only.
PlotStep
does not affect sequence evaluation; it only designates which points are plotted on the graph. If you specify
PlotStep=2
, the sequence is evaluated at each consecutive integer, but it is plotted on the graph only at every other integer.
Sequence Graphing 6–7
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Selecting Axes Combinations
Setting the Graph
Format
To display the current graph format settings, press y
[
FORMAT
]. Chapter 3 describes the format settings in detail. The other graphing modes share these format settings. The axes setting on the top line of the screen is available only in
Seq
mode.
Time Web uv vw uw
RectGC PolarGC
CoordOn CoordOff
GridOff GridOn
AxesOn AxesOff
LabelOff LabelOn
ExprOn ExprOff
Type of sequence plot (axes)
Rectangular or polar output
Cursor coordinate display on/off
Grid display off or on
Axes display on or off
Axes label display off or on
Expression display on or off
Setting Axes
Format
For sequence graphing, you can select from five axes formats.
The table below shows the values that are plotted on the xaxis and yaxis for each axes setting.
Axes Setting
Time
Web uv vw uw xaxis
n
v(n) u(n) yaxis u(n)
,
v(n)
,
w(n) u(nN1)
,
v(nN1)
,
w(nN1) u(n)
,
v(n)
,
w(n) u(n) v(n) w(n) w(n)
See pages 6.11 and 6.12 for more information on
Web
plots.
See page 6.13 for more information on phase plots (
uv
,
vw
, and
uw
axes settings).
Displaying a
Sequence Graph
To plot the selected sequence functions, press s. As a graph is plotted, the TI82 STATS updates
X
,
Y
, and
n
.
Smart Graph applies to sequence graphs (Chapter 3).
6–8 Sequence Graphing
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Exploring Sequence Graphs
FreeMoving
Cursor
TRACE
The freemoving cursor in
Seq
graphing works the same as in
Func
graphing. In
RectGC
format, moving the cursor updates the values of
X
and
Y
; if
CoordOn
format is selected,
X
and
Y
are displayed. In
PolarGC
format,
X
,
Y
,
R
, and
q
are updated; if
CoordOn
format is selected,
R
and
q
are displayed.
The axes format setting affects
TRACE
.
When
Time
,
uv
,
vw
, or
uw
axes format is selected,
TRACE moves the cursor along the sequence one
PlotStep
increment at a time. To move five plotted points at once, press y ~ or y
.
•
When you begin a trace, the trace cursor is on the first selected sequence at the term number specified by
PlotStart
, even if it is outside the viewing window.
•
Quick Zoom applies to all directions. To center the viewing window on the current cursor location after you have moved the trace cursor, press Í. The trace cursor returns to
nMin
.
In
Web
format, the trail of the cursor helps identify points with attracting and repelling behavior in the sequence. When you begin a trace, the cursor is on the xaxis at the initial value of the first selected function.
Tip: To move the cursor to a specified n during a trace, enter a value for
n, and press Í. For example, to quickly return the cursor to the beginning of the sequence, paste nMin to the n= prompt and press
Í.
Moving the Trace
Cursor to Any
Valid n Value
To move the trace cursor to any valid
n
value on the current function, enter the number. When you enter the first digit, an
n
=
prompt and the number you entered are displayed in the bottomleft corner of the screen. You can enter an expression at the
n =
prompt. The value must be valid for the current viewing window. When you have completed the entry, press Í to move the cursor.
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Exploring Sequence Graphs
(continued)
ZOOM
CALC
Evaluating u, v, and w
ZOOM
operations in
Seq
graphing work the same as in
Func
graphing. Only the
X
(
Xmin
,
Xmax
, and
Xscl
) and
Y
(
Ymin
,
Ymax
, and
Yscl
) window variables are affected.
PlotStart
,
PlotStep
,
nMin
, and
nMax
are only affected when you select
ZStandard
. The
VARS Zoom
secondary menu
ZU items
1
through
7
are the
ZOOM MEMORY
variables for
Seq
graphing.
The only
CALC
operation available in
Seq
graphing is
value
.
•
When
Time
axes format is selected,
value
displays
Y
(the
u(n)
value) for a specified
n
value.
•
When
Web
axes format is selected,
value
draws the web and displays
Y
(the
u(n)
value) for a specified
n
value.
•
When
uv
,
vw
, or
uw
axes format is selected,
value
displays
X
and
Y
according to the axes format setting. For example, for
uv
axes format,
X
represents
u(n)
and
Y
represents
v(n)
.
To enter the sequence names
u
,
v,
or
w
, press y [ u
], [ v
], or
[ w
]. You can evaluate these names in any of three ways.
•
•
•
Calculate the
n
th value in a sequence.
Calculate a list of values in a sequence.
Generate a sequence with optional; default is 1.
u(
nstart
,
nstop
[,
nstep
])
. nstep is
6–10 Sequence Graphing
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Graphing Web Plots
Graphing a Web
Plot
To select
Web
axes format, press y [
FORMAT
] ~ Í. A web plot graphs
u(n)
versus
u(nN1)
, which you can use to study longterm behavior (convergence, divergence, or oscillation) of a recursive sequence. You can see how the sequence may change behavior as its initial value changes.
Valid Functions for Web Plots
Displaying the
Graph Screen
When
Web
axes format is selected, a sequence will not graph properly or will generate an error.
•
It must be recursive with only one recursion level (
u(nN1)
but not
u(nN2)
).
•
It cannot reference
n
directly.
•
It cannot reference any defined sequence except itself.
In
Web
format, press s to display the graph screen. The
TI82 STATS:
•
Draws a y=x
reference line in
AxesOn
format.
•
Plots the selected sequences with
u(nN1)
as the independent variable.
Note: A potential convergence point occurs whenever a sequence intersects the y=x reference line. However, the sequence may or may not actually converge at that point, depending on the sequence’s initial value.
Drawing the Web
To activate the trace cursor, press r. The screen displays the sequence and the current
n
,
X
, and
Y
values (
X
represents
u(nN1)
and
Y
represents
u(n)
). Press ~ repeatedly to draw the web step by step, starting at
nMin
. In
Web
format, the trace cursor follows this course.
1. It starts on the xaxis at the initial value
u(nMin)
(when
PlotStart=1
).
2. It moves vertically (up or down) to the sequence.
3. It moves horizontally to the y=x
reference line.
4. It repeats this vertical and horizontal movement as you continue to press ~.
Sequence Graphing 6–11
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Using Web Plots to Illustrate Convergence
Example:
Convergence
1. Press o in
Seq
mode to display the sequence
Y=
editor. Make sure the graph style is set to í (dot), and then define
nMin
,
u(n)
and
u(nMin)
as shown below.
2. Press y [
FORMAT
] Í to set
Time
axes format.
3. Press p and set the variables as shown below.
nMin=1
nMax=25
Xmin=0
Xmax=25
Ymin=L10
Ymax=10
PlotStart=1
PlotStep=1
Xscl=1 Yscl=1
4. Press s to graph the sequence.
5. Press y [
FORMAT
] and select the
Web
axes setting.
6. Press p and change the variables below.
Xmin=L10 Xmax=10
7. Press s to graph the sequence.
8. Press r, and then press ~ to draw the web. The displayed cursor coordinates
n
,
X
(
u(nN1)
), and
Y
(
u(n)
) change accordingly. When you press ~, a new
n
value is displayed, and the trace cursor is on the sequence.
When you press ~ again, the
n
value remains the same, and the cursor moves to the y=x
reference line. This pattern repeats as you trace the web.
6–12 Sequence Graphing
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Graphing Phase Plots
Graphing with uv, vw, and uw
The phaseplot axes settings
uv
,
vw
, and
uw
show relationships between two sequences. To select a phaseplot axes setting, press y [
FORMAT
], press ~ until the cursor is on
uv
,
vw
, or
uw
, and then press Í.
Axes Setting uv vw uw xaxis u(n) v(n) u(n) yaxis v(n) w(n) w(n)
Example:
PredatorPrey
Model
Use the predatorprey model to determine the regional populations of a predator and its prey that would maintain population equilibrium for the two species.
This example uses the model to determine the equilibrium populations of wolves and rabbits, with initial populations of
200 rabbits (
u(nMin)
) and 50 wolves (
v(nMin)
).
These are the variables (given values are in parentheses):
R = number of rabbits
M = rabbit population growth rate without wolves
K = rabbit population death rate with wolves
W = number of wolves
G = wolf population growth rate with rabbits
D = wolf population death rate without rabbits
n
R
W
n n
= time (in months)
= R
nN1
= W
nN1
(1+MNKW
nN1
(1+GR
nN1
ND)
)
(.05)
(.001)
(.0002)
(.03)
1. Press o in
Seq
mode to display the sequence
Y=
editor.
Define the sequences and initial values for R shown below. Enter the sequence R sequence W
n
as
v(n)
.
n n
and W
n
as
as
u(n)
and enter the
Sequence Graphing 6–13
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Graphing Phase Plots
(continued)
Example:
PredatorPrey
Model
(continued)
2. Press y [
FORMAT
] Í to select
Time
axes format.
3. Press p and set the variables as shown below.
nMin=0 Xmin=0 Ymin=0
nMax=400
PlotStart=1
PlotStep=1
Xmax=400
Xscl=100
Ymax=300
Yscl=100
4. Press s to graph the sequence.
5. Press r ~ to individually trace the number of rabbits
(
u(n)
) and wolves (
v(n)
) over time (
n
).
Tip: Press a number, and then press
Í to jump to a specific n value (month) while in
TRACE.
6. Press y [
FORMAT
] ~ ~ Í to select
uv
axes format.
7. Press p and change these variables as shown below.
Xmin=84 Ymin=25
Xmax=237
Xscl=50
Ymax=75
Yscl=10
8. Press r. Trace both the number of rabbits (
X
) and the number of wolves (
Y
) through 400 generations.
Note: When you press r, the equation for u is displayed in the topleft corner. Press
} or † to see the equation for v.
6–14 Sequence Graphing
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Comparing TI82 STATS and TI82 Sequence Variables
Sequences and
Window
Variables
Refer to the table if you are familiar with the TI82. It shows
TI82 STATS sequences and sequence window variables, as well as their TI82 counterparts.
TI.82
TI82 STATS
In the
Y=
editor:
u(n) u(nMin) v(n) v(nMin) w(n) w(nMin)
In the window editor:
nMin
nMax
PlotStart
PlotStep
Un
UnStart
(window variable)
Vn
VnStart
(window variable)
not available not available
nStart
nMax
nMin
not available
Sequence Graphing 6–15
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Keystroke Differences Between TI82 STATS and TI82
Sequence
Keystroke
Changes
Refer to the table if you are familiar with the TI82. It compares
TI82 STATS sequencename syntax and variable syntax with
TI.82 sequencename syntax and variable syntax.
On TI.82, press: TI82 STATS /
TI.82
n / n u(n) / Un v(n) / Vn w(n) u(nN1) / UnN1 v(nN1) / VnN1 w(nN1)
On TI82 STATS, press:
„ y [ u
]
£ „ ¤ y [ v
]
£ „ ¤ y [ w
]
£ „ ¤ y [ u
]
£ „ ¹ À ¤ y [ v
]
£ „ ¹ À ¤ y [ w
]
£ „ ¹ À ¤ y [ y [ y [
n
]
Y.VARS
Y.VARS
not available y [
U
n
y [
V
n
N
1
]
N
1
] not available
] ¶ À
] ¶ Á
6–16 Sequence Graphing
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Contents
7
Tables
Getting Started: Roots of a Function
..........................................................
Setting Up the Table
.............................................................................................
Defining the Dependent Variables
...............................................................
Displaying the Table
.............................................................................................
4
5
2
3
Tables 7–1
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Getting Started: Roots of a Function
Getting Started is a fastpaced introduction. Read the chapter for details.
Evaluate the function Y = X 3
N 2X at each integer between L10 and 10. How many sign changes occur, and at what
X
values?
1. Press z † † † Í to set
Func
graphing mode.
2. Press o. Press „
3
to select
3
.
Then press ¹
2
„ to enter the function
Y
1
=X
3
N2X
.
3. Press y [
TBLSET
] to display the
TABLE
SETUP
screen. Press Ì
10
Í to set
TblStart=L10
. Press
1
Í to set
@Tbl=1
.
Press Í to select
Indpnt: Auto
(automatically generated independent values).
Press † Í to select
Depend: Auto
(automatically generated dependent values).
4. Press y [
TABLE
] to display the table screen.
5. Press † until you see the sign changes in the value of
Y
1
. How many sign changes occur, and at what
X
values?
7–2 Tables
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Setting Up the Table
TABLE SETUP
Screen
To display the
TABLE SETUP
screen, press y [
TBLSET
].
TblStart, @Tbl
TblStart
(table start) defines the initial value for the independent variable.
TblStart
applies only when the independent variable is generated automatically (when
Indpnt: Auto
is selected).
@Tbl
(table step) defines the increment for the independent variable.
Note: In Seq mode, both TblStart and @Tbl must be integers.
Indpnt: Auto,
Indpnt: Ask,
Depend: Auto,
Depend: Ask
Setting Up the
Table from the
Home Screen or a Program
Selections
Indpnt: Auto
Depend: Auto
Indpnt: Ask
Depend: Auto
Indpnt: Auto
Depend: Ask
Indpnt: Ask
Depend: Ask
Table Characteristics
Values are displayed automatically in both the independentvariable column and in all dependentvariable columns.
The table is empty; when you enter a value for the independent variable, all corresponding dependentvariable values are calculated and displayed automatically.
Values are displayed automatically for the independent variable; to generate a value for a dependent variable, move the cursor to that cell and press Í.
The table is empty; enter values for the independent variable; to generate a value for a dependent variable, move the cursor to that cell and press Í.
To store a value to
TblStart
,
@Tbl
, or
TblZnput
from the home screen or a program, select the variable name from the
VARS
TABLE
secondary menu.
TblZnput
is a list of independentvariable values in the current table.
When you press y [
TBLSET
] in the program editor, you can select
IndpntAuto
,
IndpntAsk
,
DependAuto
, and
DependAsk
.
Tables 7–3
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Defining the Dependent Variables
Defining
Dependent
Variables from the Y= Editor
In the
Y=
editor, enter the functions that define the dependent variables. Only functions that are selected in the
Y=
editor are displayed in the table. The current graphing mode is used. In
Par
mode, you must define both components of each parametric equation (Chapter 4).
Editing
Dependent
Variables from the Table Editor
To edit a selected
Y=
function from the table editor, follow these steps.
1. Press y [
TABLE
] to display the table, then press ~ or  to move the cursor to a dependentvariable column.
2. Press } until the cursor is on the function name at the top of the column. The function is displayed on the bottom line.
3. Press Í. The cursor moves to the bottom line. Edit the function.
4. Press Í or †. The new values are calculated. The table and the
Y=
function are updated automatically.
Note: You also can use this feature to view the function that defines a dependent variable without having to leave the table.
7–4 Tables
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Displaying the Table
The Table
To display the table, press y [
TABLE
].
Current cell
Independentvariable values in the first column
Dependentvariable values in the second and third columns
Current cell’s full value
Note: The table abbreviates the values, if necessary.
Independent and
Dependent
Variables
The current graphing mode determines which independent and dependent variables are displayed in the table (Chapter 1). In the table above, for example, the independent variable
X
and the dependent variables
Y
1
and
Y
2
are displayed because
Func
graphing mode is set.
Graphing Mode
Func
Par
Pol
Seq
(function)
(parametric)
(polar)
(sequence)
q n
Independent
Variable
X
T
Dependent
Variable
Y
1
Y
0
through
Y
9
, and
X
1T
X
6T
/
Y
1T
through
/
Y
6T r
1
through
r
6 u(n)
,
v(n)
, and
w(n)
Clearing the
Table from the
Home Screen or a Program
From the home screen, select the
ClrTable
instruction from the
CATALOG
. To clear the table, press Í.
From a program, select
9:ClrTable
from the
PRGM I/O
menu or from the
CATALOG
. The table is cleared upon execution. If
IndpntAsk
is selected, all independent and dependent variable values on the table are cleared. If
DependAsk
is selected, all dependent variable values on the table are cleared.
Tables 7–5
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Displaying the Table
(continued)
Scrolling
Independent
Variable Values
If
Indpnt: Auto
is selected, you can press } and † in the independentvariable column to display more values. As you scroll the column, the corresponding dependentvariable values also are displayed. All dependentvariable values may not be displayed if
Depend: Ask
is selected.
Note: You can scroll back from the value entered for
TblStart. As you scroll, TblStart is updated automatically to the value shown on the top line of the table. In the example above,
TblStart=0 and
@Tbl=1 generates and displays values of X=0, . . . , 6; but you can press
} to scroll back and display the table for X=M1, . . ., 5.
Displaying Other
Dependent
Variables
If you have defined more than two dependent variables, the first two selected
Y=
functions are displayed initially. Press ~ or  to display dependent variables defined by other selected
Y= functions. The independent variable always remains in the left column, except during a trace with
Par
graphing mode and
G.T
splitscreen mode set.
Tip: To simultaneously display on the table two dependent variables that are not defined as consecutive Y= functions, go to the Y= editor and deselect the Y= functions between the two you want to display.
For example, to simultaneously display
Y
4
and
Y
7
on the table, go to the Y= editor and deselect
Y
5
and
Y
6
.
7–6 Tables
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Contents
8
Draw
Instructions
Getting Started: Drawing a Tangent Line
...............................................
Using the DRAW Menu
......................................................................................
Clearing Drawings
.................................................................................................
Drawing Line Segments
.....................................................................................
Drawing Horizontal and Vertical Lines
...................................................
Drawing Tangent Lines
......................................................................................
Drawing Functions and Inverses
...................................................................
9
Shading Areas on a Graph
................................................................................
10
6
8
4
5
2
3
Drawing Circles
.......................................................................................................
11
Placing Text on a Graph
.....................................................................................
12
Using Pen to Draw on a Graph
......................................................................
13
Drawing Points on a Graph
..............................................................................
14
Drawing Pixels
.........................................................................................................
16
Storing Graph Pictures (
Pic s)
.........................................................................
17
Recalling Graph Pictures (
Pic s)
....................................................................
18
Storing Graph Databases (
GDB s)
.................................................................
19
Recalling Graph Databases (
GDB s)
............................................................
20
DRAW
Instructions 8–1
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Getting Started: Drawing a Tangent Line
Getting Started is a fastpaced introduction. Read the chapter for details.
Suppose you want to find the equation of the tangent line at X = ‡2/2 for the function
Y = sinX.
Before you begin, select
Radian
and
Func
mode from the mode screen, if necessary.
1. Press o to display the
Y= editor. Press ˜
„ ¤ to store
sin(X)
in
Y
1
.
2. Press q
7
to select
7:ZTrig
, which graphs the equation in the Zoom Trig window.
3. Press y [
DRAW
]
5
to select
5:Tangent(
. The tangent instruction is initiated.
4. Press y [
‡
]
2
¤ ¥
2
.
5. Press Í. The tangent line is drawn; the
X
value and the tangentline equation are displayed on the graph.
8–2
DRAW
Instructions
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Using the DRAW Menu
DRAW Menu
Before Drawing on a Graph
Drawing on a
Graph
To display the
DRAW
menu, press y [
DRAW
]. The
TI82 STATS interpretation of these instructions depends on whether you accessed the menu from the home screen or the program editor or directly from a graph.
DRA
W
POINTS STO
1: ClrDraw
2: Line(
3: Horizontal
4: Vertical
5: Tangent(
6: DrawF
7: Shade(
8: DrawInv
9: Circle(
0: Text(
A: Pen
Clears all drawn elements.
Draws a line segment between 2 points.
Draws a horizontal line.
Draws a vertical line.
Draws a line segment tangent to a function.
Draws a function.
Shades an area between two functions.
Draws the inverse of a function.
Draws a circle.
Draws text on a graph screen.
Activates the freeform drawing tool.
The
DRAW
instructions draw on top of graphs. Therefore, before you use the
DRAW
instructions, consider whether you want to perform one or more of the following actions.
•
Change the mode settings on the mode screen.
•
Change the format settings on the format screen.
•
Enter or edit functions in the
Y=
editor.
•
Select or deselect functions in the
Y=
editor.
•
Change the window variable values.
•
Turn stat plots on or off.
•
Clear existing drawings with
ClrDraw
(page 8.4).
Note: If you draw on a graph and then perform any of the actions listed above, the graph is replotted without the drawings when you display the graph again.
You can use any
DRAW
menu instructions except
DrawInv
to draw on
Func
,
Par
,
Pol
, and
Seq
graphs.
DrawInv
is valid only in
Func
graphing. The coordinates for all
DRAW
instructions are the display’s xcoordinate and ycoordinate values.
You can use most
DRAW
menu and
DRAW POINTS
menu instructions to draw directly on a graph, using the cursor to identify the coordinates. You also can execute these instructions from the home screen or from within a program. If a graph is not displayed when you select a
DRAW
menu instruction, the home screen is displayed.
DRAW
Instructions 8–3
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Clearing Drawings
Clearing
Drawings When a Graph Is
Displayed
All points, lines, and shading drawn on a graph with
DRAW instructions are temporary.
To clear drawings from the currently displayed graph, select
1:ClrDraw
from the
DRAW
menu. The current graph is replotted and displayed with no drawn elements.
Clearing
Drawings from the Home Screen or a Program
To clear drawings on a graph from the home screen or a program, begin on a blank line on the home screen or in the program editor. Select
1:ClrDraw
from the
DRAW
menu. The instruction is copied to the cursor location. Press Í.
When
ClrDraw
is executed, it clears all drawings from the current graph and displays the message
Done
. When you display the graph again, all drawn points, lines, circles, and shaded areas will be gone.
Note: Before you clear drawings, you can store them with
StorePic
(page 8.17).
8–4
DRAW
Instructions
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Drawing Line Segments
Drawing a Line
Segment Directly on a Graph
To draw a line segment when a graph is displayed, follow these steps.
1. Select
2:Line(
from the
DRAW
menu.
2. Place the cursor on the point where you want the line segment to begin, and then press Í.
3. Move the cursor to the point where you want the line segment to end. The line is displayed as you move the cursor. Press Í.
To continue drawing line segments, repeat steps 2 and 3. To cancel
Line(
, press ‘.
Drawing a Line
Segment from the Home Screen or a Program
Line(
also draws a line segment between the coordinates (X1,Y1) and (X2,Y2). The values may be entered as expressions.
Line(
X1
,
Y1
,
X2
,
Y2
)
To erase a line segment, enter
Line(
X1
,
Y1
,
X2
,
Y2
,0)
DRAW
Instructions 8–5
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Drawing Horizontal and Vertical Lines
Drawing a Line
Directly on a
Graph
To draw a horizontal or vertical line when a graph is displayed, follow these steps.
1. Select
3:Horizontal
or
4:Vertical
from the
DRAW
menu. A line is displayed that moves as you move the cursor.
2. Place the cursor on the ycoordinate (for horizontal lines) or xcoordinate (for vertical lines) through which you want the drawn line to pass.
3. Press Í to draw the line on the graph.
To continue drawing lines, repeat steps 2 and 3.
To cancel
Horizontal
or
Vertical
, press ‘.
8–6
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Drawing a Line from the Home
Screen or a
Program
Horizontal
(horizontal line) draws a horizontal line at
Y
=y. y can be an expression but not a list.
Horizontal
y
Vertical
(vertical line) draws a vertical line at
X
=x. x can be an expression but not a list.
Vertical
x
To instruct the TI82 STATS to draw more than one horizontal or vertical line, separate each instruction with a colon (
:
).
DRAW
Instructions 8–7
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Drawing Tangent Lines
Drawing a Tangent Line
Directly on a Graph
To draw a tangent line when a graph is displayed, follow these steps.
1. Select
5:Tangent(
from the
DRAW
menu.
2. Press † and } to move the cursor to the function for which you want to draw the tangent line. The current graph’s
Y= function is displayed in the topleft corner, if
ExprOn
is selected.
3. Press ~ and  or enter a number to select the point on the function at which you want to draw the tangent line.
4. Press Í. In
Func
mode, the
X
value at which the tangent line was drawn is displayed on the bottom of the screen, along with the equation of the tangent line. In all other modes, the
dy/dx
value is displayed.
Drawing a Tangent Line from the Home
Screen or a Program
Tip: Change the fixed decimal setting on the mode screen if you want to see fewer digits displayed for
X and the equation for Y.
Tangent(
(tangent line) draws a line tangent to expression in terms of
X
, such as
Y
1
or
X
2
, at point
X
=value.
X
can be an expression. expression is interpreted as being in
Func
mode.
Tangent(
expression
,
value
)
8–8
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Drawing Functions and Inverses
Drawing a
Function
DrawF
(draw function) draws expression as a function in terms of
X
on the current graph. When you select
6:DrawF
from the
DRAW
menu, the TI82 STATS returns to the home screen or the program editor.
DrawF
is not interactive.
DrawF
expression
Drawing an
Inverse of a
Function
Note: You cannot use a list in expression to draw a family of curves.
DrawInv
(draw inverse) draws the inverse of expression by plotting
X
values on the yaxis and
Y
values on the xaxis. When you select
8:DrawInv
from the
DRAW
menu, the TI82 STATS returns to the home screen or the program editor.
DrawInv
is not interactive.
DrawInv
works in
Func
mode only.
DrawInv
expression
Note: You cannot use a list in expression to draw a family of curves.
DRAW
Instructions 8–9
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Shading Areas on a Graph
Shading a Graph
To shade an area on a graph, select
7:Shade(
from the
DRAW menu. The instruction is pasted to the home screen or to the program editor.
Shade(
draws lowerfunc and upperfunc in terms of
X
on the current graph and shades the area that is specifically above
lowerfunc and below upperfunc. Only the areas where lowerfunc
< upperfunc are shaded.
Xleft and Xright, if included, specify left and right boundaries for the shading. Xleft and Xright must be numbers between
Xmin
and
Xmax
, which are the defaults.
pattern specifies one of four shading patterns.
pattern=
1
pattern=
2
pattern=
3
pattern=
4
vertical (default) horizontal negative—slope 45¡ positive—slope 45¡
patres specifies one of eight shading resolutions.
patres=
1
patres=
2
patres=
3
patres=
4
patres=
5
patres=
6
patres=
7
patres=
8
shades every pixel (default) shades every second pixel shades every third pixel shades every fourth pixel shades every fifth pixel shades every sixth pixel shades every seventh pixel shades every eighth pixel
Shade(
lowerfunc
,
upperfunc[
,
Xleft
,
Xright
,
pattern
,
patres]
)
8–10
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Instructions
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Drawing Circles
Drawing a Circle
Directly on a
Graph
To draw a circle directly on a displayed graph using the cursor, follow these steps.
1. Select
9:Circle(
from the
DRAW
menu.
2. Place the cursor at the center of the circle you want to draw.
Press Í.
3. Move the cursor to a point on the circumference. Press
Í to draw the circle on the graph.
Note: This circle is displayed as circular, regardless of the window variable values, because you drew it directly on the display. When you use the
Circle( instruction from the home screen or a program, the current window variables may distort the shape.
To continue drawing circles, repeat steps 2 and 3. To cancel
Circle(
, press ‘.
Drawing a Circle from the Home
Screen or a
Program
Circle(
draws a circle with center (X,Y ) and radius. These values can be expressions.
Circle(
X
,
Y
,
radius
)
Tip: When you use
Circle( on the home screen or from a program, the current window values may distort the drawn circle. Use
ZSquare
(Chapter 3) before drawing the circle to adjust the window variables and make the circle circular.
DRAW
Instructions 8–11
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Placing Text on a Graph
Placing Text
Directly on a
Graph
To place text on a graph when the graph is displayed, follow these steps.
1. Select
0:Text(
from the
DRAW
menu.
2. Place the cursor where you want the text to begin.
3. Enter the characters. Press ƒ or y [
A.LOCK
] to enter letters and q. You may enter TI82 STATS functions, variables, and instructions. The font is proportional, so the exact number of characters you can place on the graph varies. As you type, the characters are placed on top of the graph.
To cancel
Text(
, press ‘.
Placing Text on a
Graph from the
Home Screen or a Program
Text(
places on the current graph the characters comprising
value, which can include TI82 STATS functions and instructions. The topleft corner of the first character is at pixel
(row,column), where row is an integer between
0 and 57 and column is an integer between 0 and 94. Both row and column can be expressions.
Text(
row
,
column
,
value
,
value . . .
)
value can be text enclosed in quotation marks (
"
), or it can be an expression. The TI82 STATS will evaluate an expression and display the result with up to 10 characters.
Split Screen
On a
Horiz
split screen, the maximum value for row is 25. On a
G.T
split screen, the maximum value for row is 45, and the maximum value for column is 46.
8–12
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Using Pen to Draw on a Graph
Using Pen to
Draw on a Graph
Pen
draws directly on a graph only. You cannot execute
Pen
from the home screen or a program.
To draw on a displayed graph, follow these steps.
1. Select
A:Pen
from the
DRAW
menu.
2. Place the cursor on the point where you want to begin drawing. Press Í to turn on the pen.
3. Move the cursor. As you move the cursor, you draw on the graph, shading one pixel at a time.
4. Press Í to turn off the pen.
For example,
Pen
was used to create the arrow pointing to the local minimum of the selected function.
To continue drawing on the graph, move the cursor to a new position where you want to begin drawing again, and then repeat steps 2, 3, and 4. To cancel
Pen
, press ‘.
DRAW
Instructions 8–13
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Drawing Points on a Graph
DRAW POINTS
Menu
To display the
DRAW POINTS
menu, press y [
DRAW
] ~. The
TI82 STATS interpretation of these instructions depends on whether you accessed this menu from the home screen or the program editor or directly from a graph.
DRAW POINTS STO
1: PtOn(
2: PtOff(
3: PtChange(
4: PxlOn(
5: PxlOff(
6: PxlChange(
7: pxlTest(
Turns on a point.
Turns off a point.
Toggles a point on or off.
Turns on a pixel.
Turns off a pixel.
Toggles a pixel on or off.
Returns 1 if pixel on, 0 if pixel off.
Drawing Points
Directly on a
Graph with
Pt
.
On(
To draw a point on a graph, follow these steps.
1. Select
1:Pt.On(
from the
DRAW POINTS
menu.
2. Move the cursor to the position where you want to draw the point.
3. Press Í to draw the point.
To continue drawing points, repeat steps 2 and 3. To cancel
Pt.On(
, press ‘.
8–14
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Erasing Points with Pt.Off(
Changing Points with Pt.Change(
To change (toggle on or off) a point on a graph, follow these steps.
1. Select
3:Pt.Change(
(point change) from the
DRAW POINTS menu.
2. Move the cursor to the point you want to change.
3. Press Í to change the point’s on/off status.
To continue changing points, repeat steps 2 and 3. To cancel
Pt.Change(
, press ‘.
Drawing Points from the Home
Screen or a
Program
To erase (turn off) a drawn point on a graph, follow these steps.
1. Select
2:Pt.Off(
(point off) from the
DRAW POINTS
menu.
2. Move the cursor to the point you want to erase.
3. Press Í to erase the point.
To continue erasing points, repeat steps 2 and 3. To cancel
Pt.Off(
, press ‘.
Pt.On(
(point on) turns on the point at (
X
=x,
Y
=y).
Pt.Off(
turns the point off.
Pt.Change(
toggles the point on or off. mark is optional; it determines the point’s appearance; specify
1
,
2
, or
3
, where:
1
=
¦
(dot; default)
2
=
›
(box)
3
=
+
(cross)
Pt.On(
x
,
y[
,
mark]
)
Pt.Off(
x
,
y[
,
mark]
)
Pt.Change(
x
,
y
)
Note: If you specified mark to turn on a point with Pt.On(, you must specify mark when you turn off the point with
Pt.Off(. Pt.Change( does not have the mark option.
DRAW
Instructions 8–15
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Drawing Pixels
TI82 STATS
Pixels
A pixel is a square dot on the TI82 STATS display. The
Pxl.
(pixel) instructions let you turn on, turn off, or reverse a pixel
(dot) on the graph using the cursor. When you select a pixel instruction from the
DRAW POINTS
menu, the TI82 STATS returns to the home screen or the program editor. The pixel instructions are not interactive.
Turning On and
Off Pixels with
Pxl.On( and
Pxl.Off(
Pxl.On(
(pixel on) turns on the pixel at (row,column), where
row is an integer between 0 and 62 and column is an integer between 0 and 94.
Pxl.Off(
turns the pixel off.
Pxl.Change(
toggles the pixel on and off.
Pxl.On(
row
,
column
)
Pxl.Off(
row
,
column
)
Pxl.Change(
row
,
column
)
Using pxl.Test(
Split Screen pxl.Test(
(pixel test) returns 1 if the pixel at (row,column) is turned on or 0 if the pixel is turned off on the current graph. row must be an integer between 0 and 62. column must be an integer between 0 and 94.
pxl.Test(
row
,
column
)
On a
Horiz
split screen, the maximum value for row is 30 for
Pxl.On(
,
Pxl.Off(
,
Pxl.Change(
, and
pxl.Test(
.
On a
G.T
split screen, the maximum value for row is 50 and the maximum value for column is 46 for
Pxl.On(
,
Pxl.Off(
,
Pxl.Change(
, and
pxl.Test(
.
8–16
DRAW
Instructions
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Storing Graph Pictures (Pics)
DRAW STO Menu
To display the
DRAW STO
menu, press y [
DRAW
] . When you select an instruction from the
DRAW STO menu, the
TI82 STATS returns to the home screen or the program editor.
The picture and graph database instructions are not interactive.
DRAW POINTS STO
1: StorePic
2: RecallPic
3: StoreGDB
4: RecallGDB
Stores the current picture.
Recalls a saved picture.
Stores the current graph database.
Recalls a saved graph database.
Storing a Graph
Picture
You can store up to 10 graph pictures, each of which is an image of the current graph display, in picture variables
Pic1
through
Pic9
, or
Pic0
. Later, you can superimpose the stored picture onto a displayed graph from the home screen or a program.
A picture includes drawn elements, plotted functions, axes, and tick marks. The picture does not include axes labels, lower and upper bound indicators, prompts, or cursor coordinates. Any parts of the display hidden by these items are stored with the picture.
To store a graph picture, follow these steps.
1. Select
1:StorePic
from the
DRAW STO
menu.
StorePic
is pasted to the current cursor location.
2. Enter the number (from
1
to
9
, or
0
) of the picture variable to which you want to store the picture. For example, if you enter
3
, the TI82 STATS will store the picture to
Pic3
.
Note: You also can select a variable from the PICTURE secondary menu (
4). The variable is pasted next to
StorePic.
3. Press Í to display the current graph and store the picture.
DRAW
Instructions 8–17
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Recalling Graph Pictures (Pics)
Recalling a
Graph Picture
To recall a graph picture, follow these steps.
1. Select
2:RecallPic
from the
DRAW STO
menu.
RecallPic
is pasted to the current cursor location.
2. Enter the number (from
1
to
9
, or
0
) of the picture variable from which you want to recall a picture. For example, if you enter
3
, the TI82 STATS will recall the picture stored to
Pic3
.
Note: You also can select a variable from the
PICTURE secondary menu (
4). The variable is pasted next to
RecallPic.
3. Press Í to display the current graph with the picture superimposed on it.
Note: Pictures are drawings. You cannot trace a curve that is part of a picture.
Deleting a Graph
Picture
To delete graph pictures from memory, use the
MEMORY DELETE FROM
menu (Chapter 18).
8–18
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Instructions
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Storing Graph Databases (GDBs)
What Is a Graph
Database?
A graph database (
GDB
) contains the set of elements that defines a particular graph. You can recreate the graph from these elements. You can store up to 10
GDB s in variables
GDB1
through
GDB9
, or
GDB0
and recall them to recreate graphs.
A
GDB
stores five elements of a graph.
•
Graphing mode
•
Window variables
•
Format settings
•
All functions in the
Y=
editor and the selection status of each
•
Graph style for each
Y= function
GDB s do not contain drawn items or stat plot definitions.
Storing a Graph
Database
To store a graph database, follow these steps.
1. Select
3:StoreGDB
from the
DRAW STO
menu.
StoreGDB
is pasted to the current cursor location.
2. Enter the number (from
1
to
9
, or
0
) of the
GDB
variable to which you want to store the graph database. For example, if you enter
7
, the TI82 STATS will store the
GDB
to
GDB7
.
Note: You also can select a variable from the
GDB secondary menu (
3). The variable is pasted next to StoreGDB.
3. Press Í to store the current database to the specified
GDB
variable.
DRAW
Instructions 8–19
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Recalling Graph Databases (GDBs)
Recalling a
Graph Database
CAUTION: When you recall a
GDB
, it replaces all existing
Y= functions. Consider storing the current
Y=
functions to another database before recalling a stored
GDB
.
To recall a graph database, follow these steps.
1. Select
4:RecallGDB
from the
DRAW STO
menu.
RecallGDB
is pasted to the current cursor location.
2. Enter the number (from
1
to
9
, or
0
) of the
GDB
variable from which you want to recall a
GDB
. For example, if you enter
7
, the TI82 STATS will recall the
GDB
stored to
GDB7
.
Note: You also can select a variable from the
GDB secondary menu (
3). The variable is pasted next to RecallGDB.
3. Press Í to replace the current
GDB
with the recalled
GDB
. The new graph is not plotted. The TI82 STATS changes the graphing mode automatically, if necessary.
Deleting a Graph
Database
To delete a
GDB
from memory, use the
MEMORY DELETE
FROM
menu (Chapter 18).
8–20
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Instructions
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Contents
9
Split
Screen
Getting Started: Exploring the Unit Circle
.............................................
Using Split Screen
..................................................................................................
Horiz
(Horizontal) Split Screen
.....................................................................
G.T
(GraphTable) Split Screen
....................................................................
TI82 STATS Pixels in
Horiz
and
G.T
Mode
......................................
4
5
2
3
6
Split Screen 9–1
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Getting Started: Exploring the Unit Circle
Getting Started is a fastpaced introduction. Read the chapter for details.
Use
G.T
(graphtable) splitscreen mode to explore the unit circle and its relationship to the numeric values for the commonly used trigonometric angles of 0
°
, 30
°
, 45
°
,
60
°
, 90
°
, and so on.
1. Press z to display the mode screen. Press
† † ~ Í to select
Degree
mode. Press
† ~ Í to select
Par
(parametric) graphing mode.
Press † † † † ~ ~ Í to select
G.T
(graphtable) splitscreen mode.
2. Press y [
FORMAT
] to display the format screen. Press † † † † † ~ Í to select
ExprOff
.
3. Press o to display the
Y= editor for
Par
graphing mode. Press ™ „ ¤ Í to store
cos(T)
to
X
1T
. Press ˜ „ ¤
Í to store
sin(T)
to
Y
1T
.
4. Press p to display the window editor.
Enter these values for the window variables.
Tmin=0 Xmin=L2.3
Tmax=360 Xmax=2.3
Tstep=15 Xscl=1
Ymin=L2.5
Ymax=2.5
Yscl=1
5. Press r. On the left, the unit circle is graphed parametrically in
Degree
mode and the trace cursor is activated. When
T=0
(from the graph trace coordinates), you can see from the table on the right that the value of
X
1T
(
cos(T)
) is
1
and
Y
1T
(
sin(T)
) is
0
. Press ~ to move the cursor to the next 15
° angle increment. As you trace around the circle in steps of 15
°
, an approximation of the standard value for each angle is highlighted in the table.
9–2 Split Screen
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Using Split Screen
Setting a Split
Screen Mode
To set a splitscreen mode, press z, and then move the cursor to the bottom line of the mode screen.
•
Select
Horiz
(horizontal) to display the graph screen and another screen split horizontally.
•
Select
G.T
(graphtable) to display the graph screen and table screen split vertically.
$ $
The split screen is activated when you press any key that applies to either half of the split screen.
Some screens are never displayed as split screens. For example, if you press z in
Horiz
or
G.T
mode, the mode screen is displayed as a full screen. If you then press a key that displays either half of a split screen, such as r, the split screen returns.
When you press a key or key combination in either
Horiz
or
G.T
mode, the cursor is placed in the half of the display for which that key applies. For example, if you press r, the cursor is placed in the half in which the graph is displayed. If you press y [
TABLE
], the cursor is placed in the half in which the table is displayed.
The TI82 STATS will remain in splitscreen mode until you change back to
Full
screen mode.
Split Screen 9–3
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Horiz (Horizontal) Split Screen
Horiz Mode
In
Horiz
(horizontal) splitscreen mode, a horizontal line splits the screen into top and bottom halves.
The top half displays the graph.
The bottom half displays any of these editors.
•
Home screen (four lines)
•
Y=
editor (four lines)
•
Stat list editor (two rows)
•
Window editor (three settings)
•
Table editor (two rows)
Moving from Half to Half in Horiz
Mode
To use the top half of the split screen:
•
Press s or r.
•
Select a
ZOOM
or
CALC
operation.
To use the bottom half of the split screen:
•
Press any key or key combination that displays the home screen.
•
Press o (
Y=
editor).
•
Press … Í (stat list editor).
•
Press p (window editor).
•
Press y [
TABLE
] (table editor).
Full Screens in
Horiz Mode
All other screens are displayed as full screens in
Horiz
splitscreen mode.
To return to the
Horiz
split screen from a full screen when in
Horiz
mode, press any key or key combination that displays the graph, home screen,
Y=
editor, stat list editor, window editor, or table editor.
9–4 Split Screen
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G.T (GraphTable) Split Screen
G.T Mode
In
G.T
(graphtable) splitscreen mode, a vertical line splits the screen into left and right halves.
The left half displays the graph.
The right half displays the table.
Moving from Half to Half in G.T
Mode
To use the left half of the split screen:
•
Press s or r.
•
Select a
ZOOM
or
CALC
operation.
To use the right half of the split screen, press y [
TABLE
].
Using
r
G.T Mode
As you move the trace cursor along a graph in the split screen’s left half in
G.T
mode, the table on the right half automatically scrolls to match the current cursor values.
Full Screens in
G.T Mode
Note: When you trace in Par graphing mode, both components of an equation (
Xn
T
and
Yn
T
) are displayed in the two columns of the table.
As you trace, the current value of the independent variable T is displayed on the graph.
All screens other than the graph and the table are displayed as full screens in
G.T
splitscreen mode.
To return to the
G.T
split screen from a full screen when in
G.T
mode, press any key or key combination that displays the graph or the table.
Split Screen 9–5
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TI82 STATS Pixels in Horiz and G.T Modes
TI82 STATS
Pixels in Horiz and G.T Modes
DRAW POINTS
Menu Pixel
Instructions
Note: Each set of numbers in parentheses above represents the row and column of a corner pixel, which is turned on.
For
Pxl.On(
,
Pxl.Off(
,
Pxl.Change(
, and
pxl.Test(
:
•
In
Horiz
mode, row must be {30; column must be {94.
•
In
G.T
mode, row must be {50; column must be {46.
Pxl.On(
row
,
column
)
DRAW Menu
Text( Instruction
For the
Text(
instruction:
•
In
Horiz
mode, row must be {25; column must be {94.
•
In
G.T
mode, row must be {45; column must be {46.
Text(
row
,
column
,"
text
")
PRGM I/O Menu
Output(
Instruction
For the
Output(
instruction:
•
In
Horiz
mode, row must be {4; column must be {16.
•
In
G.T
mode, row must be {8; column must be {16.
Output(
row
,
column
,"
text
")
Setting a
SplitScreen
Mode from the
Home Screen or a Program
To set
Horiz
or
G.T
from a program, follow these steps.
1. Press z while the cursor is on a blank line in the program editor.
2. Select
Horiz
or
G.T
.
The instruction is pasted to the cursor location. The mode is set when the instruction is encountered during program execution.
It remains in effect after execution.
Note: You also can paste
Horiz or G.T to the home screen or program editor from the
CATALOG (Chapter 15).
9–6 Split Screen
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10
Matrices
Contents
Getting Started: Systems of Linear Equations
.....................................
Defining a Matrix
...................................................................................................
Viewing and Editing Matrix Elements
......................................................
Using Matrices with Expressions
.................................................................
Displaying and Copying Matrices
................................................................
Using Math Functions with Matrices
.........................................................
Using the
MATRX MATH
Operations
.......................................................
12
8
9
4
7
2
2
Matrices 10–1
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Getting Started: Systems of Linear Equations
Getting Started is a fastpaced introduction. Read the chapter for details.
Find the solution of X + 2Y + 3Z = 3 and 2X + 3Y + 4Z = 3. On the TI82 STATS, you can solve a system of linear equations by entering the coefficients as elements in a matrix, and then using
rref(
to obtain the reduced rowechelon form.
1. Press . Press ~ ~ to display the
MATRX EDIT
menu. Press
1
to select
1: [A]
¸
2. Press
2
Í
4
Í to define a 2×4 matrix.
The rectangular cursor indicates the current element. Ellipses (
...
) indicate additional columns beyond the screen.
3. Press
1
Í to enter the first element. The rectangular cursor moves to the second column of the first row.
4. Press
2
Í
3
Í
3
Í to complete the first row for X + 2Y + 3Z = 3.
5. Press
2
Í
3
Í
4
Í
3
Í to enter the second row for 2X + 3Y + 4Z = 3.
6. Press y [
QUIT
] to return to the home screen.
If necessary, press ‘ to clear the home screen. Press ~ to display the
MATRX
MATH
menu. Press } to wrap to the end of the menu. Select
B:rref(
to copy
rref(
to the home screen.
7. Press
1
to select
1: [A]
from the
MATRX NAMES
menu. Press ¤ Í. The reduced rowechelon form of the matrix is displayed and stored in
Ans
.
1X N 1Z = L3 so X = L3 + Z
1Y + 2Z = 3 so Y = 3 N 2Z
10–2 Matrices
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Defining a Matrix
What Is a Matrix?
A matrix is a twodimensional array. You can display, define, or edit a matrix in the matrix editor. The TI82 STATS has 10 matrix variables,
[A]
through
[J]
. You can define a matrix directly in an expression. A matrix, depending on available memory, may have up to 99 rows or columns. You can store only real numbers in TI82 STATS matrices.
Selecting a
Matrix
Before you can define or display a matrix in the editor, you first must select the matrix name. To do so, follow these steps.
1. Press  to display the
MATRX EDIT
menu. The dimensions of any previously defined matrices are displayed.
2. Select the matrix you want to define. The
MATRX EDIT screen is displayed.
Accepting or
Changing Matrix
Dimensions
The dimensions of the matrix (row × column) are displayed on the top line. The dimensions of a new matrix are
1 ×1
. You must accept or change the dimensions each time you edit a matrix.
When you select a matrix to define, the cursor highlights the row dimension.
•
To accept the row dimension, press Í.
•
To change the row dimension, enter the number of rows (up to
99
), and then press Í.
The cursor moves to the column dimension, which you must accept or change the same way you accepted or changed the row dimension. When you press Í, the rectangular cursor moves to the first matrix element.
Matrices 10–3
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Viewing and Editing Matrix Elements
Displaying Matrix
Elements
After you have set the dimensions of the matrix, you can view the matrix and enter values for the matrix elements. In a new matrix, all values are zero.
Select the matrix from the
MATRX EDIT
menu and enter or accept the dimensions. The center portion of the matrix editor displays up to seven rows and three columns of a matrix, showing the values of the elements in abbreviated form if necessary. The full value of the current element, which is indicated by the rectangular cursor, is displayed on the bottom line.
This is an 8 × 4 matrix. Ellipses in the left or right column indicate additional columns.
#
or
$
in the right column indicate additional rows.
Deleting a Matrix
To delete matrices from memory, use the
MEMORY DELETE
FROM
secondary menu (Chapter 18).
10–4 Matrices
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Viewing a Matrix
The matrix editor has two contexts, viewing and editing. In viewing context, you can use the cursor keys to move quickly from one matrix element to the next. The full value of the highlighted element is displayed on the bottom line.
Select the matrix from the
MATRX EDIT
menu, and then enter or accept the dimensions.
ViewingContext
Keys
Key
 or ~
† or }
Í
‘
Any entry character y [
INS
]
{
Function
Moves the rectangular cursor within the current row.
Moves the rectangular cursor within the current column; on the top row, } moves the cursor to the column dimension; on the column dimension, } moves the cursor to the row dimension.
Switches to editing context; activates the edit cursor on the bottom line.
Switches to editing context; clears the value on the bottom line.
Switches to editing context; clears the value on the bottom line; copies the character to the bottom line.
Nothing
Nothing
Matrices 10–5
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Viewing and Editing Matrix Elements
(continued)
Editing a Matrix
Element
In editing context, an edit cursor is active on the bottom line. To edit a matrix element value, follow these steps.
1. Select the matrix from the
MATRX EDIT
menu, and then enter or accept the dimensions.
2. Press , }, ~, and † to move the cursor to the matrix element you want to change.
3. Switch to editing context by pressing Í, ‘, or an entry key.
4. Change the value of the matrix element using the editingcontext keys described below. You may enter an expression, which is evaluated when you leave editing context.
Note: You can press
‘ Í to restore the value at the rectangular cursor if you make a mistake.
5. Press Í, }, or † to move to another element.
EditingContext
Keys
Key
 or ~
† or }
Í
‘
Any entry character y [
INS
]
{
Function
Moves the edit cursor within the value.
Stores the value displayed on the bottom line to the matrix element; switches to viewing context and moves the rectangular cursor within the column.
Stores the value displayed on the bottom line to the matrix element; switches to viewing context and moves the rectangular cursor to the next row element.
Clears the value on the bottom line.
Copies the character to the location of the edit cursor on the bottom line.
Activates the insert cursor.
Deletes the character under the edit cursor on the bottom line.
10–6 Matrices
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Using Matrices with Expressions
Using a Matrix in an Expression
To use a matrix in an expression, you can do any of the following.
•
Copy the name from the
MATRX NAMES
menu.
•
Recall the contents of the matrix into the expression with y [
RCL
] (Chapter 1).
•
Enter the matrix directly (see below).
Entering a Matrix in an Expression
You can enter, edit, and store a matrix in the matrix editor. You also can enter a matrix directly in an expression.
To enter a matrix in an expression, follow these steps.
1. Press y [
[
] to indicate the beginning of the matrix.
2. Press y [
[
] to indicate the beginning of a row.
3. Enter a value, which can be an expression, for each element in the row. Separate the values with commas.
4. Press y [
]
] to indicate the end of a row.
5. Repeat steps 2 through 4 to enter all of the rows.
6. Press y [
]
] to indicate the end of the matrix.
Note: The closing
]] are not necessary at the end of an expression or preceding
!
The resulting matrix is displayed in the form:
[[
element
1,1
,
...
,
element
1,n
],
...
,[
element m,1
,
...
,
element m,n
]]
Any expressions are evaluated when the entry is executed.
Note: The commas that you must enter to separate elements are not displayed on output.
Matrices 10–7
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Displaying and Copying Matrices
Displaying a
Matrix
To display the contents of a matrix on the home screen, select the matrix from the
MATRX NAMES
menu, and then press
Í.
Ellipses in the left or right column indicate additional columns.
#
or
$
in the right column indicate additional rows. Press ~, ,
†, and } to scroll the matrix.
Copying One
Matrix to Another
To copy a matrix, follow these steps.
1. Press to display the
MATRX NAMES
menu.
2. Select the name of the matrix you want to copy.
3. Press ¿.
4. Press again and select the name of the new matrix to which you want to copy the existing matrix.
5. Press Í to copy the matrix to the new matrix name.
Accessing a
Matrix Element
On the home screen or from within a program, you can store a value to, or recall a value from, a matrix element. The element must be within the currently defined matrix dimensions. Select
matrix from the
MATRX NAMES
menu.
[
matrix
](
row
,
column
)
10–8 Matrices
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Using Math Functions with Matrices
Using Math
Functions with
Matrices
+ (Add), –
(Subtract),
ääää
(Multiply)
You can use many of the math functions on the TI82 STATS keyboard, the
MATH
menu, the
MATH NUM
menu, and the
MATH
TEST
menu with matrices. However, the dimensions must be appropriate. Each of the functions below creates a new matrix; the original matrix remains the same.
To add (Ã) or subtract (¹) matrices, the dimensions must be the same. The answer is a matrix in which the elements are the sum or difference of the individual corresponding elements.
matrixA
+
matrixB matrixA
N
matrixB
To multiply (¯) two matrices together, the column dimension of matrixA must match the row dimension of matrixB.
matrixA
ääää
matrixB
Multiplying a matrix by a value or a value by a matrix returns a matrix in which each element of matrix is multiplied by value.
matrix
ääää
value value
ääää
matrix
L (Negation)
Negating a matrix (Ì) returns a matrix in which the sign of every element is changed (reversed).
L
matrix
Matrices 10–9
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Using Math Functions with Matrices
(continued) abs( abs(
(absolute value,
MATH NUM
menu) returns a matrix containing the absolute value of each element of matrix.
abs(
matrix
) round( round(
(
MATH NUM
menu) returns a matrix. It rounds every element in matrix to #decimals ( 9). If #decimals is omitted, the elements are rounded to 10 digits.
round(
matrix[
,
#decimals]
)
M1 (Inverse)
Use the
L1
function (—) to invert a matrix (
^L1
is not valid).
matrix must be square. The determinant cannot equal zero.
matrix
L1
Powers
To raise a matrix to a power, matrix must be square. You can use
2
(¡),
3
(
MATH
menu), or
^
power (›) for integer power between
0
and
255
.
matrix
2
matrix
3
matrix
^
power
10–10 Matrices
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Relational
Operations
To compare two matrices using the relational operations
=
and
ƒ
(
TEST
menu), they must have the same dimensions.
=
and
ƒ
compare matrixA and matrixB on an elementbyelement basis.
The other relational operations are not valid with matrices.
matrixA
=
matrixB returns
1
if every comparison is true; it returns
0
if any comparison is false.
matrixA
ƒ
matrixB returns
1
if at least one comparison is false; it returns
0
if no comparison is false.
iPart(, fPart(, int( iPart(
(integer part),
fPart(
(fractional part), and
int(
(greatest integer) are on the
MATH NUM
menu.
iPart(
returns a matrix containing the integer part of each element of matrix.
fPart(
returns a matrix containing the fractional part of each element of matrix.
int(
returns a matrix containing the greatest integer of each element of matrix.
iPart(
matrix
) fPart(
matrix
) int(
matrix
)
Matrices 10–11
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Using the MATRX MATH Operations
MATRX MATH
Menu det(
T
(Transpose)
To display the
MATRX MATH
menu, press ~.
NAMES MAT
H
1: det(
2:
T
3: dim(
4: Fill(
5: identity(
6: randM(
7: augment(
8: Matr4list(
9: List4matr(
0: cumSum(
A: ref(
B: rref(
C: rowSwap(
D: row+(
E: ärow(
F: ärow+(
EDIT
Calculates the determinant.
Transposes the matrix.
Returns the matrix dimensions.
Fills all elements with a constant.
Returns the identity matrix.
Returns a random matrix.
Appends two matrices.
Stores a matrix to a list.
Stores a list to a matrix.
Returns the cumulative sums of a matrix.
Returns the rowechelon form of a matrix.
Returns the reduced rowechelon form.
Swaps two rows of a matrix.
Adds two rows; stores in the second row.
Multiplies the row by a number.
Multiplies the row, adds to the second row.
det(
(determinant) returns the determinant (a real number) of a square matrix.
det(
matrix
)
T
(transpose) returns a matrix in which each element (row, column) is swapped with the corresponding element (column, row) of matrix.
matrix
T
Accessing Matrix
Dimensions with dim( dim(
(dimension) returns a list containing the dimensions
(
{
rows columns
}
) of matrix.
dim(
matrix
)
Note:
dim(matrix)
!
dim(matrix)
!
10–12 Matrices
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Creating a Matrix with dim(
Use
dim(
with ¿ to create a new matrixname of dimensions
rows × columns with
0
as each element.
{
rows
,
columns
}
!
matrixname
)
Redimensioning a
Matrix with dim(
Use
dim(
with ¿ to redimension an existing matrixname to dimensions rows × columns. The elements in the old
matrixname that are within the new dimensions are not changed.
Additional created elements are zeros. Matrix elements that are outside the new dimensions are deleted.
{
rows
,
columns
}
!
matrixname
)
Fill(
Fill(
stores value to every element in matrixname.
Fill(
value
,
matrixname
) identity( randM( identity(
returns the identity matrix of dimension rows ×
dimension columns.
identity(
dimension
) randM(
(create random matrix) returns a rows × columns random matrix of integers ‚ L9 and 9. The seed value stored to the
rand
function controls the values (Chapter 2).
randM(
rows
,
columns
)
Matrices 10–13
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Using the MATRX MATH Operations
(continued) augment( augment(
appends matrixA to matrixB as new columns. matrixA and matrixB both must have the same number of rows.
augment(
matrixA
,
matrixB
)
Matr4list(
List4matr(
Matr4list(
(matrix stored to list) fills each listname with elements from each column in matrix.
Matr4list(
ignores extra listname arguments. Likewise,
Matr4list(
ignores extra matrix columns.
Matr4list(
matrix
,
listnameA
,
...,listname n
)
&
Matr4list(
also fills a listname with elements from a specified
column# in matrix. To fill a list with a specific column from matrix, you must enter column# after matrix.
Matr4list(
matrix
,
column#
,
listname
)
&
List4matr(
(lists stored to matrix) fills matrixname column by column with the elements from each list. If dimensions of all lists are not equal,
List4matr(
fills each extra matrixname row with
0
.
Complex lists are not valid.
List4matr(
listA
,
...,list n
,
matrixname
)
&
10–14 Matrices
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cumSum( cumSum(
returns cumulative sums of the elements in matrix, starting with the first element. Each element is the cumulative sum of the column from top to bottom.
cumSum(
matrix
)
Row Operations
MATRX MATH
menu items
A
through
F
are row operations. You can use a row operation in an expression. Row operations do not change matrix in memory. You can enter all row numbers and values as expressions. You can select the matrix from the
MATRX NAMES
menu.
ref(, rref( ref(
(rowechelon form) returns the rowechelon form of a real
matrix. The number of columns must be greater than or equal to the number of rows.
ref(
matrix
) rref(
(reduced rowechelon form) returns the reduced rowechelon form of a real matrix. The number of columns must be greater than or equal to the number of rows.
rref(
matrix
)
Matrices 10–15
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Using the MATRX MATH Operations
(continued) rowSwap( rowSwap(
returns a matrix. It swaps rowA and rowB of matrix.
rowSwap(
matrix
,
rowA
,
rowB
) row+( row+(
(row addition) returns a matrix. It adds rowA and rowB of
matrix and stores the results in rowB.
row+(
matrix
,
rowA
,
rowB
)
äääärow(
äääärow+(
äääärow(
(row multiplication) returns a matrix. It multiplies row of
matrix by value and stores the results in row.
äääärow(
value
,
matrix
,
row
)
äääärow+( (row multiplication and addition) returns a matrix. It multiplies rowA of matrix by value, adds it to rowB, and stores the results in rowB.
äääärow+(
value
,
matrix
,
rowA
,
rowB
)
10–16 Matrices
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11
Lists
Contents
Getting Started: Generating a Sequence
..................................................
Naming Lists
..............................................................................................................
Storing and Displaying Lists
...........................................................................
Entering List Names
.............................................................................................
Attaching Formulas to List Names
..............................................................
Using Lists in Expressions
................................................................................
LIST OPS
Menu
......................................................................................................
10
LIST MATH
Menu
..................................................................................................
17
7
9
4
6
2
3
Lists 11–1
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Getting Started: Generating a Sequence
Getting Started is a fastpaced introduction. Read the chapter for details.
Calculate the first eight terms of the sequence 1/A 2 . Store the results to a usercreated list. Then display the results in fraction form. Begin this example on a blank line on the home screen.
1. Press y [
LIST
] ~ to display the
LIST OPS menu.
2. Press
5
to select
5:seq(
, which pastes
seq(
to the current cursor location.
3. Press
1
¥ ƒ [
A
] ¡ ¢ ƒ [
A
] ¢
1
¢
8
¢
1
¤ to enter the sequence.
4. Press ¿, and then press y ƒ to turn on alphalock. Press [
S
] [
E
] [
Q
], and then press
ƒ to turn off alphalock. Press
1
to complete the list name.
5. Press Í to generate the list and store it in
SEQ1
. The list is displayed on the home screen.
An ellipsis (
...
) indicates that the list continues beyond the viewing window. Press ~ repeatedly (or press and hold ~) to scroll the list and view all the list elements.
6. Press y [
LIST
] to display the
LIST NAMES menu. Press Í to paste
ÙÙÙÙSEQ1 to the current cursor location. (If
SEQ1
is not item
1
on your
LIST NAMES
menu, move the cursor to
SEQ1
before you press Í.)
7. Press to display the
MATH menu. Press
1
to select
1:4Frac
, which pastes
4Frac
to the current cursor location.
8. Press Í to show the sequence in fraction form. Press ~ repeatedly (or press and hold ~) to scroll the list and view all the list elements.
11–2 Lists
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Naming Lists
Using
TI82 STATS List
Names L
1 through L
6
The TI82 STATS has six list names in memory:
L
1
,
L
2
,
L
3
,
L
4
,
L
5
, and
L
6
. The list names
L
1
through
L
6
are on the keyboard above the numeric keys À through ¸. To paste one of these names to a valid screen, press y, and then press the appropriate key.
L
1
through
L
6
are stored in stat list editor columns
1
through
6
when you reset memory.
Creating a List
Name on the
Home Screen
To create a list name on the home screen, follow these steps.
1. Press y [
{
], enter one or more list elements, and then press y [
}
]. Separate list elements with commas. List elements can be real numbers, complex numbers, or expressions.
2. Press ¿.
3. Press ƒ [letter from A to Z or of the name.
q ] to enter the first letter
4. Enter zero to four letters, q, or numbers to complete the name.
5. Press Í. The list is displayed on the next line. The list name and its elements are stored in memory. The list name becomes an item on the
LIST NAMES
menu.
Note: If you want to view a usercreated list in the stat list editor, you must store it in the stat list editor (Chapter 12).
You also can create a list name in these four places.
•
At the
Name=
prompt in the stat list editor
•
At an
Xlist:
,
Ylist:
, or
Data List:
prompt in the stat plot editor
•
At a
List:
,
List1:
,
List2:
,
Freq:
,
Freq1:
,
Freq2:
,
XList:
, or
YList:
prompt in the inferential stat editors
•
On the home screen using
SetUpEditor
You can create as many list names as your TI82 STATS memory has space to store.
Lists 11–3
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Storing and Displaying Lists
Storing Elements to a List
You can store list elements in either of two ways.
•
Use braces and ¿ on the home screen.
•
Use the stat list editor (Chapter 12).
The maximum dimension of a list is 999 elements.
Tip: When you store a complex number to a list, the entire list is converted to a list of complex numbers. To convert the list to a list of real numbers, display the home screen, and then enter
real(listname)
!
Displaying a List on the Home
Screen
To display the elements of a list on the home screen, enter the name of the list (preceded by Ù if necessary; see page 11.16), and then press Í. An ellipsis indicates that the list continues beyond the viewing window. Press ~ repeatedly (or press and hold ~) to scroll the list and view all the list elements.
11–4 Lists
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Copying One List to Another
To copy a list, store it to another list.
Accessing a List
Element
You can store a value to or recall a value from a specific list
element. You can store to any element within the current list dimension or one element beyond.
listname
(
element
)
Deleting a List from Memory
Using Lists in
Graphing
To delete lists from memory, including
L
1
through
L
6
, use the
MEMORY DELETE FROM
secondary menu (Chapter 18).
Resetting memory restores
L
1
through
L
6
. Removing a list from the stat list editor does not delete it from memory.
You can use lists to graph a family of curves (Chapter 3).
Lists 11–5
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Entering List Names
Using the
LIST NAMES
Menu
To display the
LIST NAMES
menu, press y [
LIST
]. Each item is a usercreated list name.
LIST NAMES
menu items are sorted automatically in alphanumerical order. Only the first 10 items are labeled, using
1
through
9
, then
0
. To jump to the first list name that begins with a particular alpha character or q, press ƒ
[letter from A to Z or q
].
Tip: From the top of a menu, press
} to move to the bottom. From the bottom, press
† to move to the top.
Note: The LIST NAMES menu omits list names L
1
through
L
6
. Enter
L1
through
L
6
directly from the keyboard (page 11.3).
When you select a list name from the
LIST NAMES
menu, the list name is pasted to the current cursor location.
•
The list name symbol ÙÙÙÙ precedes a list name when the name is pasted where nonlist name data also is valid, such as the home screen.
•
The
ÙÙÙÙ
symbol does not precede a list name when the name is pasted where a list name is the only valid input, such as the stat list editor’s
Name=
prompt or the stat plot editor’s
XList:
and
YList:
prompts.
Entering a User
Created List
Name Directly
To enter an existing list name directly, follow these steps.
1. Press y [
LIST
] ~ to display the
LIST OPS
menu.
2. Select
B:
ÙÙÙÙ , which pastes ÙÙÙÙ to the current cursor location. ÙÙÙÙ is not always necessary (page 11.16).
Note: You also can paste
ÙÙÙÙ to the current cursor location from the
CATALOG (Chapter 15).
3. Enter the characters that comprise the list name.
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Attaching Formulas to List Names
Attaching a
Formula to a List
Name
You can attach a formula to a list name so that each list element is a result of the formula. When executed, the attached formula must resolve to a list.
When anything in the attached formula changes, the list to which the formula is attached is updated automatically.
•
When you edit an element of a list that is referenced in the formula, the corresponding element in the list to which the formula is attached is updated.
•
When you edit the formula itself, all elements in the list to which the formula is attached are updated.
For example, the first screen below shows that elements are stored to
L
3
, and the formula
L
3
+10
is attached to the list name
ÙÙÙÙADD10 . The quotation marks designate the formula to be attached to ÙÙÙÙADD10 . Each element of ÙÙÙÙADD10 is the sum of an element in
L
3
and 10.
The next screen shows another list,
L
4
. The elements of
L
4
are the sum of the same formula that is attached to
L
3
. However, quotation marks are not entered, so the formula is not attached to
L
4
.
On the next line,
L6
L6!
3
(1):L
, and then redisplays
L
3
.
3
changes the first element in
L
3
to
The last screen shows that editing
L
3
updated ÙÙÙÙADD10 , but did not change
L
4
. This is because the formula
L
3
+10
is attached to
ÙÙÙÙADD10 , but it is not attached to
L
4
.
Note: To view a formula that is attached to a list name, use the stat list editor (Chapter 12).
Lists 11–7
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Attaching Formulas to List Names
(continued)
Attaching a
Formula to a List on the Home
Screen or in a
Program
To attach a formula to a list name from a blank line on the home screen or from a program, follow these steps.
1. Press ƒ [
ã
], enter the formula (which must resolve to a list), and press ƒ [
ã
] again.
Note: When you include more than one list name in a formula, each list must have the same dimension.
2. Press ¿.
3. Enter the name of the list to which you want to attach the formula.
•
Press y, and then enter a TI82 STATS list name
L
1
through
L
6
.
•
Press y [
LIST
] and select a user.created list name from the
LIST NAMES
menu.
•
Enter a user.created list name directly using ÙÙÙÙ (page
11.16).
4. Press Í.
Detaching a
Formula from a
List
Note: The stat list editor displays a formulalock symbol next to each list name that has an attached formula. Chapter 12 describes how to use the stat list editor to attach formulas to lists, edit attached formulas, and detach formulas from lists.
You can detach (clear) an attached formula from a list in any of three ways.
•
Enter
""
!
listname on the home screen.
•
Edit any element of a list to which a formula is attached.
•
Use the stat list editor (Chapter 12).
Note: You also can use ClrList or ClrAllList to detach a formula from a list (Chapter 18).
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Using Lists in Expressions
Using a List in an
Expression
You can use lists in an expression in any of three ways. When you press Í, any expression is evaluated for each list element, and a list is displayed.
•
Use
L
1
–
L
6
or any usercreated list name in an expression.
•
Enter the list elements directly (step 1 on page 11.3).
•
Use y [
RCL
] to recall the contents of the list into an expression at the cursor location (Chapter 1).
&
Note: You must paste usercreated list names to the
Rcl prompt by selecting them from the LIST NAMES menu. You cannot enter them directly using
ÙÙÙÙ.
Using Lists with
Math Functions
You can use a list to input several values for some math functions. Other chapters and Appendix A specify whether a list is valid. The function is evaluated for each list element, and a list is displayed.
•
When you use a list with a function, the function must be valid for every element in the list. In graphing, an invalid element, such as
L1
in
‡({1,0,L1})
, is ignored.
This returns an error.
This graphs
X
ääää‡(1) and Xääää‡(0), but skips
X
ääää‡(L1).
•
When you use two lists with a twoargument function, the dimension of each list must be the same. The function is evaluated for corresponding elements.
•
When you use a list and a value with a twoargument function, the value is used with each element in the list.
Lists 11–9
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LIST OPS Menu
LIST OPS Menu
To display the
LIST OPS
menu, press y [
LIST
] ~.
NAMESOPS MATH
1: SortA(
2: SortD(
3: dim(
4: Fill(
5: seq(
6: cumSum(
7:
@
List(
8: Select(
9: augment(
0: List4matr(
A: Matr4list(
Sorts lists in ascending order.
Sorts lists in descending order.
Sets the list dimension.
Fills all elements with a constant.
Creates a sequence.
Returns a list of cumulative sums.
Returns difference of successive elements.
Selects specific data points.
Concatenates two lists.
Stores a list to a matrix.
Stores a matrix to a list.
Designates the listname data type.
SortA(, SortD(
SortA(
(sort ascending) sorts list elements from low to high values.
SortD(
(sort descending) sorts list elements from high to low values. Complex lists are sorted based on magnitude
(modulus).
With one list,
SortA(
and
SortD(
sort the elements of listname and update the list in memory.
SortA(
listname
) SortD(
listname
)
With two or more lists,
SortA(
and
SortD(
sort keylistname, and then sort each dependlist by placing its elements in the same order as the corresponding elements in keylistname. All lists must have the same dimension.
SortA(
keylistname
,
dependlist1[
,
dependlist2
,
...
,
dependlist n]
)
SortD(
keylistname
,
dependlist1[
,
dependlist2
,
...
,
dependlist n]
)
Note: In the example, 5 is the first element in L
4
, and 1 is the first element in
L
5
. After
SortA(L
4
,L
5
), 5 becomes the second element of
L
4
, and likewise, 1 becomes the second element of L
5
.
Note:
SortA( and SortD( are the same as SortA( and SortD( on the
STAT EDIT menu (Chapter 12).
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Using dim( to
Find List
Dimensions dim(
(dimension) returns the length (number of elements) of list.
dim(
list
)
Using dim( to
Create a List
You can use
dim(
with ¿ to create a new listname with dimension length from 1 to 999. The elements are zeros.
length
!
listname
)
Using dim( to
Redimension a
List
You can use
dim
with ¿ to redimension an existing listname to dimension length from 1 to 999.
•
The elements in the old listname that are within the new dimension are not changed.
•
Extra list elements are filled by
0
.
•
Elements in the old list that are outside the new dimension are deleted.
length
!
listname
)
Fill(
Fill(
replaces each element in listname with value.
Fill(
value
,
listname
)
Note:
dim( and Fill( are the same as dim( and Fill( on the MATRX
MATH menu (Chapter 10).
Lists 11–11
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LIST OPS Menu
(continued) seq( seq(
(sequence) returns a list in which each element is the result of the evaluation of expression with regard to variable for the values ranging from begin to end at steps of increment. variable need not be defined in memory. increment can be negative; the default value for increment is 1.
seq(
is not valid within
expression.
seq(
expression
,
variable
,
begin
,
end[
,
increment]
) cumSum( cumSum(
(cumulative sum) returns the cumulative sums of the elements in list, starting with the first element. list elements can be real or complex numbers.
cumSum(
list
)
@List(
@List(
returns a list containing the differences between consecutive elements in list.
@List
subtracts the first element in
list from the second element, subtracts the second element from the third, and so on. The list of differences is always one element shorter than the original list. list elements can be a real or complex numbers.
@List(
list
)
Select(
Select(
selects one or more specific data points from a scatter plot or xyLine plot (only), and then stores the selected data points to two new lists, xlistname and ylistname. For example, you can use
Select(
to select and then analyze a portion of plotted CBL or CBR data.
Select(
xlistname
,
ylistname
)
Note: Before you use
Select(, you must have selected (turned on) a scatter plot or xyLine plot. Also, the plot must be displayed in the current viewing window (page 11.13).
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Before Using
Select(
Before using
Select(
, follow these steps.
1. Create two list names and enter the data.
2. Turn on a stat plot, select " (scatter plot) or Ó (xyLine), and enter the two list names for
Xlist:
and
Ylist:
(Chapter 12).
3. Use
ZoomStat
to plot the data (Chapter 3).
Using Select( to
Select Data
Points from a
Plot
To select data points from a scatter plot or xyLine plot, follow these steps.
1. Press y [
LIST
] ~
8
to select
8:Select(
from the
LIST OPS menu.
Select(
is pasted to the home screen.
2. Enter xlistname, press ¢, enter ylistname, and then press ¤ to designate list names into which you want the selected data to be stored.
3. Press Í. The graph screen is displayed with
Left Bound?
in the bottomleft corner.
4. Press } or † (if more than one stat plot is selected) to move the cursor onto the stat plot from which you want to select data points.
5. Press  and ~ to move the cursor to the stat plot data point that you want as the left bound.
Lists 11–13
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LIST OPS Menu
(continued)
Using Select( to
Select Data
Points from a
Plot (continued)
6. Press Í. A
4
indicator on the graph screen shows the left bound.
Right Bound?
is displayed in the bottomleft corner.
7. Press  or ~ to move the cursor to the stat plot point that you want for the right bound, and then press Í.
The xvalues and yvalues of the selected points are stored in
xlistname and ylistname. A new stat plot of xlistname and
ylistname replaces the stat plot from which you selected data points. The list names are updated in the stat plot editor.
Note: The two new lists (xlistname and ylistname) will include the points you select as left bound and right bound. Also, leftbound
xvalue rightbound xvalue must be true.
11–14 Lists
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augment( augment(
concatenates the elements of listA and listB. The list elements can be real or complex numbers.
augment(
listA
,
listB
)
List4matr(
List4matr(
(lists stored to matrix) fills matrixname column by column with the elements from each list. If the dimensions of all lists are not equal, then
List4matr(
fills each extra matrixname row with
0
. Complex lists are not valid.
List4matr(
list1
,
list2
,
. . .
,
list n
,
matrixname
)
&
Lists 11–15
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LIST OPS Menu
(continued)
Matr4list( Matr4list(
(matrix stored to lists) fills each listname with elements from each column in matrix. If the number of listname arguments exceeds the number of columns in matrix, then
Matr4list(
ignores extra listname arguments. Likewise, if the number of columns in matrix exceeds the number of listname arguments, then
Matr4list(
ignores extra matrix columns.
Matr4list(
matrix
,
listname1
,
listname2
,
. . .
,
listname n
)
&
Matr4list(
also fills a listname with elements from a specified
column# in matrix. To fill a list with a specific column from
matrix, you must enter a column# after matrix.
Matr4list(
matrix
,
column#
,
listname
)
&
ÙÙÙÙ
preceding one to five characters identifies those characters as a usercreated listname. listname may comprise letters, q, and numbers, but it must begin with a letter from A to Z or q.
ÙÙÙÙ
listname
Generally,
ÙÙÙÙ
must precede a usercreated list name when you enter a usercreated list name where other input is valid, for example, on the home screen. Without the
ÙÙÙÙ
, the TI82 STATS may misinterpret a usercreated list name as implied multiplication of two or more characters.
ÙÙÙÙ
need not precede a usercreated list name where a list name is the only valid input, for example, at the
Name=
prompt in the stat list editor or the
Xlist:
and
Ylist:
prompts in the stat plot editor. If you enter
ÙÙÙÙ
where it is not necessary, the TI82 STATS will ignore the entry.
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LIST MATH Menu
LIST MATH Menu
To display the
LIST MATH
menu, press y [
LIST
] .
NAMES
OPS
1: min(
2: max(
3: mean(
4: median(
5: sum(
6: prod(
7: stdDev(
8: variance(
MAT
H
Returns minimum element of a list.
Returns maximum element of a list.
Returns mean of a list.
Returns median of a list.
Returns sum of elements in a list.
Returns product of elements in list.
Returns standard deviation of a list.
Returns the variance of a list.
min(, max( min(
(minimum) and
max(
(maximum) return the smallest or
largest element of listA. If two lists are compared, it returns a list of the smaller or larger of each pair of elements in listA and listB.
For a complex list, the element with smallest or largest magnitude
(modulus) is returned.
min(
listA[
,
listB]
) max(
listA[
,
listB]
) mean(, median(
Note:
min( and max( are the same as min( and max( on the MATH
NUM menu.
mean(
returns the mean value of list.
median(
returns the median value of list. The default value for freqlist is 1. Each
freqlist element counts the number of consecutive occurrences of the corresponding element in list. Complex lists are not valid.
mean(
list[
,
freqlist]
) median(
list[
,
freqlist]
)
Lists 11–17
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LIST MATH Menu
(continued) sum(, prod( sum(
(summation) returns the sum of the elements in list. start and end are optional; they specify a range of elements. list elements can be real or complex numbers.
prod(
returns the product of all elements of list. start and end elements are optional; they specify a range of list elements. list elements can be real or complex numbers.
sum(
list[
,
start
,
end]
) prod(
list[
,
start
,
end]
)
Sums and
Products of
Numeric
Sequences
You can combine
sum(
or
prod(
with
seq(
to obtain:
upper
G
expression(x)
∏
x=lower upper
∏
expression(x) x=lower
To evaluate G 2 (N–1) from N=1 to 4:
stdDev(, variance( stdDev(
returns the standard deviation of the elements in list. The default value for freqlist is 1. Each freqlist element counts the number of consecutive occurrences of the corresponding element in
list. Complex lists are not valid.
variance(
returns the variance of the elements in list. The default value for freqlist is 1. Each freqlist element counts the number of consecutive occurrences of the corresponding element in list.
Complex lists are not valid.
stdDev(
list[
,
freqlist]
) variance(
list[
,
freqlist]
)
11–18 Lists
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12
Statistics
Contents
Getting Started: Pendulum Lengths and Periods
................................
2
Setting Up Statistical Analyses
......................................................................
10
Using the Stat List Editor
..................................................................................
11
Attaching Formulas to List Names
..............................................................
14
Detaching Formulas from List Names
......................................................
16
Switching Stat List Editor Contexts
............................................................
17
Stat List Editor Contexts
....................................................................................
18
STAT EDIT
Menu
..................................................................................................
20
Regression Model Features
..............................................................................
22
STAT CALC
Menu
................................................................................................
24
Statistical Variables
...............................................................................................
29
Statistical Analysis in a Program
..................................................................
30
Statistical Plotting
...................................................................................................
31
Statistical Plotting in a Program
....................................................................
37
Statistics 12–1
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Getting Started: Pendulum Lengths and Periods
Getting Started is a fastpaced introduction. Read the chapter for details.
A group of students is attempting to determine the mathematical relationship between the length of a pendulum and its period (one complete swing of a pendulum). The group makes a simple pendulum from string and washers and then suspends it from the ceiling. They record the pendulum’s period for each of 12 string lengths.*
Length (cm)
6.5
11.0
13.2
15.0
18.0
23.1
24.4
26.6
30.5
34.3
37.6
41.5
1. Press z † † † Í to set
Func
graphing mode.
2. Press …
5
to select
5:SetUpEditor
.
SetUpEditor
is pasted to the home screen.
Press Í. This removes lists from stat list editor columns
1
through
20
, and then stores lists
L
1
through
L
6
in columns
1
through
6
.
Note: Removing lists from the stat list editor does not delete them from memory.
3. Press …
1
to select
1:Edit
from the
STAT
EDIT
menu. The stat list editor is displayed.
If elements are stored in
L
1
and
L
2
, press } to move the cursor onto
L
1
, and then press
‘ Í ~ } ‘ Í to clear both lists. Press  to move the rectangular cursor back to the first row in
L
1
.
Time (sec)
0.51
0.68
0.73
0.79
0.88
0.99
1.01
1.08
1.13
1.26
1.28
1.32
*This example is quoted and adapted from Contemporary Precalculus Through Applications, by the North Carolina School of Science and Mathematics, by permission of Janson
Publications, Inc., Dedham, MA. 1800322MATH. © 1992. All rights reserved.
12–2 Statistics
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4. Press
6
Ë
5
Í to store the first pendulum string length (6.5 cm) in
L
1
. The rectangular cursor moves to the next row.
Repeat this step to enter each of the 12 string length values in the table on page
12.2.
5. Press ~ to move the rectangular cursor to the first row in
L
2
.
Press Ë
51
Í to store the first time measurement (.51 sec) in
L
2
. The rectangular cursor moves to the next row.
Repeat this step to enter each of the 12 time values in the table on page 12.2.
6. Press o to display the
Y=
editor.
If necessary, press ‘ to clear the function
Y
1
. As necessary, press }, Í, and ~ to turn off
Plot1
,
Plot2
, and
Plot3
from the top line of the
Y=
editor (Chapter 3). As necessary, press †, , and Í to deselect functions.
7. Press y [
STAT PLOT
]
1
to select
1:Plot1
from the
STAT PLOTS
menu. The stat plot editor is displayed for plot 1.
8. Press Í to select
On
, which turns on plot 1. Press † Í to select " (scatter plot). Press † y [
L1
] to specify
Xlist:L
1
for plot 1. Press † y [
L2
] to specify
Ylist:L
2
for plot 1. Press † ~ Í to select
+
as the
Mark
for each data point on the scatter plot.
9. Press q
9
to select
9:ZoomStat
from the
ZOOM
menu. The window variables are adjusted automatically, and plot 1 is displayed. This is a scatter plot of the timeversuslength data.
Statistics 12–3
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Getting Started: Pendulum Lengths and Periods
(cont.)
Since the scatter plot of timeversuslength data appears to be approximately linear, fit a line to the data.
10. Press … ~
4
to select
4:LinReg(ax+b)
(linear regression model) from the
STAT
CALC menu.
LinReg(ax+b)
is pasted to the home screen.
11. Press y [
L1
] ¢ y [
L2
] ¢. Press
~
1
to display the
VARS Y.VARS
FUNCTION
secondary menu, and then press
1
to select
1:Y
1
.
L
1
,
L
2
, and
Y
1
are pasted to the home screen as arguments to
LinReg(ax+b)
.
12. Press Í to execute
LinReg(ax+b)
. The linear regression for the data in
L
1
and
L
2
is calculated. Values for
a
and
b
are displayed on the home screen. The linear regression equation is stored in
Y
1
. Residuals are calculated and stored automatically in the list name
RESID
, which becomes an item on the
LIST NAMES
menu.
13. Press s. The regression line and the scatter plot are displayed.
12–4 Statistics
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The regression line appears to fit the central portion of the scatter plot well. However, a residual plot may provide more information about this fit.
14. Press …
1
to select
1:Edit
. The stat list editor is displayed.
Press ~ and } to move the cursor onto
L
3
.
Press y [
INS
]. An unnamed column is displayed in column
3
;
L
3
,
L
4
,
L
5
, and
L
6
shift right one column. The
Name=
prompt is displayed in the entry line, and alphalock is on.
15. Press y [
LIST
] to display the
LIST NAMES menu.
If necessary, press † to move the cursor onto the list name
RESID
.
16. Press Í to select
RESID
and paste it to the stat list editor’s
Name=
prompt.
17. Press Í.
RESID
is stored in column
3
of the stat list editor.
Press † repeatedly to examine the residuals.
Notice that the first three residuals are negative. They correspond to the shortest pendulum string lengths in
L
1
. The next five residuals are positive, and three of the last four are negative. The latter correspond to the longer string lengths in
L
1
. Plotting the residuals will show this pattern more clearly.
Statistics 12–5
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Getting Started: Pendulum Lengths and Periods
(cont.)
18. Press y [
STAT PLOT
]
2
to select
2:Plot2
from the
STAT PLOTS
menu. The stat plot editor is displayed for plot 2.
19. Press Í to select
On
, which turns on plot 2.
Press † Í to select " (scatter plot).
Press † y [
L1
] to specify
Xlist:L
1
for plot
2. Press † [
R
] [
E
] [
S
] [
I
] [
D
] (alphalock is on) to specify
Ylist:RESID
for plot 2. Press
† Í to select
›
as the mark for each data point on the scatter plot.
20. Press o to display the
Y=
editor.
Press  to move the cursor onto the = sign, and then press Í to deselect
Y
1
. Press
} Í to turn off plot 1.
21. Press q
9
to select
9:ZoomStat
from the
ZOOM
menu. The window variables are adjusted automatically, and plot 2 is displayed. This is a scatter plot of the residuals.
Notice the pattern of the residuals: a group of negative residuals, then a group of positive residuals, and then another group of negative residuals.
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The residual pattern indicates a curvature associated with this data set for which the linear model did not account. The residual plot emphasizes a downward curvature, so a model that curves down with the data would be more accurate. Perhaps a function such as square root would fit. Try a power regression to fit a function of the form y = a ä x b .
22. Press o to display the
Y=
editor.
Press ‘ to clear the linear regression equation from
Y
1
. Press } Í to turn on plot 1. Press ~ Í to turn off plot 2.
23. Press q
9
to select
9:ZoomStat
from the
ZOOM
menu. The window variables are adjusted automatically, and the original scatter plot of timeversuslength data (plot
1) is displayed.
24. Press … ~ ƒ [
A
] to select
A:PwrReg
from the
STAT CALC menu.
PwrReg
is pasted to the home screen.
Press y [
L1
] ¢ y [
L2
] ¢. Press
~
1
to display the
VARS Y.VARS
FUNCTION
secondary menu, and then press
1
to select
1:Y
1
.
L
1
,
L
2
, and
Y
1
are pasted to the home screen as arguments to
PwrReg
.
25. Press Í to calculate the power regression. Values for
a
and
b
are displayed on the home screen. The power regression equation is stored in
Y
1
. Residuals are calculated and stored automatically in the list name
RESID
.
26. Press s. The regression line and the scatter plot are displayed.
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Getting Started: Pendulum Lengths and Periods
(cont.)
The new function y=.192x
.522 appears to fit the data well. To get more information, examine a residual plot.
27. Press o to display the
Y=
editor.
Press  Í to deselect
Y
1
.
Press } Í to turn off plot 1. Press ~
Í to turn on plot 2.
Note: Step 19 defined plot 2 to plot residuals (
RESID) versus string length (
L
1
).
28. Press q
9
to select
9:ZoomStat
from the
ZOOM
menu. The window variables are adjusted automatically, and plot 2 is displayed. This is a scatter plot of the residuals.
The new residual plot shows that the residuals are random in sign, with the residuals increasing in magnitude as the string length increases.
To see the magnitudes of the residuals, continue with these steps.
29. Press r.
Press ~ and  to trace the data. Observe the values for
Y
at each point.
With this model, the largest positive residual is about 0.041 and the smallest negative residual is about L0.027. All other residuals are less than 0.02 in magnitude.
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Now that you have a good model for the relationship between length and period, you can use the model to predict the period for a given string length. To predict the periods for a pendulum with string lengths of 20 cm and 50 cm, continue with these steps.
30. Press ~
1
to display the
VARS
Y.VARS FUNCTION
secondary menu, and then press
1
to select
1:Y
1
.
Y
1
is pasted to the home screen.
31. Press £
20
¤ to enter a string length of 20 cm.
Press Í to calculate the predicted time of about 0.92 seconds.
Based on the residual analysis, we would expect the prediction of about 0.92 seconds to be within about 0.02 seconds of the actual value.
32. Press y [
ENTRY
] to recall the Last Entry.
Press   
5
to change the string length to 50 cm.
33. Press Í to calculate the predicted time of about 1.48 seconds.
Since a string length of 50 cm exceeds the lengths in the data set, and since residuals appear to be increasing as string length increases, we would expect more error with this estimate.
Note: You also can make predictions using the table with the
TABLE SETUP settings Indpnt:Ask and
Depend:Auto (Chapter 7).
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Setting Up Statistical Analyses
Using Lists to
Store Data
Setting Up a
Statistical
Analysis
Displaying the
Stat List Editor
Data for statistical analyses is stored in lists, which you can create and edit using the stat list editor. The TI82 STATS has six list variables in memory,
L
1
through
L
6
, to which you can store data for statistical calculations. Also, you can store data to list names that you create (Chapter 11).
To set up a statistical analysis, follow these steps. Read the chapter for details.
1. Enter the statistical data into one or more lists.
2. Plot the data.
3. Calculate the statistical variables or fit a model to the data.
4. Graph the regression equation for the plotted data.
5. Graph the residuals list for the given regression model.
The stat list editor is a table where you can store, edit, and view up to 20 lists that are in memory. Also, you can create list names from the stat list editor.
To display the stat list editor, press …, and then select
1:Edit
from the
STAT EDIT
menu.
The top line displays list names.
L
1
through
L
6
are stored in columns
1
through
6
after a memory reset. The number of the current column is displayed in the topright corner.
The bottom line is the entry line. All data entry occurs on this line. The characteristics of this line change according to the current context (page 12.17).
The center area displays up to seven elements of up to three lists; it abbreviates values when necessary. The entry line displays the full value of the current element.
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Using the Stat List Editor
Entering a List
Name in the Stat
List Editor
To enter a list name in the stat list editor, follow these steps.
1. Display the
Name=
prompt in the entry line in either of two ways.
•
Move the cursor onto the list name in the column where you want to insert a list, and then press y [
INS
]. An unnamed column is displayed and the remaining lists shift right one column.
•
Press } until the cursor is on the top line, and then press
~ until you reach the unnamed column.
Note: If list names are stored to all 20 columns, you must remove a list name to make room for an unnamed column.
The
Name=
prompt is displayed and alphalock is on.
2. Enter a valid list name in any of four ways.
•
Select a name from the
LIST NAMES
menu (Chapter 11).
•
Enter
L
1
,
L
2
,
L
3
,
L
4
,
L
5
, or
L
6
from the keyboard.
•
Enter an existing usercreated list name directly from the keyboard.
•
Enter a new usercreated list name (page 12.12).
3. Press Í or † to store the list name and its elements, if any, in the current column of the stat list editor.
To begin entering, scrolling, or editing list elements, press †.
The rectangular cursor is displayed.
Note: If the list name you entered in step 2 already was stored in another stat list editor column, then the list and its elements, if any, move to the current column from the previous column. Remaining list names shift accordingly.
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Using the Stat List Editor
(continued)
Creating a Name in the Stat List
Editor
To create a name in the stat list editor, follow these steps.
1. Follow step 1 on page 12.11 to display the
Name=
prompt.
2. Press [letter from A to Z or q
] to enter the first letter of the name. The first character cannot be a number.
3. Enter zero to four letters, q, or numbers to complete the new usercreated list name. List names can be one to five characters long.
4. Press Í or † to store the list name in the current column of the stat list editor. The list name becomes an item on the
LIST NAMES
menu (Chapter 11).
Removing a List from the Stat List
Editor
To remove a list from the stat list editor, move the cursor onto the list name and then press {. The list is not deleted from memory; it is only removed from the stat list editor.
Note: To delete a list name from memory, use the
MEMORY
DELETE:List selection screen (Chapter 18).
Removing All
Lists and
Restoring L
1 through L
6
You can remove all usercreated lists from the stat list editor and restore list names
L
1
through
L
6
to columns
1
through
6
in either of two ways.
•
Use
SetUpEditor
with no arguments (page 12.21).
•
Reset all memory (Chapter 18).
Clearing All
Elements from a
List
You can clear all elements from a list in any of five ways.
•
Use
ClrList
to clear specified lists (page 12.20).
•
In the stat list editor, press } to move the cursor onto a list name, and then press ‘ Í.
•
In the stat list editor, move the cursor onto each element, and then press { one by one.
•
On the home screen or in the program editor, enter
0
!dim(
listname
(Chapter 11).
)
to set the dimension of listname to 0
•
Use
ClrAllLists
to clear all lists in memory (Chapter 18).
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Editing a List
Element
To edit a list element, follow these steps.
1. Move the rectangular cursor onto the element you want to edit.
2. Press Í to move the cursor to the entry line.
Note: If you want to replace the current value, you can enter a new value without first pressing
Í. When you enter the first character, the current value is cleared automatically.
3. Edit the element in the entry line.
•
Press one or more keys to enter the new value. When you enter the first character, the current value is cleared automatically.
•
Press ~ to move the cursor to the character before which you want to insert, press y [
INS
], and then enter one or more characters.
•
Press ~ to move the cursor to a character you want to delete, and then press { to delete the character.
To cancel any editing and restore the original element at the rectangular cursor, press ‘ Í.
Note: You can enter expressions and variables for elements.
4. Press Í, }, or † to update the list. If you entered an expression, it is evaluated. If you entered only a variable, the stored value is displayed as a list element.
When you edit a list element in the stat list editor, the list is updated in memory immediately.
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Attaching Formulas to List Names
Attaching a
Formula to a List
Name in Stat List
Editor
You can attach a formula to a list name in the stat list editor, and then display and edit the calculated list elements. When executed, the attached formula must resolve to a list. Chapter 11 describes in detail the concept of attaching formulas to list names.
To attach a formula to a list name that is stored in the stat list editor, follow these steps.
1. Press … Í to display the stat list editor.
2. Press } to move the cursor to the top line.
3. Press  or ~, if necessary, to move the cursor onto the list name to which you want to attach the formula.
Note: If a formula in quotation marks is displayed on the entry line, then a formula is already attached to the list name. To edit the formula, press
Í, and then edit the formula.
4. Press ƒ [
ã
], enter the formula, and press ƒ [
ã
].
Note: If you do not use quotation marks, the TI82 STATS calculates and displays the same initial list of answers, but does not attach the formula for future calculations.
Note: Any usercreated list name referenced in a formula must be preceded by an
ÙÙÙÙ symbol (Chapter 11).
5. Press Í. The TI82 STATS calculates each list element and stores it to the list name to which the formula is attached.
A lock symbol is displayed in the stat list editor, next to the list name to which the formula is attached.
lock symbol
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Using the Stat
List Editor When
Formula
Generated Lists
Are Displayed
When you edit an element of a list referenced in an attached formula, the TI82 STATS updates the corresponding element in the list to which the formula is attached (Chapter 11).
When a list with a formula attached is displayed in the stat list editor and you edit or enter elements of another displayed list, then the TI82 STATS takes slightly longer to accept each edit or entry than when no lists with formulas attached are in view.
Tip: To speed editing time, scroll horizontally until no lists with formulas are displayed, or rearrange the stat list editor so that no lists with formulas are displayed.
Handling Errors
Resulting from
Attached
Formulas
On the home screen, you can attach to a list a formula that references another list with dimension 0 (Chapter 11). However, you cannot display the formulagenerated list in the stat list editor or on the home screen until you enter at least one element to the list that the formula references.
All elements of a list referenced by an attached formula must be valid for the attached formula. For example, if
Real
number mode is set and the attached formula is
log(L
1
)
, then each element of
L
1
must be greater than 0, since the logarithm of a negative number returns a complex result.
Tip: If an error menu is returned when you attempt to display a formulagenerated list in the stat list editor, you can select 2:Goto, write down the formula that is attached to the list, and then press
‘ Í to detach (clear) the formula. You then can use the stat list editor to find the source of the error. After making the appropriate changes, you can reattach the formula to a list.
If you do not want to clear the formula, you can select
1:Quit, display the referenced list on the home screen, and find and edit the source of the error. To edit an element of a list on the home screen, store the new value to listname (element#) (Chapter 11).
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Detaching Formulas from List Names
Detaching a
Formula from a
List Name
Editing an
Element of a
Formula
Generated List
You can detach (clear) a formula from a list name in any of four ways.
•
In the stat list editor, move the cursor onto the name of the list to which a formula is attached. Press Í
‘ Í. All list elements remain, but the formula is detached and the lock symbol disappears.
•
In the stat list editor, move the cursor onto an element of the list to which a formula is attached. Press Í, edit the element, and then press Í. The element changes, the formula is detached, and the lock symbol disappears. All other list elements remain.
•
Use
ClrList
(page 12.20). All elements of one or more specified lists are cleared, each formula is detached, and each lock symbol disappears. All list names remain.
•
Use
ClrAllLists
(Chapter 18). All elements of all lists in memory are cleared, all formulas are detached from all list names, and all lock symbols disappear. All list names remain.
As described above, one way to detach a formula from a list name is to edit an element of the list to which the formula is attached. The TI82 STATS protects against inadvertently detaching the formula from the list name by editing an element of the formulagenerated list.
Because of the protection feature, you must press Í before you can edit an element of a formulagenerated list.
The protection feature does not allow you to delete an element of a list to which a formula is attached. To delete an element of a list to which a formula is attached, you must first detach the formula in any of the ways described above.
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Switching Stat List Editor Contexts
Stat List Editor
Contexts
The stat list editor has four contexts.
•
Viewelements context
•
Viewnames context
•
•
Editelements context
Entername context
The stat list editor is first displayed in viewelements context.
To switch through the four contexts, select
1:Edit
from the
STAT EDIT
menu and follow these steps.
1. Press } to move the cursor onto a list name. You are now in viewnames context. Press ~ and  to view list names stored in other stat list editor columns.
2. Press Í. You are now in editelements context. You may edit any element in a list. All elements of the current list are displayed in braces (
{ }
)in the entry line. Press ~ and
 to view more list elements.
3. Press Í again. You are now in viewelements context.
Press ~, , †, and } to view other list elements. The current element’s full value is displayed in the entry line.
4. Press Í again. You are now in editelements context.
You may edit the current element in the entry line.
5. Press } until the cursor is on a list name, then press y
[
INS
]. You are now in entername context.
6.
Press ‘. You are now in viewnames context.
7.
Press †. You are now back in viewelements context.
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Stat List Editor Contexts
ViewElements
Context
In viewelements context, the entry line displays the list name, the current element’s place in that list, and the full value of the current element, up to 12 characters at a time. An ellipsis (
...
) indicates that the element continues beyond 12 characters.
EditElements
Context
To page down the list six elements, press ƒ †. To page up six elements, press ƒ }. To delete a list element, press
{. Remaining elements shift up one row. To insert a new element, press y [
INS
].
0
is the default value for a new element.
In editelements context, the data displayed in the entry line depends on the previous context.
•
When you switch to editelements context from viewelements context, the full value of the current element is displayed. You can edit the value of this element, and then press † and } to edit other list elements.
&
•
When you switch to editelements context from viewnames context, the full values of all elements in the list are displayed. An ellipsis indicates that list elements continue beyond the screen. You can press ~ and  to edit any element in the list.
&
Note: In editelements context, you can attach a formula to a list name only if you switched to it from viewnames context.
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ViewNames
Context
In viewnames context, the entry line displays the list name and the list elements.
EnterName
Context
To remove a list from the stat list editor, press {. Remaining lists shift to the left one column. The list is not deleted from memory.
To insert a name in the current column, press y [
INS
].
Remaining columns shift to the right one column.
In entername context, the
Name=
prompt is displayed in the entry line, and alphalock is on.
At the
Name=
prompt, you can create a new list name, paste a list name from
L
1
to
L
6
from the keyboard, or paste an existing list name from the
LIST NAMES
menu (Chapter 11). The ÙÙÙÙ symbol is not required at the
Name=
prompt.
To leave entername context without entering a list name, press
‘. The stat list editor switches to viewnames context.
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STAT EDIT Menu
STAT EDIT Menu
To display the
STAT EDIT
menu, press ….
EDIT CALC TESTS
1: Edit...
2: SortA(
3: SortD(
4: ClrList
5: SetUpEditor
Displays the stat list editor.
Sorts a list in ascending order.
Sorts a list in descending order.
Deletes all elements of a list.
Stores lists in the stat list editor.
Note: Chapter 13: Inferential Statistics describes the
STAT TESTS menu items.
SortA(, SortD( SortA(
(sort ascending) sorts list elements from low to high values.
SortD(
(sort descending) sorts list elements from high to low values. Complex lists are sorted based on magnitude
(modulus).
SortA(
and
SortD(
each can sort in either of two ways.
•
With one listname,
SortA(
and
SortD(
sort the elements in
listname and update the list in memory.
•
With two or more lists,
SortA(
and
SortD(
sort keylistname, and then sort each dependlist by placing its elements in the same order as the corresponding elements in keylistname.
This lets you sort twovariable data on
X
and keep the data pairs together. All lists must have the same dimension.
The sorted lists are updated in memory.
SortA(
listname
)
SortD(
listname
)
SortA(
keylistname
,
dependlist1[
,
dependlist2
,
...
,
dependlist n]
)
SortD(
keylistname
,
dependlist1[
,
dependlist2
,
...
,
dependlist n]
)
ClrList
Note: SortA( and SortD( are the same as SortA( and SortD( on the
LIST OPS menu.
ClrList
clears (deletes) from memory the elements of one or more listnames.
ClrList
also detaches any formula attached to a
listname.
ClrList
listname1
,
listname2
,
...
,
listname n
Note: To clear from memory all elements of all list names, use
ClrAllLists (Chapter 18).
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SetUpEditor
With
SetUpEditor
you can set up the stat list editor to display one or more listnames in the order that you specify. You can specify zero to 20 listnames.
SetUpEditor
[listname1
,
listname2
,
...
,
listname n]
SetUpEditor
with one to 20 listnames removes all list names from the stat list editor and then stores listnames in the stat list editor columns in the specified order, beginning in column
1
.
If you enter a listname that is not stored in memory already, then listname is created and stored in memory; it becomes an item on the
LIST NAMES
menu.
Restoring L
1 through L
6
to the
Stat List Editor
SetUpEditor
with no listnames removes all list names from the stat list editor and restores list names
L
1
through
L
6
in the stat list editor columns
1
through
6
.
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Regression Model Features
Regression
Model Features
Automatic
Residual List
STAT CALC
menu items
3
through
C
are regression models
(page 12.24). The automatic residual list and automatic regression equation features apply to all regression models.
Diagnostics display mode applies to some regression models.
When you execute a regression model, the automatic residual list feature computes and stores the residuals to the list name
RESID
.
RESID
becomes an item on the
LIST NAMES
menu
(Chapter 11).
Automatic
Regression
Equation
The TI82 STATS uses the formula below to compute
RESID
list elements. The next section describes the variable
RegEQ
.
RESID
= Ylistname N
RegEQ
(Xlistname)
Each regression model has an optional argument, regequ, for which you can specify a
Y=
variable such as
Y
1
. Upon execution, the regression equation is stored automatically to the specified
Y= variable and the
Y=
function is selected.
Regardless of whether you specify a
Y=
variable for regequ, the regression equation always is stored to the TI82 STATS variable
RegEQ
, which is item
1
on the
VARS Statistics EQ secondary menu.
Note: For the regression equation, you can use the fixeddecimal mode setting to control the number of digits stored after the decimal point (Chapter 1). However, limiting the number of digits to a small number could affect the accuracy of the fit.
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Diagnostics
Display Mode
When you execute some regression models, the TI82 STATS computes and stores diagnostics values for
r
(correlation coefficient) and
r
2
(coefficient of determination) or for
R
2
(coefficient of determination).
r
and
r
2
are computed and stored for these regression models.
LinReg(ax+b)
LinReg(a+bx)
LnReg
ExpReg
PwrReg
R
2
is computed and stored for these regression models.
QuadReg CubicReg QuartReg
The
r
and
r
2
that are computed for
LnReg
,
ExpReg
, and
PwrReg
are based on the linearly transformed data. For example, for
ExpReg
(y=ab^x),
r
and
r
2
are computed on ln y=ln a+x(ln b).
By default, these values are not displayed with the results of a regression model when you execute it. However, you can set the diagnostics display mode by executing the
DiagnosticOn
or
DiagnosticOff
instruction. Each instruction is in the
CATALOG
(Chapter 15).
Note: To set
DiagnosticOn or DiagnosticOff from the home screen, press y [
CATALOG
], and then select the instruction for the mode you want. The instruction is pasted to the home screen. Press
Í to set the mode.
When
DiagnosticOn
is set, diagnostics are displayed with the results when you execute a regression model.
When
DiagnosticOff
is set, diagnostics are not displayed with the results when you execute a regression model.
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STAT CALC Menu
STAT CALC
Menu
Frequency of
Occurrence for
Data Points
To display the
STAT CALC
menu, press … ~.
EDIT CALC TESTS
1: 1Var Stats
2: 2Var Stats
3: MedMed
4: LinReg(ax+b)
5: QuadReg
6: CubicReg
7: QuartReg
8: LinReg(a+bx)
9: LnReg
0: ExpReg
A: PwrReg
B: Logistic
C: SinReg
Calculates 1variable statistics.
Calculates 2variable statistics.
Calculates a medianmedian line.
Fits a linear model to data.
Fits a quadratic model to data.
Fits a cubic model to data.
Fits a quartic model to data.
Fits a linear model to data.
Fits a logarithmic model to data.
Fits an exponential model to data.
Fits a power model to data.
Fits a logistic model to data.
Fits a sinusoidal model to data.
For each
STAT CALC
menu item, if neither Xlistname nor
Ylistname is specified, then the default list names are
L
1
and
L
2
.
If you do not specify freqlist, then the default is
1
occurrence of each list element.
For most
STAT CALC
menu items, you can specify a list of data occurrences, or frequencies (freqlist).
Each element in freqlist indicates how many times the corresponding data point or data pair occurs in the data set you are analyzing.
For example, if
L
1
={15,12,9,14}
and
ÙÙÙÙFREQ={1,4,1,3}
, then the
TI82 STATS interprets the instruction
1.Var Stats L
1
,
ÙÙÙÙFREQ to mean that
15
occurs once,
12
occurs four times,
9
occurs once, and
14
occurs three times.
Each element in freqlist must be ‚ 0, and at least one element must be > 0.
Noninteger freqlist elements are valid. This is useful when entering frequencies expressed as percentages or parts that add up to 1. However, if freqlist contains noninteger frequencies,
Sx
and
Sy
are undefined; values are not displayed for
Sx
and
Sy
in the statistical results.
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1.Var Stats 1.Var Stats
(onevariable statistics) analyzes data with one measured variable. Each element in freqlist is the frequency of occurrence for each corresponding data point in Xlistname.
freqlist elements must be real numbers > 0.
1.Var Stats
[Xlistname
,
freqlist]
2.Var Stats
Med.Med
(ax+b)
2.Var Stats
(twovariable statistics) analyzes paired data.
Xlistname is the independent variable. Ylistname is the dependent variable. Each element in freqlist is the frequency of occurrence for each data pair (Xlistname,Ylistname).
2.Var Stats
[Xlistname
,
Ylistname
,
freqlist]
Med.Med
(medianmedian) fits the model equation y=ax+b to the data using the medianmedian line (resistant line) technique, calculating the summary points
x
1
,
y
1
,
x
2
,
y
2
,
x
3
, and
y
3
.
Med.Med
displays values for
a
(slope) and
b
(yintercept).
Med.Med
[Xlistname
,
Ylistname
,
freqlist
,
regequ]
LinReg
(ax+b)
QuadReg
(ax2+bx+c)
LinReg(ax+b)
(linear regression) fits the model equation y=ax+b to the data using a leastsquares fit. It displays values for
a
(slope) and
b
(yintercept); when
DiagnosticOn
is set, it also displays values for
r
2
and
r
.
LinReg(ax+b)
[Xlistname
,
Ylistname
,
freqlist
,
regequ]
QuadReg
(quadratic regression) fits the seconddegree polynomial y=ax and
c
; when
DiagnosticOn
is set, it also displays a value for
R
are required.
2
+bx+c to the data. It displays values for
a
,
b
,
For three data points, the equation is a polynomial fit; for four or more, it is a polynomial regression. At least three data points
2
.
QuadReg
[Xlistname
,
Ylistname
,
freqlist
,
regequ]
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STAT CALC Menu
(continued)
CubicReg
(ax
3
+bx
2
+cx+d)
CubicReg
(cubic regression) fits the thirddegree polynomial y=ax 3 +bx 2 +cx+d to the data. It displays values for
a
,
b
,
c
, and
d
; when
DiagnosticOn
is set, it also displays a value for
R
2
. For four points, the equation is a polynomial fit; for five or more, it is a polynomial regression. At least four points are required.
CubicReg
[Xlistname
,
Ylistname
,
freqlist
,
regequ]
QuartReg
(ax
4
+bx
3
+cx
2
+ dx+e)
LinReg
(a+bx)
LnReg
(a+b ln(x))
ExpReg
(ab x
)
QuartReg
(quartic regression) fits the fourthdegree polynomial y=ax 4 +bx 3 +cx 2 +dx+e to the data. It displays values for
a
,
b
,
c
,
d
, and
R
2 e
. For five points, the equation is a polynomial fit; for six or more, it is a polynomial regression. At least five points are required.
; when
DiagnosticOn
is set, it also displays a value for
QuartReg
[Xlistname
,
Ylistname
,
freqlist
,
regequ]
LinReg(a+bx)
(linear regression) fits the model equation y=a+bx to the data using a leastsquares fit. It displays values for
a
(yintercept) and
b
(slope); when
DiagnosticOn
is set, it also displays values for
r
2
and
r
.
LinReg(a+bx)
[Xlistname
,
Ylistname
,
freqlist
,
regequ]
LnReg
(logarithmic regression) fits the model equation y=a+b ln(x) to the data using a leastsquares fit and transformed values ln(x) and y. It displays values for
a
and
b
; when
DiagnosticOn
is set, it also displays values for
r
2
and
r
.
LnReg
[Xlistname
,
Ylistname
,
freqlist
,
regequ]
ExpReg
(exponential regression) fits the model equation y=ab x
to the data using a leastsquares fit and transformed values x and ln(y). It displays values for
a
and
b
; when
DiagnosticOn
is set, it also displays values for
r
2
and
r
.
ExpReg
[Xlistname
,
Ylistname
,
freqlist
,
regequ]
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PwrReg
(ax b
)
Logistic c / (1+a
ääääe
Lbx )
SinReg a sin(bx+c)+d
PwrReg
(power regression) fits the model equation y=ax b to the data using a leastsquares fit and transformed values ln(x) and ln(y). It displays values for
a
and
b
; when
DiagnosticOn
is set, it also displays values for
r
2
and
r
.
PwrReg
[Xlistname
,
Ylistname
,
freqlist
,
regequ]
Logistic
fits the model equation y=c / (1+aäe
Lbx
) to the data using an iterative leastsquares fit. It displays values for
a
,
b
, and
c
.
Logistic
[Xlistname
,
Ylistname
,
freqlist
,
regequ]
SinReg
(sinusoidal regression) fits the model equation
y=a sin(bx+c)+d to the data using an iterative leastsquares fit. It displays values for
a
,
b
,
c
, and
d
. At least four data points are required. At least two data points per cycle are required in order to avoid aliased frequency estimates.
SinReg
[iterations,Xlistname,Ylistname,period,regequ]
iterations is the maximum number of times the algorithm will iterate to find a solution. The value for iterations can be an integer ‚ 1 and 16; if not specified, the default is 3. The algorithm may find a solution before iterations is reached.
Typically, larger values for iterations result in longer execution times and better accuracy for
SinReg
, and vice versa.
A period guess is optional. If you do not specify period, the difference between time values in Xlistname must be equal and the time values must be ordered in ascending sequential order. If you specify period, the algorithm may find a solution more quickly, or it may find a solution when it would not have found one if you had omitted a value for period. If you specify period, the differences between time values in Xlistname can be unequal.
Note: The output of
SinReg is always in radians, regardless of the
Radian/Degree mode setting.
A
SinReg
example is shown on the next page.
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STAT CALC Menu
(continued)
SinReg Example:
Daylight Hours in
Alaska for One
Year
Compute the regression model for the number of hours of daylight in Alaska during one year.
&
&
1 period
With noisy data, you will achieve better convergence results when you specify an accurate estimate for period. You can obtain a period guess in either of two ways.
•
Plot the data and trace to determine the xdistance between the beginning and end of one complete period, or cycle. The illustration above and to the right graphically depicts a complete period, or cycle.
•
Plot the data and trace to determine the xdistance between the beginning and end of N complete periods, or cycles.
Then divide the total distance by N.
After your first attempt to use
SinReg
and the default value for
iterations to fit the data, you may find the fit to be approximately correct, but not optimal. For an optimal fit, execute
SinReg 16,
Xlistname
,
Ylistname
,2p /
b where b is the value obtained from the previous
SinReg
execution.
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Statistical Variables
The statistical variables are calculated and stored as indicated below. To access these variables for use in expressions, press , and select
5:Statistics
. Then select the
VARS
menu shown in the column below under
VARS
menu. If you edit a list or change the type of analysis, all statistical variables are cleared.
Variables Other
mean of sum of values sum of
x
2
sample standard deviation of
x
population standard deviation of number of data points mean of
y
values sum of
y
values sum of
y
2
values sample standard deviation of
y x
population standard deviation of
y
sum of
x
…
y
minimum of
x
values maximum of
x
values minimum of
y
values maximum of
y
values
1st quartile median
x x
values
values
3rd quartile regression/fit coefficients polynomial,
Logistic
, and
SinReg
coefficients correlation coefficient coefficient of determination regression equation summary points (
Med.Med
only)
1.Var
Stats v
Gx
Gx
2
Sx sx n minX maxX
Q
1
Med
Q
3 sx n w
Gy
Gy
2
Sy sy
Gxy minX maxX minY maxY
2.Var
Stats v
Gx
Gx
2
Sx
RegEQ x1 y2 a
,
b a
,
b
,
c
,
d
,
e r r
2
,
R
2
,
y1
,
x2
,
,
x3
,
y3
VARS
menu
XY
G
G
XY
XY
XY
XY
G
G
XY
XY
XY
PTS
PTS
PTS
G
XY
XY
XY
EQ
EQ
EQ
EQ
EQ
PTS
Q
1
and Q
3
The first quartile (
Q
1
) is the median of points between
minX
and
Med
(median). The third quartile (
Q
3
) is the median of points between
Med
and
maxX
.
Statistics 12–29
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Statistical Analysis in a Program
Entering Stat
Data
You can enter statistical data, calculate statistical results, and fit models to data from a program. You can enter statistical data into lists directly within the program (Chapter 11).
Statistical
Calculations
To perform a statistical calculation from a program, follow these steps.
1. On a blank line in the program editor, select the type of calculation from the
STAT CALC
menu.
2. Enter the names of the lists to use in the calculation. Separate the list names with a comma.
3. Enter a comma and then the name of a
Y=
variable, if you want to store the regression equation to a
Y=
variable.
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Statistical Plotting
Steps for Plotting
Statistical Data in
Lists
You can plot statistical data that is stored in lists. The six types of plots available are scatter plot, xyLine, histogram, modified box plot, regular box plot, and normal probability plot. You can define up to three plots.
To plot statistical data in lists, follow these steps.
1. Store the stat data in one or more lists.
2. Select or deselect
Y=
functions as appropriate.
3. Define the stat plot.
4. Turn on the plots you want to display.
5. Define the viewing window.
6. Display and explore the graph.
"
(Scatter)
Scatter
plots plot the data points from
Xlist
and
Ylist
as coordinate pairs, showing each point as a box (
›
), cross (
+
), or dot (
¦
).
Xlist
and
Ylist
must be the same length. You can use the same list for
Xlist
and
Ylist
.
Ó
(xyLine) xyLine
is a scatter plot in which the data points are plotted and connected in order of appearance in
Xlist
and
Ylist
. You may want to use
SortA(
or
SortD(
to sort the lists before you plot them (page 12.20).
Statistics 12–31
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Statistical Plotting
(continued)
Ò
(Histogram)
Histogram
plots onevariable data. The
Xscl
window variable value determines the width of each bar, beginning at
Xmin
.
ZoomStat
adjusts
Xmin
,
Xmax
,
Ymin
, and
Ymax
to include all values, and also adjusts
Xscl
. The inequality
(
Xmax
N
Xmin
) à
Xscl
47 must be true. A value that occurs on the edge of a bar is counted in the bar to the right.
Õ
(ModBoxplot)
ModBoxplot
(modified box plot) plots onevariable data, like the regular box plot, except points that are 1.5 ääää Interquartile
Range beyond the quartiles. (The Interquartile Range is defined as the difference between the third quartile
Q
3
and the first quartile
Q
1
.) These points are plotted individually beyond the whisker, using the
Mark
(
›
or
+
or
¦
) you select. You can trace these points, which are called outliers.
The prompt for outlier points is
x=
, except when the outlier is the maximum point (
maxX
) or the minimum point (
minX
).
When outliers exist, the end of each whisker will display
x=
.
When no outliers exist,
minX
and
maxX
are the prompts for the end of each whisker.
Q
1
,
Med
(median), and
Q
3
define the box
(page 12.29).
Box plots are plotted with respect to
Xmin
and
Xmax
, but ignore
Ymin
and
Ymax
. When two box plots are plotted, the first one plots at the top of the screen and the second plots in the middle.
When three are plotted, the first one plots at the top, the second in the middle, and the third at the bottom.
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Ö
(Boxplot)
Boxplot
(regular box plot) plots onevariable data. The whiskers on the plot extend from the minimum data point in the set
(
minX
) to the first quartile (
Q
1
) and from the third quartile (
Q
3
) to the maximum point (
maxX
). The box is defined by
Q
1
,
Med
(median), and
Q
3
(page 12.29).
Box plots are plotted with respect to
Xmin
and
Xmax
, but ignore
Ymin
and
Ymax
. When two box plots are plotted, the first one plots at the top of the screen and the second plots in the middle.
When three are plotted, the first one plots at the top, the second in the middle, and the third at the bottom.
Ô
(NormProbPlot)
NormProbPlot
(normal probability plot) plots each observation
X
in
Data List
versus the corresponding quantile
z
of the standard normal distribution. If the plotted points lie close to a straight line, then the plot indicates that the data are normal.
Enter a valid list name in the
Data List
field. Select
X
or
Y
for the
Data Axis
setting.
•
If you select
X
, the TI82 STATS plots the data on the xaxis and the zvalues on the yaxis.
•
If you select
Y
, the TI82 STATS plots the data on the yaxis and the zvalues on the xaxis.
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Statistical Plotting
(continued)
Defining the
Plots
To define a plot, follow these steps.
1. Press y [
STAT PLOT
]. The
STAT PLOTS
menu is displayed with the current plot definitions.
2. Select the plot you want to use. The stat plot editor is displayed for the plot you selected.
3. Press Í to select
On
if you want to plot the statistical data immediately. The definition is stored whether you select
On
or
Off
.
4. Select the type of plot. Each type prompts for the options checked in this table.
Plot Type
XList YList Mark Freq Data
List
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
Data
Axis
œ
œ
œ
œ
œ
5. Enter list names or select options for the plot type.
•
Xlist
(list name containing independent data)
•
Ylist
(list name containing dependent data)
•
Mark
(
›
or
+
or
¦
)
•
Freq
(frequency list for
Xlist
elements; default is
1
)
•
Data List
(list name for
NormProbPlot
)
•
Data Axis
(axis on which to plot
Data List
)
12–34 Statistics
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Displaying Other
Stat Plot Editors
Each stat plot has a unique stat plot editor. The name of the current stat plot (
Plot1
,
Plot2
, or
Plot3
) is highlighted in the top line of the stat plot editor. To display the stat plot editor for a different plot, press }, ~, and  to move the cursor onto the name in the top line, and then press Í. The stat plot editor for the selected plot is displayed, and the selected name remains highlighted.
Turning On and
Turning Off Stat
Plots
PlotsOn
and
PlotsOff
allow you to turn on or turn off stat plots from the home screen or a program. With no plot number,
PlotsOn
turns on all plots and
PlotsOff
turns off all plots. With one or more plot numbers (
1
,
2
, and
3
),
PlotsOn
turns on specified plots, and
PlotsOff
turns off specified plots.
PlotsOff
[
1,2,3
]
PlotsOn
[
1,2,3
]
Note: You also can turn on and turn off stat plots in the top line of the
Y= editor (Chapter 3).
Statistics 12–35
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PM Page 35 of 38
Statistical Plotting
(continued)
Defining the
Viewing Window
Stat plots are displayed on the current graph. To define the viewing window, press p and enter values for the window variables.
ZoomStat
redefines the viewing window to display all statistical data points.
Tracing a Stat
Plot
When you trace a scatter plot or xyLine, tracing begins at the first element in the lists.
When you trace a histogram, the cursor moves from the top center of one column to the top center of the next, starting at the first column.
When you trace a box plot, tracing begins at
Med
(the median).
Press  to trace to
Q
1
and
minX
. Press ~ to trace to
Q
3
and
maxX
.
When you press } or † to move to another plot or to another
Y= function, tracing moves to the current or beginning point on that plot (not the nearest pixel).
The
ExprOn
/
ExprOff
format setting applies to stat plots
(Chapter 3).When
ExprOn
is selected, the plot number and plotted data lists are displayed in the topleft corner.
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Statistical Plotting in a Program
Defining a Stat
Plot in a Program
To display a stat plot from a program, define the plot, and then display the graph.
To define a stat plot from a program, begin on a blank line in the program editor and enter data into one or more lists; then, follow these steps.
1. Press y [
STAT PLOT
] to display the
STAT PLOTS
menu.
2. Select the plot to define, which pastes
Plot1(
,
Plot2(
, or
Plot3(
to the cursor location.
3. Press y [
STAT PLOT
] ~ to display the
STAT TYPE
menu.
4. Select the type of plot, which pastes the name of the plot type to the cursor location.
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Statistical Plotting in a Program
(continued)
Defining a Stat
Plot in a Program
(continued)
5. Press ¢. Enter the list names, separated by commas.
6. Press ¢ y [
STAT PLOT
]  to display the
STAT PLOT MARK
menu. (This step is not necessary if you selected
3:Histogram
or
5:Boxplot
in step 4.)
Select the type of mark (
›
or
+
or
¦
) for each data point. The selected mark symbol is pasted to the cursor location.
7. Press ¤ Í to complete the command line.
Displaying a Stat
Plot from a
Program
To display a plot from a program, use the
DispGraph
instruction
(Chapter 16) or any of the
ZOOM
instructions (Chapter 3).
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13
Inferential Statistics and Distributions
Contents
Getting Started: Mean Height of a Population
.....................................
Inferential Stat Editors
.........................................................................................
STAT TESTS Menu
.............................................................................................
9
Inferential Statistics Input Descriptions
...................................................
26
2
6
Test and Interval Output Variables
..............................................................
28
Distribution Functions
.........................................................................................
29
Distribution Shading
.............................................................................................
35
Inferential Statistics and Distributions 13–1
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Getting Started: Mean Height of a Population
Getting Started is a fastpaced introduction. Read the chapter for details.
Suppose you want to estimate the mean height of a population of women given the random sample below. Because heights among a biological population tend to be normally distributed, a t distribution confidence interval can be used when estimating the mean. The 10 height values below are the first 10 of 90 values, randomly generated from a normally distributed population with an assumed mean of 165.1 cm.
and a standard deviation of 6.35 cm. (
randNorm(165.1,6.35,90)
with a seed of 789).
Height (in cm.) of Each of 10 Women
169.43 168.33 159.55 169.97 159.79 181.42 171.17 162.04 167.15 159.53
1. Press … Í to display the stat list editor.
Press } to move the cursor onto
L
1
, and then press y [
INS
]. The
Name=
prompt is displayed on the bottom line. The
Ø cursor indicates that alphalock is on. The existing list name columns shift to the right.
Note: Your stat editor may not look like the one pictured here, depending on the lists you have already stored.
2. Enter [
H
] [
G
] [
H
] [
T
] at the
Name=
prompt, and then press Í. The list to which you will store the women’s height data is created.
Press † to move the cursor onto the first row of the list.
HGHT(1)=
is displayed on the bottom line.
3. Press
169
Ë
43
to enter the first height value.
As you enter it, it is displayed on the bottom line.
Press Í. The value is displayed in the first row, and the rectangular cursor moves to the next row.
Enter the other nine height values the same way.
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4. Press …  to display the
STAT TESTS menu, and then press † until
8:TInterval
is highlighted.
5. Press Í to select
8:TInterval
. The inferential stat editor for
TInterval
is displayed. If
Data
is not selected for
Inpt:
, press  Í to select
Data
.
Press † and [
H
] [
G
] [
H
] [
T
] at the
List:
prompt
(alphalock is on).
Press † † Ë
99
to enter a 99 percent confidence level at the
C.Level:
prompt.
6. Press † to move the cursor onto
Calculate
, and then press Í. The confidence interval is calculated, and the
TInterval
results are displayed on the home screen.
Interpret the results.
The first line,
(159.74,173.94)
, shows that the 99 percent confidence interval for the population mean is between about 159.74 cm. and 173.94 cm. This is about a 14.2
cm. spread.
The .99 confidence level indicates that in a very large number of samples, we expect
99 percent of the intervals calculated to contain the population mean. The actual mean of the population sampled is 165.1 cm. (introduction; page 13.2), which is in the calculated interval.
The second line gives the mean height of the sample þ used to compute this interval.
The third line gives the sample standard deviation
Sx
. The bottom line gives the sample size
n
.
Inferential Statistics and Distributions 13–3
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Getting Started: Mean Height of a Population
(cont.)
To obtain a more precise bound on the population mean
m
of women’s heights, increase the sample size to 90. Use a sample mean þ of 163.8 and sample standard deviation
Sx
of 7.1 calculated from the larger random sample (introduction; page
13.2). This time, use the
Stats
(summary statistics) input option.
7. Press … 
8
to display the inferential stat editor for
TInterval
.
Press ~ Í to select
Inpt:Stats
. The editor changes so that you can enter summary statistics as input.
8. Press †
163
Ë
8
Í to store 163.8 to þ .
Press
7
Ë
1
Í to store 7.1 to
Sx
.
Press
90
Í to store 90 to
n
.
9. Press † to move the cursor onto
Calculate
, and then press Í to calculate the new 99 percent confidence interval. The results are displayed on the home screen.
If the height distribution among a population of women is normally distributed with a mean
m
of 165.1 cm. and a standard deviation σσσσ of 6.35 cm., what height is exceeded by only 5 percent of the women (the 95th percentile)?
10. Press ‘ to clear the home screen.
Press y [
DISTR
] to display the
DISTR
(distributions) menu.
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11. Press
3
to paste
invNorm(
to the home screen.
Press Ë
95
¢
165
Ë
1
¢
6
Ë
35
¤ Í.
.95
is the area,
165.1
is µµµµ , and
6.35
is σσσσ .
The result is displayed on the home screen; it shows that five percent of the women are taller than 175.5 cm.
Now graph and shade the top 5 percent of the population.
12. Press p and set the window variables to these values.
Xmin=145
Xmax=185
Xscl=5
Ymin=L.02
Ymax=.08
Yscl=0
Xres=1
13. Press y [
DISTR
] ~ to display the
DISTR
DRAW
menu.
14. Press Í to paste
ShadeNorm(
to the home screen.
Press y [
ANS
] ¢
1
y [
EE
]
99
¢
165
Ë
1
¢
6
Ë
35
¤.
Ans
(175.5448205 from step 11) is the lower bound. 1å99 is the upper bound. The normal curve is defined by a mean µµµµ of 165.1 and a standard deviation σσσσ of 6.35.
15. Press Í to plot and shade the normal curve.
Area
is the area above the 95th percentile.
low
is the lower bound.
up
is the upper bound.
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Inferential Stat Editors
Displaying the
Inferential Stat
Editors
When you select a hypothesis test or confidence interval instruction from the home screen, the appropriate inferential statistics editor is displayed. The editors vary according to each test or interval’s input requirements. Below is the inferential stat editor for
T.Test
.
Using an
Inferential Stat
Editor
Note: When you select the
ANOVA( instruction, it is pasted to the home screen. ANOVA( does not have an editor screen.
To use an inferential stat editor, follow these steps.
1. Select a hypothesis test or confidence interval from the
STAT
TESTS
menu. The appropriate editor is displayed.
2. Select
Data
or
Stats
input, if the selection is available. The appropriate editor is displayed.
3. Enter real numbers, list names, or expressions for each argument in the editor.
4. Select the alternative hypothesis (
ƒ
,
<
, or
>
) against which to test, if the selection is available.
5. Select
No
or
Yes
for the
Pooled
option, if the selection is available.
6. Select
Calculate
or
Draw
(when
Draw
is available) to execute the instruction.
•
When you select
Calculate
, the results are displayed on the home screen.
•
When you select
Draw
, the results are displayed in a graph.
This chapter describes the selections in the above steps for each hypothesis test and confidence interval instruction.
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Select
Data
or
Stats
input
Select an alternative hypothesis
Enter values for arguments
Select or
Calculate
Draw
output
Selecting Data or
Stats
Most inferential stat editors prompt you to select one of two types of input. (
1.PropZInt
and
2.PropZTest
,
1.PropZInt
and
2.PropZInt
,
c
2
.Test
, and
LinRegTTest
do not.)
•
Select
Data
to enter the data lists as input.
•
Select
Stats
to enter summary statistics, such as
þ
,
Sx
, and
n
, as input.
To select
Data
or
Stats
, move the cursor to either
Data
or
Stats
, and then press Í.
Entering the
Values for
Arguments
Selecting an
Alternative
Hypothesis
(ƒ < >)
Inferential stat editors require a value for every argument. If you do not know what a particular argument symbol represents, see the tables on pages 13.26 and 13.27.
When you enter values in any inferential stat editor, the
TI82 STATS stores them in memory so that you can run many tests or intervals without having to reenter every value.
Most of the inferential stat editors for the hypothesis tests prompt you to select one of three alternative hypotheses.
•
The first is a
ƒ
alternative hypothesis, such as
mƒm
0
for the
Z.Test
.
•
The second is a
<
alternative hypothesis, such as
m1<m2
for the
2.SampTTest
.
•
The third is a
>
alternative hypothesis, such as
p1>p2
for the
2.PropZTest
.
To select an alternative hypothesis, move the cursor to the appropriate alternative, and then press Í.
Inferential Statistics and Distributions 13–7
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Inferential Stat Editors
(continued)
Selecting the
Pooled Option
Pooled
(
2.SampTTest
and
2.SampTInt
only) specifies whether the variances are to be pooled for the calculation.
•
Select
No
if you do not want the variances pooled.
Population variances can be unequal.
•
Select
Yes
if you want the variances pooled. Population variances are assumed to be equal.
To select the
Pooled
option, move the cursor to
Yes
, and then press Í.
Selecting
Calculate or
Draw for a
Hypothesis Test
After you have entered all arguments in an inferential stat editor for a hypothesis test, you must select whether you want to see the calculated results on the home screen (
Calculate
) or on the graph screen (
Draw
).
•
Calculate
calculates the test results and displays the outputs on the home screen.
•
Draw
draws a graph of the test results and displays the test statistic and pvalue with the graph. The window variables are adjusted automatically to fit the graph.
To select
Calculate
or
Draw
, move the cursor to either
Calculate
or
Draw
, and then press Í. The instruction is immediately executed.
Selecting
Calculate for a
Confidence
Interval
Bypassing the
Inferential Stat
Editors
After you have entered all arguments in an inferential stat editor for a confidence interval, select
Calculate
to display the results.
The
Draw
option is not available.
When you press Í,
Calculate
calculates the confidence interval results and displays the outputs on the home screen.
To paste a hypothesis test or confidence interval instruction to the home screen without displaying the corresponding inferential stat editor, select the instruction you want from the
CATALOG
menu. Appendix A describes the input syntax for each hypothesis test and confidence interval instruction.
Note: You can paste a hypothesis test or confidence interval instruction to a command line in a program. From within the program editor, select the instruction from either the
CATALOG (Chapter 15) or the STAT TESTS menu.
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STAT TESTS Menu
STAT TESTS
Menu
Inferential Stat
Editors for the
STAT TESTS
Instructions
To display the
STAT TESTS
menu, press … . When you select an inferential statistics instruction, the appropriate inferential stat editor is displayed.
Most
STAT TESTS
instructions store some output variables to memory. Most of these output variables are in the
TEST secondary menu (
VARS
menu;
5:Statistics
). For a list of these variables, see page 13.28.
EDIT CALC TESTS
1: ZTest...
2: TTest...
3: 2SampZTest...
4: 2SampTTest...
5: 1PropZTest...
6: 2PropZTest...
7: ZInterval...
8: TInterval...
9: 2SampZInt...
0: 2SampTInt...
A: 1PropZInt...
B: 2PropZInt...
C: c2Test...
D: 2SampÛ
E: LinRegTTest...
F: ANOVA(
Test for 1 m, known s
Test for 1 m, unknown s
Test comparing 2 m’s, known s’s
Test comparing 2 m’s, unknown s’s
Test for 1 proportion
Test comparing 2 proportions
Confidence interval for 1 m, known s
Confidence interval for 1 m, unknown s
Conf. int. for diff. of 2 m’s, known s’s
Conf. int. for diff. of 2 m’s, unknown s’s
Confidence int. for 1 proportion
Confidence int. for diff. of 2 props
Chisquare test for 2way tables
Test comparing 2 s’s
t test for regression slope and r
Oneway analysis of variance
Note: When a new test or interval is computed, all previous output variables are invalidated.
In this chapter, the description of each
STAT TESTS
instruction shows the unique inferential stat editor for that instruction with example arguments.
•
Descriptions of instructions that offer the
Data
/
Stats
input choice show both types of input screens.
•
Descriptions of instructions that do not offer the
Data
/
Stats
input choice show only one input screen.
The description then shows the unique output screen for that instruction with the example results.
•
Descriptions of instructions that offer the
Calculate
/
Draw
output choice show both types of screens: calculated and graphic results.
•
Descriptions of instructions that offer only the
Calculate
output choice show the calculated results on the home screen.
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STAT TESTS Menu
(continued)
Z.Test
Z.Test
(onesample z test; item
1
) performs a hypothesis test for a single unknown population mean
m
when the population standard deviation
H s
is known. It tests the null hypothesis
0
: m=m
0
against one of the alternatives below.
•
H a
: mƒm
0
(
m:ƒm
0
)
•
H a
: m<m
0
(
m:<m
0
)
•
H a
: m>m
0
(
m:>m
0
)
In the example:
L
1
={299.4 297.7 301 298.9 300.2 297}
Data Stats
Input:
, ,
Calculated results:
, ,
Drawn results:
Note: All examples on pages13.10 through 13.25 assume a fixeddecimal mode setting of
4 (Chapter 1). If you set the decimal mode to
Float or a different fixeddecimal setting, your output may differ from the output in the examples.
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T.Test
Input:
T.Test
(onesample t test; item
2
) performs a hypothesis test for a single unknown population mean
m
when the population standard deviation s is unknown. It tests the null hypothesis
H
0
: m=m
0
against one of the alternatives below.
•
H a
: mƒm
0
(
m:ƒm
0
)
•
H a
: m<m
0
(
m:<m
0
)
•
H a
: m>m
0
(
m:>m
0
)
In the example:
TEST={91.9 97.8 111.4 122.3 105.4 95}
Data Stats
, ,
Calculated results:
, ,
Drawn results:
Inferential Statistics and Distributions 13–11
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STAT TESTS Menu
(continued)
2.SampZTest
2.SampZTest
(twosample z test; item
3
) tests the equality of the means of two populations (m
1
and m
2
0
: m
1
=m
) based on independent samples when both population standard deviations (s are known. The null hypothesis H of the alternatives below.
1
and s
2
)
2
is tested against one
•
H a
: m
1
ƒm
2
(
m1:ƒm2
)
•
H a
: m
1
<m
•
H a
: m
1
>m
2
2
(
m1:<m2
)
(
m1:>m2
)
In the example:
LISTA={154 109 137 115 140}
LISTB={108 115 126 92 146}
Data Stats
Input:
, ,
Calculated results:
, ,
Drawn results:
13–12 Inferential Statistics and Distributions
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2.SampTTest
2.SampTTest
(twosample t test; item
4
) tests the equality of the means of two populations (m samples when neither population standard deviation (s known. The null hypothesis H the alternatives below.
1
and m
2
) based on independent
0
: m
1
=m
1
or s
2
) is
2
is tested against one of
•
H a
: m
1
ƒm
2
(
m1:ƒm2
)
•
H a
: m
1
<m
•
H a
: m
1
>m
2
2
(
m1:<m2
)
(
m1:>m2
)
In the example:
SAMP1={12.207 16.869 25.05 22.429 8.456 10.589}
SAMP2={11.074 9.686 12.064 9.351 8.182 6.642}
Data Stats
Input:
, ,
Calculated results:
, ,
Drawn results:
Inferential Statistics and Distributions 13–13
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STAT TESTS Menu
(continued)
1.PropZTest
1.PropZTest
(oneproportion z test; item
5
) computes a test for an unknown proportion of successes (prop). It takes as input the count of successes in the sample x and the count of observations in the sample n.
1.PropZTest
tests the null hypothesis
H
0
: prop=p
0
against one of the alternatives below.
•
H a
: propƒp
•
H a
: prop<p
•
H a
: prop>p
0
(
prop:ƒp
0
)
0
(
prop:<p
0
)
0
(
prop:>p
0
)
Input:
,
Calculated results:
,
Drawn results:
13–14 Inferential Statistics and Distributions
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2.PropZTest
2.PropZTest
(twoproportion z test; item
6
) computes a test to compare the proportion of successes (p
1
and p
2
) from two populations. It takes as input the count of successes in each sample (x
1 and x
2
(n
1
and n
2
).
) and the count of observations in each sample
2.PropZTest
tests the null hypothesis H
0
: p
1
=p
(using the pooled sample proportion Ç) against one of the alternatives below.
2
•
H a
: p
1
ƒp
2
(
p1:ƒp2
)
•
H a
: p
1
<p
•
H a
: p
1
>p
2
(
p1:<p2
)
2
(
p1:>p2
)
Input:
,
Calculated results:
,
Drawn results:
Inferential Statistics and Distributions 13–15
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STAT TESTS Menu
(continued)
ZInterval ZInterval
(onesample z confidence interval; item
7
) computes a confidence interval for an unknown population mean m when the population standard deviation s
is known. The computed confidence interval depends on the userspecified confidence level.
In the example:
L
1
={299.4 297.7 301 298.9 300.2 297}
Data Stats
Input:
, ,
Calculated results:
13–16 Inferential Statistics and Distributions
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TInterval
Input:
TInterval
(onesample t confidence interval; item
8
) computes a confidence interval for an unknown population mean m when the population standard deviation s is unknown. The computed confidence interval depends on the userspecified confidence level.
In the example:
L
6
={1.6 1.7 1.8 1.9}
Data Stats
, ,
Calculated results:
Inferential Statistics and Distributions 13–17
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STAT TESTS Menu
(continued)
2.SampZInt
2.SampZInt
(twosample z confidence interval; item
9
) computes a confidence interval for the difference between two population means (m deviations ( s
1
and s
2
1
Nm
2
) when both population standard
) are known. The computed confidence interval depends on the userspecified confidence level.
In the example:
LISTC={154 109 137 115 140}
LISTD={108 115 126 92 146}
Data Stats
Input:
, ,
Calculated results:
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2.SampTInt
2.SampTInt
(twosample t confidence interval; item
0
) computes a confidence interval for the difference between two population means (m deviations ( s
1
and s
2
1
Nm
2
) when both population standard
) are unknown. The computed confidence interval depends on the userspecified confidence level.
In the example:
SAMP1={12.207 16.869 25.05 22.429 8.456 10.589}
SAMP2={11.074 9.686 12.064 9.351 8.182 6.642}
Data Stats
Input:
, ,
Calculated results:
Inferential Statistics and Distributions 13–19
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STAT TESTS Menu
(continued)
1.PropZInt
1.PropZInt
(oneproportion z confidence interval; item
A
) computes a confidence interval for an unknown proportion of successes. It takes as input the count of successes in the sample
x and the count of observations in the sample n. The computed confidence interval depends on the userspecified confidence level.
Input:
,
Calculated results:
13–20 Inferential Statistics and Distributions
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2.PropZInt
2.PropZInt
(twoproportion z confidence interval; item
B
) computes a confidence interval for the difference between the proportion of successes in two populations (p input the count of successes in each sample (x count of observations in each sample (n
1
1
Np
2
). It takes as
and n
1
2
and x
). The computed confidence interval depends on the userspecified confidence level.
2
) and the
Input:
,
Calculated results:
Inferential Statistics and Distributions 13–21
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STAT TESTS Menu
(continued) c
2
.Test
Matrix editor:
c
2
.Test
(chisquare test; item
C
) computes a chisquare test for association on the twoway table of counts in the specified
Observed matrix. The null hypothesis H
0
for a twoway table is: no association exists between row variables and column variables. The alternative hypothesis is: the variables are related.
Before computing a c 2
.Test, enter the observed counts in a matrix. Enter that matrix variable name at the
Observed:
prompt in the c 2
.Test editor; default=
[A]
. At the
Expected:
prompt, enter the matrix variable name to which you want the computed expected counts to be stored; default=
[B]
.
Note: Press
~ ~ 1 to select 1:[A] from the MATRX
EDIT menu.
Input:
,
Note: Press
[B] Í to display matrix [B].
Calculated results:
,
Drawn results:
13–22 Inferential Statistics and Distributions
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Input:
(twosample Ûtest; item
D
) computes an Ûtest to compare two normal population standard deviations (s
1
and s
2
).
The population means and standard deviations are all unknown.
2.SampÜ
Sx1
2
/Sx2
2
, which uses the ratio of sample variances
, tests the null hypothesis H
0 alternatives below.
: s
1
=s
2
against one of the
•
H a
: s
1
ƒs
2
(
s1:ƒs2
)
•
H a
: s
1
<s
2
(
s1:<s2
)
•
H a
: s
1
>s
2
(
s1:>s2
)
In the example:
SAMP4={ 7 L4 18 17 L3 L5 1 10 11 L2}
SAMP5={ L1 12 L1 L3 3 L5 5 2 L11 L1 L3}
Data Stats
, ,
Calculated results:
, ,
Drawn results:
Inferential Statistics and Distributions 13–23
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STAT TESTS Menu
(continued)
LinRegTTest LinRegTTest
(linear regression t test; item
E
) computes a linear regression on the given data and a t test on the value of slope b and the correlation coefficient r for the equation y=a+bx. It tests the null hypothesis H of the alternatives below.
0
: b=0 (equivalently, r
=0) against one
•
H a
: bƒ0 and rƒ0 (
b & r:ƒ0
)
•
H a
: b<0 and r<0 (
b & r:<0
)
•
H a
: b>0 and r>0 (
b & r:>0
)
The regression equation is automatically stored to
RegEQ
(
VARS Statistics EQ
secondary menu). If you enter a
Y=
variable name at the
RegEQ:
prompt, the calculated regression equation is automatically stored to the specified
Y=
equation. In the example below, the regression equation is stored to
Y
1
, which is then selected (turned on).
In the example:
L
3
={38 56 59 64 74}
L
4
={41 63 70 72 84}
Input:
,
Calculated results:
When
LinRegTTest
is executed, the list of residuals is created and stored to the list name
RESID
automatically.
RESID
is placed on the
LIST NAMES
menu.
Note: For the regression equation, you can use the fix decimal mode setting to control the number of digits stored after the decimal point
(Chapter 1). However, limiting the number of digits to a small number could affect the accuracy of the fit.
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ANOVA( ANOVA(
(oneway analysis of variance; item
F
) computes a oneway analysis of variance for comparing the means of two to 20 populations. The
ANOVA
procedure for comparing these means involves analysis of the variation in the sample data. The null hypothesis H not all m
1
...m
0 k
: m
1
=m
2
=...=m are equal.
k
is tested against the alternative H a
:
ANOVA(
list1
,
list2[
,
...
,
list20]
)
In the example:
L
1
={7 4 6 6 5}
L
2
={6 5 5 8 7}
L
3
={4 7 6 7 6}
Input:
,
Calculated results:
Note:
SS is sum of squares and MS is mean square.
Inferential Statistics and Distributions 13–25
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Inferential Statistics Input Descriptions
The tables in this section describe the inferential statistics inputs discussed in this chapter. You enter values for these inputs in the inferential stat editors. The tables present the inputs in the same order that they appear in this chapter.
Input m
0 s
List
Freq
Calculate v
,
Sx
,
n s1 s2
List1
Freq1 v1
,
Sx2
/
Draw
,
List2
,
Freq2
Sx1
,
n2
Pooled
,
n1
,
v2
,
Description
Hypothesized value of the population mean that you are testing.
The known population standard deviation; must be a real number > 0.
The name of the list containing the data you are testing.
The name of the list containing the frequency values for the data in
List
. Default=1. All elements must be integers  0.
Determines the type of output to generate for tests and intervals.
Calculate
displays the output on the home screen. In tests,
Draw
draws a graph of the results.
Summary statistics (mean, standard deviation, and sample size) for the onesample tests and intervals.
The known population standard deviation from the first population for the twosample tests and intervals. Must be a real number > 0.
The known population standard deviation from the second population for the twosample tests and intervals. Must be a real number > 0.
The names of the lists containing the data you are testing for the twosample tests and intervals. Defaults are
L
1
and
L
2
, respectively.
The names of the lists containing the frequencies for the data in
List1
and
List2
for the twosample tests and intervals.
Defaults=1. All elements must be integers  0.
Summary statistics (mean, standard deviation, and sample size) for sample one and sample two in the twosample tests and intervals.
Specifies whether variances are to be pooled for
2.SampTTest
and
2.SampTInt
.
No
instructs the TI82 STATS not to pool the variances.
Yes
instructs the TI82 STATS to pool the variances.
13–26 Inferential Statistics and Distributions
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Input p
0
x n x1 x2 n1 n2
C.Level
Observed (Matrix)
Expected (Matrix)
Xlist
,
Ylist
RegEQ
Description
The expected sample proportion for
1.PropZTest
. Must be a real number, such that 0 < p
0
< 1.
The count of successes in the sample for the
1.PropZTest
and
1.PropZInt
. Must be an integer ‚ 0.
The count of observations in the sample for the
1.PropZTest
and
1.PropZInt
. Must be an integer > 0.
The count of successes from sample one for the
2.PropZTest
and
2.PropZInt
. Must be an integer ‚ 0.
The count of successes from sample two for the
2.PropZTest
and
2.PropZInt
. Must be an integer ‚ 0.
The count of observations in sample one for the
2.PropZTest
and
2.PropZInt
. Must be an integer > 0.
The count of observations in sample two for the
2.PropZTest
and
2.PropZInt
. Must be an integer > 0.
The confidence level for the interval instructions. Must be ‚ 0 and <100. If it is ‚ 1, it is assumed to be given as a percent and is divided by 100. Default=0.95.
The matrix name that represents the columns and rows for the observed values of a twoway table of counts for the
Observed
be at least 2×2.
c
2
.Test
.
must contain all integers ‚ 0. Matrix dimensions must
The matrix name that specifies where the expected values should be stored.
Expected
is created upon successful completion of the c 2
.
Test
.
The names of the lists containing the data for
LinRegTTest
.
Defaults are
L
1
and
L
2
, respectively. The dimensions of
Xlist
and
Ylist
must be the same.
The prompt for the name of the
Y= variable where the calculated regression equation is to be stored. If a
Y= variable is specified, that equation is automatically selected (turned on). The default is to store the regression equation to the
RegEQ
variable only.
Inferential Statistics and Distributions 13–27
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Test and Interval Output Variables
The inferential statistics variables are calculated as indicated below. To access these variables for use in expressions, press ,
5
(
5:Statistics
), and then select the
VARS
menu listed in the last column below.
Variables
pvalue test statistics degrees of freedom sample mean of x values for sample
1 and sample 2 sample standard deviation of x for sample 1 and sample 2 number of data points for sample 1 and sample 2 pooled standard deviation estimated sample proportion estimated sample proportion for population 1 estimated sample proportion for population 2 confidence interval pair
Tests Intervals p z
,
t
,
c
2
, Ü
df
Sx1,
Sx2
SxP df v1
,
v2 v1
,
v2
Sx1
Sx2
SxP
,
n1
,
n2 n1
,
n2
LinRegTTest,
ANOVA p t
, Ü
df
SxP
TEST
TEST
TEST
TEST
TEST
TEST
TEST mean of x values sample standard deviation of x number of data points standard error about the line regression/fit coefficients correlation coefficient coefficient of determination regression equation
v
Sx n lower upper
,
v
Sx n s a
,
b r r
2
RegEQ
VARS
Menu
TEST
TEST
TEST
TEST
EQ
EQ
EQ
EQ
XY
XY
XY
TEST
13–28 Inferential Statistics and Distributions
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Distribution Functions
DISTR menu normalpdf(
To display the
DISTR
menu, press y [
DISTR
].
DISTR DRAW
1: normalpdf(
2: normalcdf(
3: invNorm(
4: tpdf(
5: tcdf(
6: c
2 pdf(
7: c
2 cdf
8: Üpdf(
9: Ücdf(
0: binompdf(
A: binomcdf(
B: poissonpdf(
C: poissoncdf(
D: geometpdf(
E: geometcdf(
Normal probability density
Normal distribution probability
Inverse cumulative normal distribution
Studentt probability density
Studentt distribution probability
Chisquare probability density
Chisquare distribution probability
Û probability density
Û distribution probability
Binomial probability
Binomial cumulative density
Poisson probability
Poisson cumulative density
Geometric probability
Geometric cumulative density
Note: L1å99 and 1å99 specify infinity. If you want to view the area left of upperbound, for example, specify lowerbound=L1å99.
norwmalpdf(
computes the probability density function (pdf) for the normal distribution at a specified x value. The defaults are mean m
=0 and standard deviation s
=1. To plot the normal distribution, paste
normalpdf(
to the
Y=
editor. The probability density function (pdf) is:
f x
=
1
2
π σ
e
−
( x
−
2
σ
µ
2
)
2
,
σ >
0
normalpdf(
x[
,
m
,
s]
)
Note: For this example,
Xmin = 28
Xmax = 42
Ymin = 0
Ymax = .25
Tip: For plotting the normal distribution, you can set window variables
Xmin and Xmax so that the mean m falls between them, and then select 0:ZoomFit from the ZOOM menu.
Inferential Statistics and Distributions 13–29
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Distribution Functions
(continued) normalcdf( normalcdf(
computes the normal distribution probability between lowerbound and upperbound for the specified mean and standard deviation and s
=1.
s
. The defaults are m
=0 m
normalcdf(
lowerbound
,
upperbound[
,
m
,
s
]
) invNorm( invNorm(
computes the inverse cumulative normal distribution function for a given area under the normal distribution curve specified by mean m
and standard deviation value associated with an area to the left of the x value.
0 area 1 must be true. The defaults are m s
. It calculates the x
=0 and s
=1.
invNorm(
area[
,
m
,
s
]
) tpdf( tpdf(
computes the probability density function (pdf) for the
Studentt distribution at a specified x value. df (degrees of freedom) must be >0. To plot the Studentt distribution, paste
tpdf(
to the
Y=
editor. The probability density function (pdf) is:
=
Γ
[(
df
Γ
(
df
+
/
2 )
/
( 1
+
/
)
−
(
df
+
π
df
tpdf(
x
,
df
)
Note: For this example,
Xmin = L4.5
Xmax = 4.5
Ymin = 0
Ymax = .4
13–30 Inferential Statistics and Distributions
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tcdf( c
2 pdf( tcdf(
computes the Studentt distribution probability between
lowerbound and upperbound for the specified df (degrees of freedom), which must be > 0.
tcdf(
lowerbound
,
upperbound
,
df
)
c
2 pdf(
computes the probability density function (pdf) for the c 2
(chisquare) distribution at a specified x value. df (degrees of freedom) must be an integer > 0. To plot the c 2 paste c
(pdf) is:
2 pdf(
to the
Y=
distribution,
editor. The probability density function
=
1
Γ
(
df /
2 )
c
2 pdf(
x
,
df
)
(1/2)
df /
2
x df /
2
−
1
e
−
x /
2
, x
≥
0
Note: For this example,
Xmin = 0
Xmax = 30
Ymin = L.02
Ymax = .132
c
2 cdf( c
2 cdf(
computes the c 2 (chisquare) distribution probability between lowerbound and upperbound for the specified df
(degrees of freedom), which must be an integer > 0.
c
2 cdf(
lowerbound
,
upperbound
,
df
)
Inferential Statistics and Distributions 13–31
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Distribution Functions
(continued)
computes the probability density function (pdf) for the Û distribution at a specified x value. numerator df (degrees of freedom) and denominator df must be integers > 0. To plot the Û distribution, paste Ü density function (pdf) is:
to the
Y=
editor. The probability
=
Γ
[(
Γ
(
n /
2
Γ
d /
2 )
n d
n
/
2
x n /
( 1
+
)
−
(
n
+
d
)
/
2
, x
≥
0 where n = numerator degrees of freedom
d = denominator degrees of freedom
x
,
numerator df
,
denominator df
)
Note: For this example,
Xmin = 0
Xmax = 5
Ymin = 0
Ymax = 1
computes the Û distribution probability between
lowerbound and upperbound for the specified numerator df
(degrees of freedom) and denominator df. numerator df and
denominator df must be integers >0.
lowerbound
,
upperbound
,
numerator df
,
denominator df
)
13–32 Inferential Statistics and Distributions
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binompdf( binompdf(
computes a probability at x for the discrete binomial distribution with the specified numtrials and probability of success (p) on each trial. x can be an integer or a list of integers.
0p1 must be true. numtrials must be an integer > 0. If you do not specify x, a list of probabilities from 0 to numtrials is returned. The probability density function (pdf) is:
=
n
x p x
( 1
−
p
)
n
−
x
, x
=
n
where
n = numtrials
binompdf(
numtrials
,
p[
,
x ]
) binomcdf( binomcdf(
computes a cumulative probability at x for the discrete binomial distribution with the specified numtrials and probability of success (p) on each trial. x can be a real number or a list of real numbers. 0p1 must be true. numtrials must be an integer > 0. If you do not specify x, a list of cumulative probabilities is returned.
binomcdf(
numtrials
,
p[
,
x ]
) poissonpdf( poissonpdf(
computes a probability at x for the discrete Poisson distribution with the specified mean m, which must be a real number > 0. x can be an integer or a list of integers. The probability density function (pdf) is:
f x
=
e
− µ
µ
x
/ x x
=
poissonpdf(
m
,
x
)
Inferential Statistics and Distributions 13–33
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Distribution Functions
(continued) poissoncdf( poissoncdf(
computes a cumulative probability at x for the discrete Poisson distribution with the specified mean m, which must be a real number > 0. x can be a real number or a list of real numbers.
poissoncdf(
m
,
x
) geometpdf( geometpdf(
computes a probability at x, the number of the trial on which the first success occurs, for the discrete geometric distribution with the specified probability of success p. 0p1 must be true. x can be an integer or a list of integers. The probability density function (pdf) is:
f x
=
p
( 1
−
p
)
x
−
1
, x
=
geometpdf(
p
,
x
) geometcdf( geometcdf(
computes a cumulative probability at x, the number of the trial on which the first success occurs, for the discrete geometric distribution with the specified probability of success
p. 0p1 must be true. x can be a real number or a list of real numbers.
geometcdf(
p
,
x
)
13–34 Inferential Statistics and Distributions
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Distribution Shading
DISTR DRAW
Menu
ShadeNorm(
To display the
DISTR DRAW
menu, press y [
DISTR
] ~.
DISTR DRAW
instructions draw various types of density functions, shade the area specified by lowerbound and
upperbound, and display the computed area value.
To clear the drawings, select
1:ClrDraw
from the
DRAW
menu
(Chapter 8).
Note: Before you execute a
DISTR DRAW instruction, you must set the window variables so that the desired distribution fits the screen.
DISTR DRA
W
1: ShadeNorm(
2: Shade_t(
3: Shadec
4: ShadeÛ
2
(
Shades normal distribution.
Shades Studentt distribution.
Shades c 2 distribution.
Shades Û distribution.
Note: L1å99 and 1å99 specify infinity. If you want to view the area left of upperbound, for example, specify lowerbound=L1å99.
ShadeNorm(
draws the normal density function specified by mean m and standard deviation s and shades the area between
lowerbound and upperbound. The defaults are m =0 and s =1.
ShadeNorm(
lowerbound
,
upperbound[
,
m
,
s]
)
Note: For this example,
Xmin = 55
Xmax = 72
Ymin = L.05
Ymax = .2
Inferential Statistics and Distributions 13–35
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Distribution Shading
(continued)
Shade_t( Shade_t(
draws the density function for the Studentt distribution specified by df (degrees of freedom) and shades the area between lowerbound and upperbound.
Shade_t(
lowerbound
,
upperbound
,
df
)
Note: For this example,
Xmin = L3
Xmax = 3
Ymin = L.15
Ymax = .5
Shadec
2
( Shadec
2
(
draws the density function for the c 2 (chisquare) distribution specified by df (degrees of freedom) and shades the area between lowerbound and upperbound.
Shadec
2
(
lowerbound
,
upperbound
,
df
)
Note: For this example,
Xmin = 0
Xmax = 35
Ymin = L.025
Ymax = .1
Shade
Ü(
Shade
Ü( draws the density function for the Û distribution specified by numerator df (degrees of freedom) and
denominator df and shades the area between lowerbound and
upperbound.
Shade
Ü(
lowerbound
,
upperbound
,
numerator df
,
denominator df
)
Note: For this example,
Xmin = 0
Xmax = 5
Ymin = L.25
Ymax = .9
13–36 Inferential Statistics and Distributions
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14
Financial
Functions
Contents
Getting Started: Financing a Car
...................................................................
Getting Started: Computing Compound Interest
................................
Using the TVM Solver
.........................................................................................
Using the Financial Functions
........................................................................
Calculating Time Value of Money ( TVM )
..............................................
Calculating Cash Flows
......................................................................................
Calculating Amortization
...................................................................................
9
Calculating Interest Conversion
....................................................................
12
6
8
Finding Days between Dates/Defining Payment Method
.......................
13
Using the
TVM
Variables
...................................................................................
14
4
5
2
3
Financial Functions 14–1
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Getting Started: Financing a Car
Getting Started is a fastpaced introduction. Read the chapter for details.
You have found a car you would like to buy. The car costs 9,000. You can afford payments of 250 per month for four years. What annual percentage rate (APR) will make it possible for you to afford the car?
1. Press z † ~ ~ ~ Í to set the fixeddecimal mode setting to
2
. The
TI82 STATS will display all numbers with two decimal places.
2. Press y [
FINANCE
] to display the
FINANCE CALC
menu.
3. Press Í to select
1:TVM Solver
. The
TVM
Solver
is displayed.
Press
48
Í to store 48 months to
Ú
. Press
†
9000
Í to store 9,000 to
PV
. Press Ì
250
Í to store L250 to
PMT
. (Negation indicates cash outflow.) Press
0
Í to store
0 to
FV
. Press
12
Í to store 12 payments per year to
P/Y
and 12 compounding periods per year to
C/Y
. Setting
P/Y
to 12 will compute an annual percentage rate
(compounded monthly) for
æ
. Press † Í to select
PMT:END
, which indicates that payments are due at the end of each period.
4. Press } } } } } } to move the cursor to the for
æ
æ prompt. Press ƒ [
SOLVE
] to solve
. What APR should you look for?
14–2 Financial Functions
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Getting Started: Computing Compound Interest
At what annual interest rate, compounded monthly, will 1,250 accumulate to 2,000 in
7 years?
Note: Because there are no payments when you solve compound interest problems,
PMT
must be set to 0 and P/Y must be set to 1.
1. Press y [
FINANCE
] to display the
FINANCE
CALC
menu.
2. Press Í to select
1:TVM Solver
. Press
7
to enter the number of periods in years. Press †
† Ì
1250
to enter the present value as a cash outflow (investment). Press †
0
to specify no payments. Press †
2000
to enter the future value as a cash inflow (return). Press †
1
to enter payment periods per year. Press †
12
to set compounding periods per year to
12
.
3. Press } } } } } to place the cursor on the
prompt.
4. Press ƒ [
SOLVE
] to solve for æ, the annual interest rate.
Financial Functions 14–3
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PM Page 3 of 14
Using the TVM Solver
Using the TVM
Solver
The
TVM Solver
displays the timevalueofmoney (
TVM
) variables. Given four variable values, the
TVM Solver
solves for the fifth variable.
The
FINANCE VARS
menu section (page 14.14) describes the five
TVM
variables ( Ú , æ ,
PV
,
PMT
, and
FV
) and
P/Y
and
C/Y
.
PMT: END BEGIN
in the
TVM Solver
corresponds to the
FINANCE CALC
menu items
Pmt_End
(payment at the end of each period) and
Pmt_Bgn
(payment at the beginning of each period).
To solve for an unknown
TVM
variable, follow these steps.
1. Press y [
FINANCE
] Í to display the
TVM Solver
. The screen below shows the default values with the fixeddecimal mode set to two decimal places.
2. Enter the known values for four
TVM
variables.
Note: Enter cash inflows as positive numbers and cash outflows as negative numbers.
3. Enter a value for
P/Y
, which automatically enters the same value for
C/Y
; if
P/Y
ƒ
C/Y
, enter a unique value for
C/Y
.
4. Select
END
or
BEGIN
to specify the payment method.
5. Place the cursor on the
TVM
variable for which you want to solve.
6. Press ƒ [
SOLVE
]. The answer is computed, displayed in the
TVM Solver
, and stored to the appropriate
TVM
variable.
An indicator square in the left column designates the solution variable.
14–4 Financial Functions
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Using the Financial Functions
Entering Cash
Inflows and Cash
Outflows
When using the TI82 STATS financial functions, you must enter cash inflows (cash received) as positive numbers and cash outflows (cash paid) as negative numbers. The TI82 STATS follows this convention when computing and displaying answers.
FINANCE CALC
Menu
To display the
FINANCE CALC
menu, press y [
FINANCE
].
CAL
C
VARS
1: TVM Solver...
2: tvm_Pmt
4: tvm_PV
6: tvm_FV
7: npv(
8: irr(
9: bal(
0: GPrn(
A: GInt(
B: 4Nom(
C: 4Eff(
D: dbd(
E: Pmt_End
F: Pmt_Bgn
Displays the
TVM Solver.
Computes the amount of each payment.
Computes the interest rate per year.
Computes the present value.
Computes the number of payment periods.
Computes the future value.
Computes the net present value.
Computes the internal rate of return.
Computes the amortization sched. balance.
Computes the amort. sched. principal sum.
Computes the amort. sched. interest sum.
Computes the nominal interest rate.
Computes the effective interest rate.
Calculates the days between two dates.
Selects ordinary annuity (end of period).
Selects annuity due (beginning of period).
Use these functions to set up and perform financial calculations on the home screen.
TVM Solver TVM Solver
displays the
TVM Solver
(page 14.4).
Financial Functions 14–5
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Calculating Time Value of Money (TVM)
Calculating Time
Value of Money
Use timevalueofmoney (
TVM
) functions (menu items
2
through
6
) to analyze financial instruments such as annuities, loans, mortgages, leases, and savings.
Each
TVM
function takes zero to six arguments, which must be real numbers. The values that you specify as arguments for these functions are not stored to the
TVM
variables (page 14.14).
Note: To store a value to a
TVM variable, use the TVM Solver (page
14.4) or use ¿ and any TVM variable on the FINANCE VARS menu (page 14.14).
If you enter less than six arguments, the TI82 STATS substitutes a previously stored
TVM
variable value for each unspecified argument.
If you enter any arguments with a
TVM
function, you must place the argument or arguments in parentheses.
tvm_Pmt tvm_Pmt
computes the amount of each payment.
tvm_Pmt
[
(
Ú
,
æ
,
PV
,
FV
,
P/Y
,
C/Y
)
]
Note: In the example above, the values are stored to the
TVM variables in the
TVM Solver. Then the payment (tvm_Pmt) is computed on the home screen using the values in the
TVM Solver.
Next, the interest rate is changed to 9.5 to illustrate the effect on the payment amount.
14–6 Financial Functions
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tvm_
æ
tvm_
æ computes the annual interest rate.
tvm_
æ [
(
Ú
,
PV
,
PMT
,
FV
,
P/Y
,
C/Y
)
]
tvm_PV tvm_PV
computes the present value.
tvm_PV
[
(
Ú
,
æ
,
PMT
,
FV
,
P/Y
,
C/Y
)
]
tvm_
Ú
tvm_
Ú
computes the number of payment periods.
tvm_
Ú
[
(
æ
,
PV
,
PMT
,
FV
,
P/Y
,
C/Y
)
]
tvm_FV tvm_FV
computes the future value.
tvm_FV
[
(
Ú
,
æ
,
PV
,
PMT
,
P/Y
,
C/Y
)
]
Financial Functions 14–7
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PM Page 7 of 14
Calculating Cash Flows
Calculating a
Cash Flow
Use the cash flow functions (menu items
7
and
8
) to analyze the value of money over equal time periods. You can enter unequal cash flows, which can be cash inflows or outflows. The syntax descriptions for
npv( and
irr( use these arguments.
•
interest rate is the rate by which to discount the cash flows
(the cost of money) over one period.
•
CF0 is the initial cash flow at time 0; it must be a real number.
•
CFList is a list of cash flow amounts after the initial cash flow CF0.
•
CFFreq is a list in which each element specifies the frequency of occurrence for a grouped (consecutive) cash flow amount, which is the corresponding element of CFList.
The default is 1; if you enter values, they must be positive integers < 10,000.
For example, express this uneven cash flow in lists.
2000 2000
2000 4000
4000
npv(, irr(
 3000
CF0 =
2000
CFList =
{2000,L3000,4000}
CFFreq =
{2,1,2} npv(
(net present value) is the sum of the present values for the cash inflows and outflows. A positive result for
npv
indicates a profitable investment.
npv(
interest rate
,
CF0
,
CFList[
,
CFFreq]
) irr(
(internal rate of return) is the interest rate at which the net present value of the cash flows is equal to zero.
irr(
CF0
,
CFList[
,
CFFreq]
)
1000
0 5000
3000
 2000  2500
14–8 Financial Functions
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Calculating Amortization
Calculating an
Amortization
Schedule bal(
Use the amortization functions (menu items
9
,
0
, and
A
) to calculate balance, sum of principal, and sum of interest for an amortization schedule.
bal(
computes the balance for an amortization schedule using stored values for æ ,
PV
, and
PMT
. npmt is the number of the payment at which you want to calculate a balance. It must be a positive integer < 10,000. roundvalue specifies the internal precision the calculator uses to calculate the balance; if you do not specify roundvalue, then the TI82 STATS uses the current
Float
/
Fix
decimalmode setting.
bal(
npmt[
,
roundvalue]
)
GPrn(, GInt(
GPrn(
computes the sum of the principal during a specified period for an amortization schedule using stored values for æ ,
PV
, and
PMT
. pmt1 is the starting payment. pmt2 is the ending payment in the range. pmt1 and pmt2 must be positive integers < 10,000.
roundvalue specifies the internal precision the calculator uses to calculate the principal; if you do not specify roundvalue, the
TI82 STATS uses the current
Float
/
Fix
decimalmode setting.
Note: You must enter values for
æ, PV, PMT, and before computing the principal.
GPrn(
pmt1
,
pmt2[
,
roundvalue]
)
GInt(
computes the sum of the interest during a specified period for an amortization schedule using stored values for
æ
,
PV
, and
PMT
. pmt1 is the starting payment. pmt2 is the ending payment in the range. pmt1 and pmt2 must be positive integers < 10,000.
roundvalue specifies the internal precision the calculator uses to calculate the interest; if you do not specify roundvalue, the
TI82 STATS uses the current
Float
/
Fix
decimalmode setting.
GInt(
pmt1
,
pmt2[
,
roundvalue]
)
Financial Functions 14–9
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Calculating Amortization
(continued)
Amortization
Example:
Calculating an
Outstanding
Loan Balance
You want to buy a home with a 30year mortgage at 8 percent
APR. Monthly payments are 800. Calculate the outstanding loan balance after each payment and display the results in a graph and in the table.
1. Press z. Press † ~ ~ ~ Í to set the fixeddecimal mode setting to
2
. Press † † ~ Í to select
Par
graphing mode.
2. Press y [
FINANCE
] Í to display the
TVM Solver
.
3. Press
360
to enter number of payments. Press †
8
to enter the interest rate. Press † † Ì
800
to enter the payment amount. Press †
0
to enter the future value of the mortgage.
Press †
12
to enter the payments per year, which also sets the compounding periods per year to
12
. Press † † Í to select
PMT:END
.
4. Press } } } } } to place the cursor on the
PV
prompt. Press
ƒ [
SOLVE
] to solve for the present value.
5. Press o to display the parametric
Y=
editor. Turn off all stat plots. Press „ to define
X
1T
as
T
. Press † y
[
FINANCE
]
9
„¤ to define
Y
1T
as
bal(T)
.
14–10 Financial Functions
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Amortization
Example:
Calculating an
Outstanding
Loan Balance
(continued)
6. Press p to display the window variables. Enter the values below.
Tmin=0 Xmin=0 Ymin=0
Tmax=360
Tstep=12
Xmax=360
Xscl=50
Ymax=125000
Yscl=10000
7. Press r to draw the graph and activate the trace cursor.
Press ~ and  to explore the graph of the outstanding balance over time. Press a number and then press Í to view the balance at a specific time
T
.
8. Press y [
TBLSET
] and enter the values below.
TblStart=0
@Tbl=12
9. Press y [
TABLE
] to display the table of outstanding balances (
Y
1T
).
10.Press z † † † † † † † ~ ~ Í to select
G.T
splitscreen mode, in which the graph and table are displayed simultaneously.
Press r to display
X
1T
(time) and
Y
1T
(balance) in the table.
Financial Functions 14–11
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Calculating Interest Conversion
Calculating an
Interest
Conversion
4Nom(
Use the interest conversion functions (menu items
B
and
C
) to convert interest rates from an annual effective rate to a nominal rate (
4Nom(
) or from a nominal rate to an annual effective rate
(
4Eff(
).
4Nom(
computes the nominal interest rate. effective rate and
compounding periods must be real numbers. compounding
periods must be >0.
4Nom(
effective rate
,
compounding periods
)
4Eff(
4Eff(
computes the effective interest rate. nominal rate and
compounding periods must be real numbers. compounding
periods must be >0.
4Eff(
nominal rate
,
compounding periods
)
14–12 Financial Functions
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Finding Days between Dates/Defining Payment Method
dbd(
Use the date function
dbd(
(menu item
D
) to calculate the number of days between two dates using the actualdaycount method. date1 and date2 can be numbers or lists of numbers within the range of the dates on the standard calendar.
Note: Dates must be between the years 1950 through 2049.
dbd(
date1
,
date2
)
You can enter date1 and date2 in either of two formats.
•
MM.DDYY (United States)
•
DDMM.YY (Europe)
The decimal placement differentiates the date formats.
Defining the
Payment Method
Pmt_End
and
Pmt_Bgn
(menu items
E
and
F
) specify a transaction as an ordinary annuity or an annuity due. When you execute either command, the
TVM Solver
is updated.
Pmt_End
Pmt_Bgn
Pmt_End
(payment end) specifies an ordinary annuity, where payments occur at the end of each payment period. Most loans are in this category.
Pmt_End
is the default.
Pmt_End
On the
TVM Solver
’s
PMT:END BEGIN
line, select
END
to set
PMT
to ordinary annuity.
Pmt_Bgn
(payment beginning) specifies an annuity due, where payments occur at the beginning of each payment period. Most leases are in this category.
Pmt_Bgn
On the
TVM Solver
’s
PMT:END BEGIN
line, select
BEGIN
to set
PMT
to annuity due.
Financial Functions 14–13
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Using the TVM Variables
FINANCE VARS
Menu
To display the
FINANCE VARS
menu, press y [
FINANCE
] ~.
You can use
TVM
variables in
TVM
functions and store values to them on the home screen.
CALC VAR
S
1: Ú
3: PV
4: PMT
5: FV
6: P/Y
7: C/Y
Total number of payment periods
Annual interest rate
Present value
Payment amount
Future value
Number of payment periods per year
Number of compounding periods/year
FV
P/Y and C/Y
, æ ,
PV
,
PMT
, and
FV
are the five
TVM
variables. They represent the elements of common financial transactions, as described in the table above. æ is an annual interest rate that is converted to a perperiod rate based on the values of
P/Y
and
C/Y
.
P/Y
is the number of payment periods per year in a financial transaction.
C/Y
is the number of compounding periods per year in the same transaction.
When you store a value to
P/Y
, the value for
C/Y
automatically changes to the same value. To store a unique value to
C/Y
, you must store the value to
C/Y
after you have stored a value to
P/Y
.
14–14 Financial Functions
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15
CATALOG, Strings,
Hyperbolic Functions
Contents
Browsing the TI82 STATS CATALOG
..................................................
Entering and Using Strings
...............................................................................
Storing Strings to String Variables
..............................................................
String Functions and Instructions in the CATALOG
........................
Hyperbolic Functions in the CATALOG
..................................................
10
2
3
4
6
CATALOG
, Strings, Hyperbolic Functions 15–1
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AM Page 1 of 10
Browsing the TI82 STATS CATALOG
What Is the
CATALOG?
The
CATALOG
is an alphabetical list of all functions and instructions on the TI82 STATS. You also can access each
CATALOG
item from a menu or the keyboard, except:
•
The six string functions (page 15.6)
•
The six hyperbolic functions (page 15.10)
•
The
solve(
instruction without the equation solver editor
(Chapter 2)
•
The inferential stat functions without the inferential stat editors (Chapter 13)
Note: The only CATALOG programming commands you can execute from the home screen are
GetCalc(, Get(, and Send(.
Selecting an Item from the
CATALOG
To select a
CATALOG
item, follow these steps.
1. Press y ã
CATALOG
ä to display the CATALOG
.
The
4
in the first column is the selection cursor.
2. Press † or } to scroll the
CATALOG
until the selection cursor points to the item you want.
•
To jump to the first item beginning with a particular letter, press that letter; alphalock is on.
•
Items that begin with a number are in alphabetical order according to the first letter after the number. For example,
2.PropZTest(
is among the items that begin with the letter
P
.
•
Functions that appear as symbols, such as
+
,
L1
,
<
, and
‡(
, follow the last item that begins with
Z
. To jump to the first symbol,
!
, press [ q
].
3. Press Í to paste the item to the current screen.
Tip: From the top of the
CATALOG menu, press } to move to the bottom. From the bottom, press
† to move to the top.
15–2
CATALOG
, Strings, Hyperbolic Functions
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Entering and Using Strings
What Is a String?
A string is a sequence of characters that you enclose within quotation marks. On the TI82 STATS, a string has two primary applications.
•
It defines text to be displayed in a program.
•
It accepts input from the keyboard in a program.
Characters are the units that you combine to form a string.
•
Count each number, letter, and space as one character.
•
Count each instruction or function name, such as
sin(
or
cos(
, as one character; the TI82 STATS interprets each instruction or function name as one character.
Entering a String
To enter a string on a blank line on the home screen or in a program, follow these steps.
1. Press ƒ [
ã
] to indicate the beginning of the string.
2. Enter the characters that comprise the string.
•
Use any combination of numbers, letters, function names, or instruction names to create the string.
•
To enter a blank space, press ƒ [
'
].
•
To enter several alpha characters in a row, press y
[
A.LOCK
] to activate alphalock.
3. Press ƒ [
ã
] to indicate the end of the string.
"
string
"
4. Press Í. On the home screen, the string is displayed on the next line without quotations. An ellipsis (
...
) indicates that the string continues beyond the screen. To scroll the entire string, press ~ and .
Note: Quotation marks do not count as string characters.
CATALOG
, Strings, Hyperbolic Functions 15–3
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Storing Strings to String Variables
String Variables
The TI82 STATS has 10 variables to which you can store strings. You can use string variables with string functions and instructions.
To display the
VARS STRING
menu, follow these steps.
1. Press to display the
VARS
menu. Move the cursor to
7:String
.
2. Press Í to display the
STRING
secondary menu.
15–4
CATALOG
, Strings, Hyperbolic Functions
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AM Page 4 of 10
Storing a String to a String
Variable
To store a string to a string variable, follow these steps.
1. Press ƒ [
ã
], enter the string, and press ƒ [
ã
].
2. Press ¿.
3. Press
7
to display the
VARS STRING
menu.
4. Select the string variable (from
Str1
to
Str9
, or
Str0
) to which you want to store the string.
The string variable is pasted to the current cursor location, next to the store symbol ( !
).
5. Press Í to store the string to the string variable. On the home screen, the stored string is displayed on the next line without quotation marks.
Displaying the
Contents of a
String Variable
To display the contents of a string variable on the home screen, select the string variable from the
VARS STRING
menu, and then press Í. The string is displayed.
CATALOG
, Strings, Hyperbolic Functions 15–5
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String Functions and Instructions in the CATALOG
Displaying String
Functions and
Instructions in the CATALOG
String functions and instructions are available only from the
CATALOG
. The table below lists the string functions and instructions in the order in which they appear among the other
CATALOG
menu items. The ellipses in the table indicate the presence of additional
CATALOG
items.
CATALOG
...
Equ4String( expr(
...
inString(
...
length(
...
String4Equ( sub(
...
Converts an equation to a string.
Converts a string to an expression.
Returns a character’s place number.
Returns a string’s character length.
Converts a string to an equation.
Returns a string subset as a string.
+ (Concatenation)
To concatenate two or more strings, follow these steps.
1. Enter string1, which can be a string or string name.
2. Press Ã.
3. Enter string2, which can be a string or string name. If necessary, press Ã and enter string3, and so on.
string1
+
string2
+
string3. . .
4. Press Í to display the strings as a single string.
Selecting a String
Function from the CATALOG
To select a string function or instruction and paste it to the current screen, follow the steps on page 15.2.
15–6
CATALOG
, Strings, Hyperbolic Functions
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Equ4String( Equ4String(
converts to a string an equation that is stored to any
VARS Y.VARS
variable.
Y
n contains the equation.
Str
n (from
Str1
to
Str9
, or
Str0
) is the string variable to which you want the equation to be stored as a string.
Equ4String(Y
n
,Str
n
) expr( expr(
converts the character string contained in string to an expression and executes it. string can be a string or a string variable.
expr(
string
) inString( inString(
returns the character position in string of the first character of substring. string can be a string or a string variable.
start is an optional character position at which to start the search; the default is 1.
inString(
string
,
substring[
,
start]
)
Note: If string does not contain substring, or start is greater than the length of string,
inString( returns 0.
CATALOG
, Strings, Hyperbolic Functions 15–7
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String Functions and Instructions in the CATALOG
(cont.) length( length(
returns the number of characters in string. string can be a string or string variable.
Note: An instruction or function name, such as
sin( or cos(, counts as one character.
length(
string
)
String4Equ( String4Equ(
converts string into an equation and stores the equation to
Y
n. string can be a string or string variable.
String4Equ(
is the inverse of
Equ4String(
.
String4Equ(
string
,Y
n
)
15–8
CATALOG
, Strings, Hyperbolic Functions
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AM Page 8 of 10
sub( sub(
returns a string that is a subset of an existing string. string can be a string or a string variable. begin is the position number of the first character of the subset. length is the number of characters in the subset.
sub(
string
,
begin
,
length
)
Entering a
Function to
Graph during
Program
Execution
In a program, you can enter a function to graph during program execution using these commands.
Note: When you execute this program, enter a function to store to
Y3
at the
ENTRY= prompt.
CATALOG
, Strings, Hyperbolic Functions 15–9
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Hyperbolic Functions in the CATALOG
Hyperbolic
Functions sinh(, cosh(, tanh(
The hyperbolic functions are available only from the
CATALOG
.
The table below lists the hyperbolic functions in the order in which they appear among the other
CATALOG
menu items. The ellipses in the table indicate the presence of additional
CATALOG
items.
CATALOG
...
cosh( cosh
L1
(
...
sinh( sinh
L1
(
...
tanh( tanh
L1
(
...
Hyperbolic cosine
Hyperbolic arccosine
Hyperbolic sine
Hyperbolic arcsine
Hyperbolic tangent
Hyperbolic arctangent
sinh(
,
cosh(
, and
tanh(
are the hyperbolic functions. Each is valid for real numbers, expressions, and lists.
sinh(
value
) cosh(
value
) tanh(
value
) sinh L1 (, cosh L1 (, tanh L1 ( sinh
L1
(
is the hyperbolic arcsine function.
cosh
L1
(
is the hyperbolic arccosine function.
tanh
L1
(
is the hyperbolic arctangent function. Each is valid for real numbers, expressions, and lists.
sinh
L1
(
value
) cosh
L1
( sinh
L1
(
value
)
value
)
15–10
CATALOG
, Strings, Hyperbolic Functions
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16
Programming
Contents
Getting Started: Volume of a Cylinder
.....................................................
Creating and Deleting Programs
...................................................................
Entering Command Lines and Executing Programs
........................
Editing Programs
....................................................................................................
Copying and Renaming Programs
...............................................................
PRGM CTL
(Control) Instructions
..............................................................
PRGM I/O
(Input/Output) Instructions
.....................................................
16
Calling Other Programs as Subroutines
...................................................
22
7
8
5
6
2
4
Programming 16–1
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Getting Started: Volume of a Cylinder
Getting Started is a fastpaced introduction. Read the chapter for details.
A program is a set of commands that the TI82 STATS executes sequentially, as if you had entered them from the keyboard. Create a program that prompts for the radius R and the height H of a cylinder and then computes its volume.
1. Press ~ ~ to display the
PRGM NEW menu.
2. Press Í to select
1:Create New
. The
Name=
prompt is displayed, and alphalock is on. Press [
C
] [
Y
] [
L
] [
I
] [
N
] [
D
] [
E
] [
R
], and then press Í to name the program
CYLINDER
.
You are now in the program editor. The colon
(
:
) in the first column of the second line indicates the beginning of a command line.
3. Press ~
2
to select
2:Prompt
from the
PRGM I/O
menu.
Prompt
is copied to the command line. Press ƒ [
R
] ¢ ƒ [
H
] to enter the variable names for radius and height. Press Í.
4. Press y ãpä ƒ [
R
] ¡ ƒ [
H
] ¿
ƒ [
V
] Í to enter the expression
pR
2
H
and store it to the variable
V
.
16–2 Programming
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PM Page 2 of 22
5. Press ~
3
to select
3:Disp
from the
PRGM I/O
menu.
Disp
is pasted to the command line. Press y [
A
.
LOCK
] ããä [
V
] [
O
]
[
L
] [
U
] [
M
] [
E
][
'
] [
I
] [
S
] ããä ƒ ¢ ƒ
[
V
] Í to set up the program to display the text
VOLUME IS
on one line and the calculated value of
V
on the next.
6. Press y [
QUIT
] to display the home screen.
7. Press to display the
PRGM EXEC menu.
The items on this menu are the names of stored programs.
8. Press Í to paste
prgmCYLINDER
to the current cursor location. (If
CYLINDER
is not item
1
on your
PRGM EXEC menu, move the cursor to
CYLINDER
before you press Í.)
9. Press Í to execute the program. Enter
1.5
for the radius, and then press Í. Enter
3
for the height, and then press Í. The text
VOLUME IS
, the value of
V
, and
Done
are displayed.
Repeat steps 7 through 9 and enter different values for
R
and
H
.
Programming 16–3
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Creating and Deleting Programs
What Is a
Program?
Creating a New
Program
A program is a set of one or more command lines. Each line contains one or more instructions. When you execute a program, the TI82 STATS performs each instruction on each command line in the same order in which you entered them. The number and size of programs that the TI82 STATS can store is limited only by available memory.
To create a new program, follow these steps.
1. Press  to display the
PRGM NEW
menu.
Managing
Memory and
Deleting a
Program
2. Press Í to select
1:Create New
. The
Name=
prompt is displayed, and alphalock is on.
3. Press a letter from A to Z or q to enter the first character of the new program name.
Note: A program name can be one to eight characters long. The first character must be a letter from A to Z or q. The second through eighth characters can be letters, numbers, or q.
4. Enter zero to seven letters, numbers, or q to complete the new program name.
5. Press Í. The program editor is displayed.
6. Enter one or more program commands (page 16.5).
7. Press y [
QUIT
] to leave the program editor and return to the home screen.
To check whether adequate memory is available for a program you want to enter, press y [
MEM
], and then select
1:Check RAM
from the
MEMORY
menu (Chapter 18).
To increase available memory, press y [
MEM
], and then select
2:Delete
from the
MEMORY
menu (Chapter 18).
To delete a specific program, press y [
MEM
], select
2:Delete
from the
MEMORY
menu, and then select
7:Prgm
from the
DELETE FROM
secondary menu (Chapter 18).
16–4 Programming
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Entering Command Lines and Executing Programs
Entering a
Program
Command Line
You can enter on a command line any instruction or expression that you could execute from the home screen. In the program editor, each new command line begins with a colon. To enter more than one instruction or expression on a single command line, separate each with a colon.
Note: A command line can be longer than the screen is wide; long command lines wrap to the next screen line.
While in the program editor, you can display and select from menus. You can return to the program editor from a menu in either of two ways.
•
Select a menu item, which pastes the item to the current command line.
•
Press ‘.
When you complete a command line, press Í. The cursor moves to the next command line.
Programs can access variables, lists, matrices, and strings saved in memory. If a program stores a new value to a variable, list, matrix, or string, the program changes the value in memory during execution.
You can call another program as a subroutine (page 16.15 and page 16.22).
Executing a
Program
Breaking a
Program
To execute a program, begin on a blank line on the home screen and follow these steps.
1. Press to display the
PRGM EXEC
menu.
2. Select a program name from the
PRGM EXEC
menu (page
16.7).
prgm
name is pasted to the home screen (for example,
prgmCYLINDER
).
3. Press Í to execute the program. While the program is executing, the busy indicator is on.
Last Answer (
Ans
) is updated during program execution. Last
Entry is not updated as each command is executed (Chapter 1).
The TI82 STATS checks for errors during program execution.
It does not check for errors as you enter a program.
To stop program execution, press É. The
ERR:BREAK
menu is displayed.
•
To return to the home screen, select
1:Quit
.
•
To go where the interruption occurred, select
2:Goto
.
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Editing Programs
Editing a
Program
To edit a stored program, follow these steps.
1. Press ~ to display the
PRGM EDIT
menu.
2. Select a program name from the
PRGM EDIT
menu (page
16.7). Up to the first seven lines of the program are displayed.
Note: The program editor does not display a $ to indicate that a program continues beyond the screen.
3. Edit the program command lines.
•
Move the cursor to the appropriate location, and then delete, overwrite, or insert.
•
Press ‘ to clear all program commands on the command line (the leading colon remains), and then enter a new program command.
Tip: To move the cursor to the beginning of a command line, press y ; to move to the end, press y ~. To scroll the cursor down seven command lines, press
ƒ †. To scroll the cursor up seven command lines, press
ƒ }.
Inserting and
Deleting
Command Lines
To insert a new command line anywhere in the program, place the cursor where you want the new line, press y [
INS
], and then press Í. A colon indicates a new line.
To delete a command line, place the cursor on the line, press
‘ to clear all instructions and expressions on the line, and then press { to delete the command line, including the colon.
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Copying and Renaming Programs
Copying and
Renaming a
Program
To copy all command lines from one program into a new program, follow steps 1 through 5 for Creating a New Program
(page 16.4), and then follow these steps.
1. Press y [
RCL
].
Rcl
is displayed on the bottom line of the program editor in the new program (Chapter 1).
2. Press  to display the
PRGM EXEC
menu.
3. Select a name from the menu.
prgm
name is pasted to the bottom line of the program editor.
4. Press Í. All command lines from the selected program are copied into the new program.
Copying programs has at least two convenient applications.
•
You can create a template for groups of instructions that you use frequently.
•
You can rename a program by copying its contents into a new program.
Note: You also can copy all the command lines from one existing program to another existing program using
RCL.
Scrolling the
PRGM EXEC and
PRGM EDIT
Menus
The TI82 STATS sorts
PRGM EXEC
and
PRGM EDIT
menu items automatically into alphanumerical order. Each menu only labels the first 10 items using
1
through
9
, then
0
.
To jump to the first program name that begins with a particular alpha character or q, press ƒ [letter from A to Z or q
].
Tip: From the top of either the
PRGM EXEC or PRGM EDIT menu, press
} to move to the bottom. From the bottom, press † to move to the top. To scroll the cursor down the menu seven items, press
ƒ
†. To scroll the cursor up the menu seven items, press ƒ }.
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PRGM CTL (Control) Instructions
PRGM CTL Menu
To display the
PRGM CTL
(program control) menu, press from the program editor only.
CTL I/O EXEC
1: If
2: Then
3: Else
4: For(
5: While
6: Repeat
7: End
8: Pause
9: Lbl
0: Goto
A: IS>(
B: DS<(
C: Menu(
D: prgm
E: Return
F: Stop
G: DelVar
H: GraphStyle(
Creates a conditional test.
Executes commands when
If
is true.
Executes commands when
If
is false.
Creates an incrementing loop.
Creates a conditional loop.
Creates a conditional loop.
Signifies the end of a block.
Pauses program execution.
Defines a label.
Goes to a label.
Increments and skips if greater than.
Decrements and skips if less than.
Defines menu items and branches.
Executes a program as a subroutine.
Returns from a subroutine.
Stops execution.
Deletes a variable from within program.
Designates the graph style to be drawn.
These menu items direct the flow of an executing program.
They make it easy to repeat or skip a group of commands during program execution. When you select an item from the menu, the name is pasted to the cursor location on a command line in the program.
To return to the program editor without selecting an item, press
‘.
Controlling
Program Flow
Program control instructions tell the TI82 STATS which command to execute next in a program.
If
,
While
, and
Repeat
check a defined condition to determine which command to execute next. Conditions frequently use relational or Boolean tests (Chapter 2), as in:
If A<7:A+1
!A or
If N=1 and M=1:Goto Z
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If
Use
If
for testing and branching. If condition is false (zero), then the command immediately following
If
is skipped. If condition is true (nonzero), then the next command is executed.
If
instructions can be nested.
:If
condition
:
command (if true)
:
command
Program Output
If.Then
Then
following an
If
executes a group of commands if condition is true (nonzero).
End
identifies the end of the group of
commands.
:If
condition
:Then
:
command (if true)
:
command (if true)
:End
:
command
Program Output
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PRGM CTL (Control) Instructions
(continued)
If.Then.Else
Else
following
If.Then
executes a group of commands if
condition is false (zero).
End
identifies the end of the group of
commands.
:If
condition
:Then
:
command (if true)
:
command (if true)
:Else
:
command (if false)
:
command (if false)
:End
:
command
Program Output
For(
For(
loops and increments. It increments variable from begin to
end by increment. increment is optional (default is 1) and can be negative (end<begin). end is a maximum or minimum value not to be exceeded.
End
identifies the end of the loop.
For(
loops can be nested.
:For(
variable
,
begin
,
end[
,
increment]
)
:
command (while end not exceeded)
:
command (while end not exceeded)
:End
:
command
Program Output
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While While
performs a group of commands while condition is true.
condition is frequently a relational test (Chapter 2). condition is tested when
While
is encountered. If condition is true (nonzero), the program executes a group of commands.
End
signifies the end of the group. When condition is false (zero), the program executes each command following
End
.
While
instructions can be nested.
:While
condition
:
command (while condition is true)
:
command (while condition is true)
:End
:
command
Program Output
Repeat
Repeat
repeats a group of commands until condition is true
(nonzero). It is similar to
While
, but condition is tested when
End
is encountered; therefore, the group of commands is always executed at least once.
Repeat
instructions can be nested.
:Repeat
condition
:
command (until condition is true)
:
command (until condition is true)
:End
:
command
Program Output
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PRGM CTL (Control) Instructions
(continued)
End
Pause
End
identifies the end of a group of commands. You must include an
End
instruction at the end of each
For(
,
While
, or
Repeat
loop. Also, you must paste an
End
instruction at the end of each
If.Then
group and each
If.Then.Else
group.
Pause
suspends execution of the program so that you can see answers or graphs. During the pause, the pause indicator is on in the topright corner. Press Í to resume execution.
•
Pause
without a value temporarily pauses the program. If the
DispGraph
or
Disp
instruction has been executed, the appropriate screen is displayed.
•
Pause
with value displays value on the current home screen.
value can be scrolled.
Pause
[value]
Program Output
16–12 Programming
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Lbl, Goto Lbl
(label) and
Goto
(go to) are used together for branching.
Lbl
specifies the label for a command. label can be one or two characters (
A
through
Z
,
0
through
99
, or
q
).
Lbl
label
Goto
causes the program to branch to label when
Goto
is encountered.
Goto
label
Program Output
IS>(
IS>(
(increment and skip) adds 1 to variable. If the answer is >
value (which can be an expression), the next command is skipped; if the answer is { value, the next command is executed.
variable cannot be a system variable.
:IS>(
variable
,
value
)
:
command (if answer value)
:
command (if answer > value)
Program Output
Note:
IS>( is not a looping instruction.
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PRGM CTL (Control) Instructions
(continued)
DS<( DS<(
(decrement and skip) subtracts 1 from variable. If the answer is < value (which can be an expression), the next
command is skipped; if the answer is  value, the next command is executed. variable cannot be a system variable.
:DS<(
variable
,
value
)
:
command (if answer ‚ value)
:
command (if answer < value)
Program Output
Menu(
Note: DS<( is not a looping instruction.
Menu(
sets up branching within a program. If
Menu(
is encountered during program execution, the menu screen is displayed with the specified menu items, the pause indicator is on, and execution pauses until you select a menu item.
The menu title is enclosed in quotation marks (
"
). Up to seven pairs of menu items follow. Each pair comprises a text item
(also enclosed in quotation marks) to be displayed as a menu selection, and a label item to which to branch if you select the corresponding menu selection.
Menu("
title
","
text1
",
label1
,"
text2
",
label2
,
. . .
)
Program Output
The program above pauses until you select
1
or
2
. If you select
2
, for example, the menu disappears and the program continues execution at
Lbl B
.
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prgm
Return
Stop
DelVar
Use
prgm
to execute other programs as subroutines (page
16.22). When you select
prgm
, it is pasted to the cursor location. Enter characters to spell a program name. Using
prgm
is equivalent to selecting existing programs from the
PRGM
EXEC
menu; however, it allows you to enter the name of a program that you have not yet created.
prgm
name
Note: You cannot directly enter the subroutine name when using
RCL. You must paste the name from the PRGM EXEC menu (page
16.7).
Return
quits the subroutine and returns execution to the calling program (page 16.22), even if encountered within nested loops.
Any loops are ended. An implied
Return
exists at the end of any program that is called as a subroutine. Within the main program,
Return
stops execution and returns to the home screen.
Stop
stops execution of a program and returns to the home screen.
Stop
is optional at the end of a program.
DelVar
deletes from memory the contents of variable.
DelVar
variable
GraphStyle( GraphStyle(
designates the style of the graph to be drawn.
function# is the number of the
Y=
function name in the current graphing mode. graphstyle is a number from
1
to
7
that corresponds to the graph style, as shown below.
1
2
3
= ç (line)
= è (thick)
= é (shade above)
4
= ê (shade below)
5
= ë (path)
6
= ì (animate)
7
= í (dot)
GraphStyle(
function#
,
graphstyle
)
For example,
GraphStyle(1,5)
in
Func
mode sets the graph style for
Y
1
to ë (path;
5
).
Not all graph styles are available in all graphing modes. For a detailed description of each graph style, see the Graph Styles table in Chapter 3.
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PRGM I/O (Input/Output) Instructions
PRGM I/O Menu
To display the
PRGM I/O
(program input/output) menu, press
~ from within the program editor only.
CTL I/O EXEC
1: Input
2: Prompt
3: Disp
4: DispGraph
5: DispTable
6: Output(
7: getKey
8: ClrHome
9: ClrTable
0: GetCalc(
A: Get(
B: Send(
Enters a value or uses the cursor.
Prompts for entry of variable values.
Displays text, value, or the home screen.
Displays the current graph.
Displays the current table.
Displays text at a specified position.
Checks the keyboard for a keystroke.
Clears the display.
Clears the current table.
Gets a variable from another TI82 STATS.
Gets a variable from CBL or CBR.
Sends a variable to CBL or CBR.
These instructions control input to and output from a program during execution. They allow you to enter values and display answers during program execution.
To return to the program editor without selecting an item, press
‘.
Displaying a
Graph with Input
Input
without a variable displays the current graph. You can move the freemoving cursor, which updates
X
and
Y
(and
R
and
q
for
PolarGC
format). The pause indicator is on. Press Í to resume program execution.
Input
Program Output
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Storing a
Variable Value with Input
Input
with variable displays a
?
(question mark) prompt during execution. variable may be a real number, complex number, list, matrix, string, or
Y=
function. During program execution, enter a value, which can be an expression, and then press Í. The value is evaluated and stored to variable, and the program resumes execution.
Input
[variable]
You can display text or the contents of
Str
n (a string variable) of up to 16 characters as a prompt. During program execution, enter a value after the prompt and then press Í. The value is stored to variable, and the program resumes execution.
Input
[
"
text
",
variable]
Input
[
Str
n
,
variable]
Program Output
Note: When a program prompts for input of lists and
Yn functions during execution, you must include the braces ( { } ) around the list elements and quotation marks (
" ) around the expressions.
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PRGM I/O (Input/Output) Instructions
(continued)
Prompt
During program execution,
Prompt
displays each variable, one at a time, followed by
=?
. At each prompt, enter a value or expression for each variable, and then press Í. The values are stored, and the program resumes execution.
Prompt
variableA[
,
variableB
,
...
,
variable n]
Program Output
Displaying the
Home Screen
Displaying
Values and
Messages
Note: Y= functions are not valid with Prompt.
Disp
(display) without a value displays the home screen. To view the home screen during program execution, follow the
Disp
instruction with a
Pause
instruction.
Disp
Disp
with one or more values displays the value of each.
Disp
[valueA
,
valueB
,
valueC
,
...
,
value n]
•
If value is a variable, the current value is displayed.
•
If value is an expression, it is evaluated and the result is displayed on the right side of the next line.
•
If value is text within quotation marks, it is displayed on the left side of the current display line.
!
is not valid as text.
Program Output
If
Pause
is encountered after
Disp
, the program halts temporarily so you can examine the screen. To resume execution, press Í.
Note: If a matrix or list is too large to display in its entirety, ellipses
(...) are displayed in the last column, but the matrix or list cannot be scrolled. To scroll, use Pause value (page 16.12).
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DispGraph
DispTable
Output(
DispGraph
(display graph) displays the current graph. If
Pause
is encountered after
DispGraph
, the program halts temporarily so you can examine the screen. Press Í to resume execution.
DispTable
(display table) displays the current table. The program halts temporarily so you can examine the screen. Press
Í to resume execution.
Output(
displays text or value on the current home screen beginning at row (
1
through
8
) and column (
1
through
16
), overwriting any existing characters.
Tip: You may want to precede
Output( with ClrHome (page 16.20).
Expressions are evaluated and values are displayed according to the current mode settings. Matrices are displayed in entry format and wrap to the next line. !
is not valid as text.
Output(
row
,
column
,"
text
")
Output(
row
,
column
,
value
)
Program Output
For
Output(
on a
Horiz
split screen, the maximum value for row is 4.
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PRGM I/O (Input/Output) Instructions
(continued) getKey getKey
returns a number corresponding to the last key pressed, according to the key code diagram below. If no key has been pressed,
getKey
returns 0. Use
getKey
inside loops to transfer control, for example, when creating video games.
Program Output
TI82 STATS Key
Code Diagram
Note:
, , , and
Í were pressed during program execution.
Note: You can press
É at any time during execution to break the program (page 16.5).
ClrHome,
ClrTable
ClrHome
(clear home screen) clears the home screen during program execution.
ClrTable
(clear table) clears the values in the table during program execution.
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GetCalc(
Get(, Send(
GetCalc(
gets the contents of variable on another TI82 STATS and stores it to variable on the receiving TI82 STATS. variable can be a real or complex number, list element, list name, matrix element, matrix name, string,
Y=
variable, graph database, or picture.
GetCalc(
variable
)
Note:
GetCalc( does not work between TI.82 and TI82 STATS.
Get(
gets data from the CalculatorBased Laboratoryé (CBLé)
System or CalculatorBased Rangeré (CBRé) and stores it to
variable on the receiving TI82 STATS. variable can be a real number, list element, list name, matrix element, matrix name, string,
Y=
variable, graph database, or picture.
Get(
variable
)
Note: If you transfer a program that references the
Get( command to the TI82 STATS from a TI.82, the TI82 STATS will interpret it as the
Get( described above. Use GetCalc( to get data from another
TI82 STATS.
Send(
sends the contents of variable to the CBL or CBR. You cannot use it to send to another TI82 STATS. variable can be a real number, list element, list name, matrix element, matrix name, string,
Y=
variable, graph database, or picture. variable can be a list of elements.
Send(
variable
)
Note: This program gets sound data and time in seconds from CBL.
Note: You can access
Get(, Send(, and GetCalc( from the
CATALOG to execute them from the home screen (Chapter 15).
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Calling Other Programs as Subroutines
Calling a
Program from
Another Program
On the TI82 STATS, any stored program can be called from another program as a subroutine. Enter the name of the program to use as a subroutine on a line by itself.
You can enter a program name on a command line in either of two ways.
•
Press  to display the
PRGM EXEC
menu and select the name of the program (page 16
.
7).
prgm
name is pasted to the current cursor location on a command line.
•
Select
prgm
from the
PRGM CTL
menu, and then enter the program name (page 16
.
15).
prgm
name
When
prgm
name is encountered during execution, the next command that the program executes is the first command in the second program. It returns to the subsequent command in the first program when it encounters either
Return
or the implied
Return
at the end of the second program.
Program Output
&
Subroutine ( '
Notes about
Calling Programs
Variables are global.
label used with
Goto
and
Lbl
is local to the program where it is located. label in one program is not recognized by another program. You cannot use
Goto
to branch to a label in another program.
Return
exits a subroutine and returns to the calling program, even if it is encountered within nested loops.
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17
Applications
Contents
Comparing Test Results Using Box Plots
...............................................
Graphing Piecewise Functions
.......................................................................
Graphing Inequalities
...........................................................................................
Solving a System of Nonlinear Equations
..............................................
Using a Program to Create the Sierpinski Triangle
..........................
Graphing Cobweb Attractors
..........................................................................
Using a Program to Guess the Coefficients
...........................................
9
Graphing the Unit Circle and Trigonometric Curves
......................
10
7
8
5
6
2
4
Finding the Area between Curves
................................................................
11
Using Parametric Equations: Ferris Wheel Problem
........................
12
Demonstrating the Fundamental Theorem of Calculus
..................
14
Computing Areas of Regular NSided Polygons
................................
16
Computing and Graphing Mortgage Payments
...................................
18
Applications 17–1
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Comparing Test Results Using Box Plots
Problem
Procedure
An experiment found a significant difference between boys and girls pertaining to their ability to identify objects held in their left hands, which are controlled by the right side of their brains, versus their right hands, which are controlled by the left side of their brains. The TI Graphics team conducted a similar test for adult men and women.
The test involved 30 small objects, which participants were not allowed to see. First, they held 15 of the objects one by one in their left hands and guessed what they were. Then they held the other 15 objects one by one in their right hands and guessed what they were. Use box plots to compare visually the correctguess data from this table.
Correct Guesses
Women
Left
8
9
12
11
10
8
12
7
9
11
Women
Right
12
11
11
13
4
1
8
12
11
12
Men
Left
5
7
8
11
7
8
7
4
10
14
13
5
Men
Right
12
6
12
12
7
11
12
8
12
11
9
9
1. Press …
5
to select
5:SetUpEditor
. Enter list names
WLEFT
,
WRGHT
,
MLEFT
, and
MRGHT
, separated by commas. Press Í. The stat list editor now contains only these four lists.
2. Press …
1
to select
1:Edit
.
3. Enter into
WLEFT
the number of correct guesses each woman made using her left hand ( Women Left ). Press ~ to move to
WRGHT
and enter the number of correct guesses each woman made using her right hand ( Women Right ).
4. Likewise, enter each man’s correct guesses in
MLEFT
( Men
Left) and
MRGHT
( Men Right ).
5. Press y [
STAT PLOT
]. Select
1:Plot1
. Turn on plot 1; define it as a modified box plot
Õ
that uses
WLEFT
. Move the cursor to the top line and select
Plot2
. Turn on plot 2; define it as a modified box plot that uses
WRGHT
.
17–2 Applications
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Procedure
(continued)
6. Press o. Turn off all functions.
7. Press p. Set
Xscl=1
and
Yscl=0
. Press q
9
to select
9:ZoomStat
. This adjusts the viewing window and displays the box plots for the women’s results.
8. Press r.
%
Women’s lefthand data
%
Women’s righthand data
Use  and ~ to examine
minX
,
Q
1
,
Med
,
Q
3
, and
maxX
for each plot. Notice the outlier to the women’s righthand data.
What is the median for the left hand? For the right hand?
With which hand were the women more accurate guessers, according to the box plots?
9. Examine the men’s results. Redefine plot 1 to use
MLEFT
, redefine plot 2 to use
MRGHT
. Press r.
%
Men’s lefthand data
%
Men’s righthand data
Press  and ~ to examine
minX
,
Q
1
,
Med
,
Q
3
, and
maxX
for each plot. What difference do you see between the plots?
10.Compare the lefthand results. Redefine plot 1 to use
WLEFT
, redefine plot 2 to use
MLEFT
, and then press r to examine
minX
,
Q
1
,
Med
,
Q
3
, and
maxX
for each plot. Who were the better lefthand guessers, men or women?
11.Compare the righthand results. Define plot 1 to use
WRGHT
, define plot 2 to use
MRGHT
, and then press r to examine
minX
,
Q
1
,
Med
,
Q
3
, and
maxX
for each plot. Who were the better righthand guessers?
In the original experiment boys did not guess as well with right hands, while girls guessed equally well with either hand. This is not what our box plots show for adults. Do you think that this is because adults have learned to adapt or because our sample was not large enough?
Applications 17–3
82501F~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 1:49 PM Printed: 10/27/05 3:04
PM Page 3 of 20
Graphing Piecewise Functions
Problem
Procedure
The fine for speeding on a road with a speed limit of 45 kilometers per hour (kph) is 50; plus 5 for each kph from 46 to
55 kph; plus 10 for each kph from 56 to 65 kph; plus 20 for each kph from 66 kph and above. Graph the piecewise function that describes the cost of the ticket.
The fine (Y) as a function of kilometers per hour (X) is:
Y = 0
Y = 50 + 5 (X N 45)
Y = 50 + 5 … 10 + 10 (X N 55)
Y = 50 + 5 … 10 + 10 … 10 + 20 (X N 65)
0 < X 45
45 < X 55
55 < X 65
65 < X
1. Press z. Select
Func
and the default settings.
2. Press o. Turn off all functions and stat plots. Enter the
Y=
function to describe the fine. Use the
TEST
menu operations to define the piecewise function. Set the graph style for
Y
1
to í (dot).
3. Press p and set
Xmin=L2
,
Xscl=10
,
Ymin=L5
, and
Yscl=10
. Ignore
Xmax
and
Ymax
; they are set by
@X
and
@Y
in step 4.
4. Press y [
QUIT
] to return to the home screen. Store
1
to
@X
, and then store
5
to
@Y
.
@X
and
@Y
are on the
VARS Window
X/Y
secondary menu.
@X
and
@Y
specify the horizontal and vertical distance between the centers of adjacent pixels.
Integer values for
@X
and
@Y
produce nice values for tracing.
5. Press r to plot the function. At what speed does the ticket exceed 250?
17–4 Applications
82501F~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 1:49 PM Printed: 10/27/05 3:04
PM Page 4 of 20
Graphing Inequalities
Problem
Procedure
Graph the inequality 0
.
4X
3 is true and where it is false.
N 3X + 5 < 0
.
2X + 4. Use the
TEST menu operations to explore the values of X where the inequality
1. Press z. Select
Dot
,
Simul
, and the default settings.
Setting
Dot
mode changes all graph style icons to í (dot) in the
Y=
editor.
2. Press o. Turn off all functions and stat plots. Enter the left side of the inequality as
Y
4
and the right side as
Y
5
.
3. Enter the statement of the inequality as
Y
6
. This function evaluates to
1
if true or
0
if false.
4. Press q
6
to graph the inequality in the standard window.
5. Press r † † to move to
Y
6
. Then press  and ~ to trace the inequality, observing the value of
Y
.
6. Press o. Turn off
Y
4
,
Y
5
, and
Y
6
. Enter equations to graph only the inequality.
7. Press r. Notice that the values of
Y
7
and
Y
8
are zero where the inequality is false.
Applications 17–5
82501F~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 1:49 PM Printed: 10/27/05 3:04
PM Page 5 of 20
Solving a System of Nonlinear Equations
Problem
Procedure
Using a graph, solve the equation X 3
N 2X = 2cos(X). Stated another way, solve the system of two equations and two unknowns: Y = X 3
N2X and Y = 2cos(X). Use ZOOM
factors to control the decimal places displayed on the graph.
1. Press z. Select the default mode settings. Press o. Turn off all functions and stat plots. Enter the functions.
2. Press q
4
to select
4:ZDecimal
. The display shows that two solutions may exist (points where the two functions appear to intersect).
3. Press q ~
4
to select
4:SetFactors
from the
ZOOM
MEMORY
menu. Set
XFact=10
and
YFact=10
.
4. Press q
2
to select
2:Zoom In
. Use , ~, }, and † to move the freemoving cursor onto the apparent intersection of the functions on the right side of the display. As you move the cursor, notice that the
X
and
Y
values have one decimal place.
5. Press Í to zoom in. Move the cursor over the intersection. As you move the cursor, notice that now the
X
and
Y
values have two decimal places.
6. Press Í to zoom in again. Move the freemoving cursor onto a point exactly on the intersection. Notice the number of decimal places.
7. Press y [
CALC
]
5
to select
5:intersect
. Press Í to select the first curve and Í to select the second curve.
To guess, move the trace cursor near the intersection. Press
Í. What are the coordinates of the intersection point?
8. Press q
4
to select
4:ZDecimal
to redisplay the original graph.
9. Press q. Select
2:Zoom In
and repeat steps 4 through 8 to explore the apparent function intersection on the left side of the display.
17–6 Applications
82501F~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 1:49 PM Printed: 10/27/05 3:04
PM Page 6 of 20
Using a Program to Create the Sierpinski Triangle
Setting up the
Program
Program
This program creates a drawing of a famous fractal, the
Sierpinski Triangle, and stores the drawing to a picture. To begin, press ~ ~
1
. Name the program
SIERPINS
, and then press Í. The program editor is displayed.
PROGRAM:SIERPINS
:FnOff :ClrDraw
:PlotsOff
:AxesOff
!
!
Set viewing window.
:For(K,1,3000)
:rand!
:If N1 à 3
:Then
:.5X!
!
:End
:If 1 à 3 <N and N2 à 3
:Then
!
!
:End
:If 2 à 3 <N
:Then
:.5(1+X)!
:.5Y!
:End
:PtOn(X,Y)
:End
:StorePic 6
Beginning of
If
If
If
/
Then
group
/
Then
group.
/
Then
group.
For
Draw point.
End of
For
group.
Store picture.
group.
After you execute the program above, you can recall and display the picture with the instruction
RecallPic 6
.
Applications 17–7
82501F~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 1:49 PM Printed: 10/27/05 3:04
PM Page 7 of 20
Graphing Cobweb Attractors
Problem
Procedure
Using
Web
format, you can identify points with attracting and repelling behavior in sequence graphing.
1. Press z. Select
Seq
and the default mode settings. Press y [
FORMAT
]. Select
Web
format and the default format settings.
2. Press o. Clear all functions and turn off all stat plots. Enter the sequence that corresponds to the expression Y = K
X(1NX).
u(n)=Ku(nN1)(1Nu(nN1)) u(nMin)=.01
3. Press y [
QUIT
] to return to the home screen, and then store
2.9
to
K
.
4. Press p. Set the window variables.
nMin=0 Xmin=0
nMax=10
PlotStart=1
PlotStep=1
Xmax=1
Xscl=1
Ymin=M.26
Ymax=1.1
Yscl=1
5. Press r to display the graph, and then press ~ to trace the cobweb. This is a cobweb with one attractor.
6. Change
K
to
3.44
and trace the graph to show a cobweb with two attractors.
7. Change
K
to
3.54
and trace the graph to show a cobweb with four attractors.
17–8 Applications
82501F~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 1:49 PM Printed: 10/27/05 3:04
PM Page 8 of 20
Using a Program to Guess the Coefficients
Setting Up the
Program
Program
This program graphs the function A sin(BX) with random integer coefficients between 1 and 10. Try to guess the coefficients and graph your guess as C sin(DX). The program continues until your guess is correct.
PROGRAM:GUESS
:PlotsOff :Func
:FnOff :Radian
:ClrHome
!
!
:GraphStyle(1,1)
:GraphStyle(2,5)
:FnOff 2
!
:randInt(1,10)!
:0!
!
!Xmin
!
!
!
:L10!
!
!
:1!
!
:DispGraph
:Pause
:FnOn 2
:Lbl Z
:Prompt C,D
:DispGraph
:Pause
:If C=A
:Text(1,1,"C IS OK")
:If CƒA
:Text(1,1,"C IS WRONG")
:If D=B
:Text(1,50,"D IS OK")
:If DƒB
:Text(1,50,"D IS WRONG")
:DispGraph
:Pause
:If C=A and D=B
:Stop
:Goto Z
Define equations.
Set line and path graph styles.
Initialize coefficients.
Set viewing window.
Display graph.
Prompt for guess.
Display graph.
Display results.
Display graph.
Quit if guesses are correct.
Applications 17–9
82501F~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 1:49 PM Printed: 10/27/05 3:04
PM Page 9 of 20
Graphing the Unit Circle and Trigonometric Curves
Problem
Procedure
Using parametric graphing mode, graph the unit circle and the sine curve to show the relationship between them.
Any function that can be plotted in
Func
mode can be plotted in
Par
mode by defining the
X
component as
T
and the
Y
component as F
(T)
.
1. Press z. Select
Par
,
Simul
, and the default settings.
2. Press p. Set the viewing window.
Tmin=0
Tmax=2p
Tstep=.1
Xmin=L2
Xmax=7.4
Xscl=pà2
Ymin=L3
Ymax=3
Yscl=1
3. Press o. Turn off all functions and stat plots. Enter the expressions to define the unit circle centered on (0,0).
4. Enter the expressions to define the sine curve.
5. Press r. As the graph is plotting, you may press Í to pause and Í again to resume graphing as you watch the sine function “unwrap” from the unit circle.
Note: You can generalize the unwrapping. Replace
sin(T) in Y
2T
with any other trig function to unwrap that function.
17–10 Applications
82501F~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 1:49 PM Printed: 10/27/05 3:04
PM Page 10 of 20
Finding the Area between Curves
Problem
Procedure
Find the area of the region bounded by f(x) g(x) x
= 300x / ( x 2 + 625)
= 3cos(
= 75
.
1x)
1. Press z. Select the default mode settings.
2. Press p. Set the viewing window.
Xmin=0
Xmax=100
Xscl=10
Ymin=L5
Ymax=10
Yscl=1
Xres=1
3. Press o. Turn off all functions and stat plots. Enter the upper and lower functions.
Y
1
=300Xà(X
2
+625)
Y
2
=3cos(.1X)
4. Press y [
CALC
]
5
to select
5:Intersect
. The graph is displayed. Select a first curve, second curve, and guess for the intersection toward the left side of the display. The solution is displayed, and the value of
X
at the intersection, which is the lower limit of the integral, is stored in
Ans
and
X
.
5. Press y [
QUIT
] to go to the home screen. Press y [
DRAW
]
7
and use
Shade(
to see the area graphically.
Shade(Y
2
,Y
1
,Ans,75)
6. Press y [
QUIT
] to return to the home screen. Enter the expression to evaluate the integral for the shaded region.
fnInt(Y
1
–Y
2
,X,Ans,75)
The area is
325.839962
.
Applications 17–11
82501F~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 1:49 PM Printed: 10/27/05 3:04
PM Page 11 of 20
Using Parametric Equations: Ferris Wheel Problem
Problem
Procedure
Using two pairs of parametric equations, determine when two objects in motion are closest to each other in the same plane.
A ferris wheel has a diameter (d) of 20 meters and is rotating counterclockwise at a rate (s) of one revolution every 12 seconds. The parametric equations below describe the location of a ferris wheel passenger at time T, where a is the angle of rotation, (0,0) is the bottom center of the ferris wheel, and
(10,10) is the passenger’s location at the rightmost point, when
T=0.
X(T) = r cos a
Y(T) = r + r sin a where a = 2pTs and r = d à2
A person standing on the ground throws a ball to the ferris wheel passenger. The thrower’s arm is at the same height as the bottom of the ferris wheel, but 25 meters (b) to the right of the ferris wheel’s lowest point (25,0). The person throws the ball with velocity (v
0
) of 22 meters per second at an angle (q) of 66¡ from the horizontal. The parametric equations below describe the location of the ball at time T.
X(T) = b N Tv
Y(T) = Tv
0
cosq
sinq N (g à2 ) T
2
9.8 m/ sec
2
0 where g =
1. Press z. Select
Par
,
Simul
, and the default settings.
Simul
(simultaneous) mode simulates the two objects in motion over time.
2. Press p. Set the viewing window.
Tmin=0
Tmax=12
Xmin=L13
Xmax=34
Tstep=.1
Xscl=10
Ymin=0
Ymax=31
Yscl=10
3. Press o. Turn off all functions and stat plots. Enter the expressions to define the path of the ferris wheel and the path of the ball. Set the graph style for
X
2T
to ëëëë (path).
17–12 Applications
Tip: Try setting the graph styles to
ëëëë X
1T
and
ìììì X
2T
, which simulates a chair on the ferris wheel and the ball flying through the air when you press s.
82501F~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 1:49 PM Printed: 10/27/05 3:04
PM Page 12 of 20
Procedure
(continued)
4. Press s to graph the equations. Watch closely as they are plotted. Notice that the ball and the ferris wheel passenger appear to be closest where the paths cross in the topright quadrant of the ferris wheel.
5. Press p. Change the viewing window to concentrate on this portion of the graph.
Tmin=1 Xmin=0 Ymin=10
Tmax=3
Tstep=.03
Xmax=23.5
Xscl=10
Ymax=25.5
Yscl=10
6. Press r. After the graph is plotted, press ~ to move near the point on the ferris wheel where the paths cross.
Notice the values of
X
,
Y
, and
T
.
7. Press † to move to the path of the ball. Notice the values of
X
and
Y
(
T
is unchanged). Notice where the cursor is located.
This is the position of the ball when the ferris wheel passenger passes the intersection. Did the ball or the passenger reach the intersection first?
You can use r to, in effect, take snapshots in time and explore the relative behavior of two objects in motion.
Applications 17–13
82501F~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 1:49 PM Printed: 10/27/05 3:04
PM Page 13 of 20
Demonstrating the Fundamental Theorem of Calculus
Problem 1
Procedure 1
Using the functions
fnInt(
and
nDeriv(
from the
MATH
menu to graph functions defined by integrals and derivatives demonstrates graphically that:
F(x) =
D x
[‰
‰
1 x
1àt dt = ln(x), x > 0 and that
1 x
1àt dt
]
= 1àx
1. Press z. Select the default settings.
2. Press p. Set the viewing window.
Xmin=.01
Xmax=10
Xscl=1
Ymin=M1.5
Ymax=2.5
Yscl=1
Xres=3
3. Press o. Turn off all functions and stat plots. Enter the numerical integral of 1àT from 1 to X and the function ln(X). Set the graph style for
Y
1
to ç (line) and
Y
2
to
ë (path).
4. Press r. Press , }, ~, and † to compare the values of
Y
1
and
Y
2
.
5. Press o. Turn off
Y
1
and
Y
2
, and then enter the numerical derivative of the integral of 1àX and the function 1àX. Set the graph style for
Y
3
to
çççç
(line) and
Y
4
to
è
(thick).
6. Press r. Again, use the cursor keys to compare the values of the two graphed functions,
Y
3
and
Y
4
.
17–14 Applications
82501F~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 1:49 PM Printed: 10/27/05 3:04
PM Page 14 of 20
Problem 2
Procedure 2
Explore the functions defined by y =
‰
M
2 x
t 2 dt,
‰
0 x
t 2 dt, and
‰
2 x
t 2 dt
1. Press o. Turn off all functions and stat plots. Use a list to define these three functions simultaneously. Store the function in
Y
5.
2. Press q
6
to select
6:ZStandard
.
3. Press r. Notice that the functions appear identical, only shifted vertically by a constant.
4. Press o. Enter the numerical derivative of
Y
5
in
Y
6
.
5. Press r. Notice that although the three graphs defined by
Y
5
are different, they share the same derivative.
Applications 17–15
82501F~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 1:49 PM Printed: 10/27/05 3:04
PM Page 15 of 20
Computing Areas of Regular NSided Polygons
Problem
Use the equation solver to store a formula for the area of a regular Nsided polygon, and then solve for each variable, given the other variables. Explore the fact that the limiting case is the area of a circle, pr 2 .
Consider the formula A = NB 2 sin(pàN) cos(pàN) for the area of a regular polygon with N sides of equal length and B distance from the center to a vertex.
Procedure
N = 4 sides N = 8 sides N = 12 sides
1. Press
0
to select
0:Solver
from the
MATH
menu. Either the equation editor or the interactive solver editor is displayed. If the interactive solver editor is displayed, press
} to display the equation editor.
2. Enter the formula as
0=ANNB
2 sin(p / N)cos(p / N)
, and then press Í. The interactive solver editor is displayed.
3. Enter
N=4
and
B=6
to find the area (
A
) of a square with a distance (
B
) from center to vertex of 6 centimeters.
4. Press } } to move the cursor onto
A
, and then press ƒ
[
SOLVE
]. The solution for
A
is displayed on the interactive solver editor.
5. Now solve for
B
for a given area with various number of sides. Enter
A=200
and
N=6
. To find the distance
B
, move the cursor onto
B
, and then press ƒ [
SOLVE
].
6. Enter
N=8
. To find the distance
B
, move the cursor onto
B
, and then press ƒ [
SOLVE
]. Find
B
for
N=9
, and then for
N=10
.
17–16 Applications
82501F~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 1:49 PM Printed: 10/27/05 3:04
PM Page 16 of 20
Procedure
(continued)
Find the area given
B=6
, and
N=10
,
100
,
150
,
1000
, and
10000
.
Compare your results with p6
2
(the area of a circle with radius
6), which is approximately 113.097.
7. Enter
B=6
. To find the area
A
, move the cursor onto
A
, and then press ƒ [
SOLVE
]. Find
A
for
N=10
, then
N=100
, then
N=150
, then
N=1000
, and finally
N=10000
. Notice that as
N
gets large, the area
A
approaches
pB
2
.
Now graph the equation to see visually how the area changes as the number of sides gets large.
8. Press z. Select the default mode settings.
9. Press p. Set the viewing window.
Xmin=0
Xmax=200
Xscl=10
Ymin=0
Ymax=150
Yscl=10
Xres=1
10.Press o. Turn off all functions and stat plots. Enter the equation for the area. Use
X
in place of
N
. Set the graph styles as shown.
11.Press r. After the graph is plotted, press
100
Í to trace to
X=100
. Press
150
Í. Press
188
Í. Notice that as
X
increases, the value of approximately 113.097.
Y
2
=pB
2
Y
converges to p6 , which is
(the area of the circle) is a horizontal asymptote to
Y
1
. The area of an Nsided regular polygon, with r as the distance from the center to a vertex, approaches the area of a circle with radius r (pr large.
2
2
) as N gets
Applications 17–17
82501F~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 1:49 PM Printed: 10/27/05 3:04
PM Page 17 of 20
Computing and Graphing Mortgage Payments
Problem
Procedure
You are a loan officer at a mortgage company, and you recently closed on a 30year home mortgage at 8 percent interest with monthly payments of 800. The new home owners want to know how much will be applied to the interest and how much will be applied to the principal when they make the 240th payment 20 years from now.
1. Press z and set the fixeddecimal mode to
2
decimal places. Set the other mode settings to the defaults.
2. Press y [
FINANCE
]
1
to display the
TVM Solver
. Enter these values.
Note: Enter a positive number (
800) to show PMT as a cash inflow. Payment values will be displayed as positive numbers on the graph. Enter
0 for FV, since the future value of a loan is 0 once it is paid in full. Enter PMT: END, since payment is due at the end of a period.
3. Move the cursor onto the
PV=
prompt, and then press ƒ
[
SOLVE
]. The present value, or mortgage amount, of the house is displayed at the
PV=
prompt.
17–18 Applications
82501F~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 1:49 PM Printed: 10/27/05 3:04
PM Page 18 of 20
Procedure
(continued)
Now compare the graph of the amount of interest with the graph of the amount of principal for each payment.
4. Press z. Set
Par
and
Simul
.
5. Press o. Turn off all functions and stat plots. Enter these equations and set the graph styles as shown.
Note: GPrn( and GInt( are located on the FINANCE CALC menu.
6. Press p. Set these window variables.
Tmin=1 Xmin=0 Ymin=0
Tmax=360
Tstep=12
Xmax=360
Xscl=10
Ymax=1000
Yscl=100
Tip: To increase the graph speed, change
Tstep to 24.
7. Press r. After the graph is drawn, press
240
Í to move the trace cursor to
T=240
, which is equivalent to 20 years of payments.
The graph shows that for the 240th payment (
X=240
), 358.03
of the 800 payment is applied to principal (
Y=358.03
).
Note: The sum of the payments (
Y
3T
=Y
1T
+Y
2T
) is always 800.
Applications 17–19
82501F~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 1:49 PM Printed: 10/27/05 3:04
PM Page 19 of 20
Computing and Graphing Mortgage Payments
(cont.)
Procedure
(continued)
8. Press † to move the cursor onto the function for interest defined by
X
2T
and
Y
2T
. Enter
240
.
The graph shows that for the 240th payment (
X=240
), 441.97
of the 800 payment is interest (
Y=441.97
).
9. Press y [
QUIT
] y [
FINANCE
]
9
to paste
9:bal(
to the home screen. Check the figures from the graph.
At which monthly payment will the principal allocation surpass the interest allocation?
17–20 Applications
82501F~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 1:49 PM Printed: 10/27/05 3:04
PM Page 20 of 20
18
Memory
Management
Contents
Checking Available Memory
..........................................................................
Deleting Items from Memory
.........................................................................
Clearing Entries and List Elements
.............................................................
Resetting the TI82 STATS
.............................................................................
4
5
2
3
Memory Management 18–1
82D304~1.DOC TI83 international English Bob Fedorisko Revised: 10/28/05 9:19 AM Printed: 10/28/05 9:21
AM Page 1 of 6
Checking Available Memory
MEMORY Menu
Displaying the
Check RAM
Screen
To display the
MEMORY
menu, press y [
MEM
].
MEMO
RY
1: Check RAM...
2: Delete...
3: Clear Entries
4: ClrAllLists
5: Reset...
Reports memory availability/usage.
Displays
Clears
Displays
DELETE FROM
ENTRY
(lastentry storage).
Clears all lists in memory.
RESET menu.
menu (all/defaults).
Check RAM
displays the
Check RAM
screen. The top line reports the total amount of available memory. The remaining lines report the amount of memory each variable type is using.
You can check this screen to see whether you need to delete variables from memory to make room for new data, such as programs.
To check RAM usage, follow these steps.
1. Press y [
MEM
] to display the
MEMORY
menu.
2. Select
1:Check RAM
to display the
Check RAM
screen. The
TI82 STATS expresses memory quantities in bytes.
Note: The $ in the left column of the bottom row indicates that you can scroll or page down to view more variable types.
Note:
Real, List, Y.Vars, and Prgm variable types never reset to zero, even after memory is cleared.
To leave the
Check RAM
screen, press either y [
QUIT
] or
‘. Both options display the home screen.
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Deleting Items from Memory
Deleting an Item
To increase available memory by deleting the contents of any variable (real or complex number, list, matrix,
Y=
variable, program, picture, graph database, or string), follow these steps.
1. Press y [
MEM
] to display the
MEMORY
menu.
2. Select
2:Delete
to display the
DELETE FROM
secondary menu.
3. Select the type of data you want to delete, or select
1:All
for a list of all variables of all types. A screen is displayed listing each variable of the type you selected and the number of bytes each variable is using.
For example, if you select
4:List
, the
DELETE:List
screen is displayed.
4. Press } and † to move the selection cursor (
4
) next to the item you want to delete, and then press Í. The variable is deleted from memory. You can delete individual variables one by one from this screen.
To leave any
DELETE:
screen without deleting anything, press y [
QUIT
], which displays the home screen.
Note: You cannot delete some system variables, such as the lastanswer variable Ans and the statistical variable RegEQ.
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Clearing Entries and List Elements
Clear Entries Clear Entries
clears the contents of the
ENTRY
(last entry) storage area (Chapter 1). To clear the
ENTRY
storage area, follow these steps.
1. Press y [
MEM
] to display the
MEMORY
menu.
2. Select
3:Clear Entries
to paste the instruction to the home screen.
3. Press Í to clear the
ENTRY
storage area.
ClrAllLists
To cancel
Clear Entries
, press ‘.
Note: If you select
3:Clear Entries from within a program, the Clear
Entries instruction is pasted to the program editor, and the Entry
(last entry) is cleared when the program is executed.
ClrAllLists
sets to
0
the dimension of each list in memory.
To clear all elements from all lists, follow these steps.
1. Press y [
MEM
] to display the
MEMORY
menu.
2. Select
4:ClrAllLists
to paste the instruction to the home screen.
3. Press Í to set to
0
the dimension of each list in memory.
To cancel
ClrAllLists
, press ‘.
ClrAllLists
does not delete list names from memory, from the
LIST NAMES
menu, or from the stat list editor.
Note: If you select
4:ClrAllLists from within a program, the
ClrAllLists instruction is pasted to the program editor. The lists are cleared when the program is executed.
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Resetting the TI82 STATS
RESET
Secondary Menu
The
RESET
secondary menu gives you the option of resetting all memory (including default settings) or resetting the default settings while preserving other data stored in memory, such as programs and
Y=
functions.
Resetting All
Memory
Resetting all memory on the TI82 STATS restores memory to the factory settings. It deletes all nonsystem variables and all programs. It resets all system variables to the default settings.
Tip: Before you reset all memory, consider restoring sufficient available memory by deleting only selected data (page 18 .3).
To reset all memory on the TI82 STATS, follow these steps.
1. Press y [
MEM
] to display the
MEMORY
menu.
2. Select
5:Reset
to display the
RESET
secondary menu.
3. Select
1:All Memory
to display the
RESET MEMORY
tertiary menu.
4. Read the message below the
RESET MEMORY
menu.
•
To cancel memory reset and return to the home screen, select
1:No
.
•
To erase from memory all data and programs, select
2:Reset
. All factory defaults are restored.
Mem cleared
is displayed on the home screen.
Note: When you clear memory, the contrast sometimes changes. If the screen is faded or blank, adjust the contrast (Chapter 1).
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Resetting the TI82 STATS
(continued)
Resetting
Defaults
When you reset defaults on the TI82 STATS, all defaults are restored to the factory settings. Stored data and programs are not changed.
These are some examples of TI82 STATS defaults that are restored by resetting the defaults.
•
Mode settings such as
Normal
(notation);
Func
(graphing);
Real
(numbers); and
Full
(screen)
•
Y=
functions off
•
Window variable values such as
Xmin=L10
;
Xmax=10
;
Xscl=1
;
Yscl=1
; and
Xres=1
•
Stat plots off
•
Format settings such as
CoordOn
(graphing coordinates on);
AxesOn
; and
ExprOn
(expression on)
•
rand
seed value to 0
To reset all TI82 STATS factory defaults, follow these steps.
1. Press y [
MEM
] to display the
MEMORY
menu.
2. Select
5:Reset
to display the
RESET
secondary menu.
3. Select
2:Defaults
to display the
RESET DEFAULTS
tertiary menu.
4. Consider the consequences of resetting defaults.
•
To cancel reset and return to the home screen, select
1:No
.
•
To restore factory default settings, select
2:Reset
.
Default settings are restored.
Defaults set
is displayed on the home screen.
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19
Communication
Link
Contents
Getting Started: Sending Variables
.............................................................
TI82 STATS LINK
...............................................................................................
Selecting Items to Send
.......................................................................................
Receiving Items
.......................................................................................................
Transmitting Items
.................................................................................................
Transmitting Lists to a TI

82
..........................................................................
Transmitting from a TI

82 to a TI82 STATS
.....................................
9
Backing Up Memory
............................................................................................
10
6
8
4
5
2
3
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Getting Started: Sending Variables
Getting Started is a fastpaced introduction. Read the chapter for details.
Create and store a variable and a matrix, and then transfer them to another
TI82 STATS.
1. On the home screen of the sending unit, press
5
Ë
5
¿ ƒ
Q
. Press Í to store
5.5 to
Q
.
2. Press y [
[
] y [
[
]
1
¢
2
y [
]
] y [
[
]
3
¢
4
y [
]
] y [
]
] ¿
1
. Press
Í to store the matrix to
[A]
.
3. Connect the calculators with the link cable.
Push both ends in firmly.
4. On the receiving unit, press y [
LINK
] ~ to display the
RECEIVE
menu. Press
1
to select
1:Receive
. The message
Waiting...
is displayed and the busy indicator is on.
5. On the sending unit, press y [
LINK
] to display the
SEND
menu.
6. Press
2
to select
2:AllN
. The
AllN SELECT screen is displayed.
7. Press † until the selection cursor (
4
) is next to
[A] MATRX
. Press Í.
8. Press † until the selection cursor is next to
Q REAL
. Press Í. A square dot next to
[A]
and
Q
indicates that each is selected to send.
9. On the sending unit, press ~ to display the
TRANSMIT
menu.
10. On the sending unit, press
1
to select
1:Transmit
and begin transmission. The receiving unit displays the message
Receiving...
.When the items are transmitted, both units display the name and type of each transmitted variable.
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TI82 STATS LINK
TI82 STATS Link
Capabilities
The TI82 STATS has a port to connect and communicate with another TI82 STATS, a TI82 STATS, the CalculatorBased
Laboratoryé (CBLé) System, the CalculatorBased Rangeré
(CBRé), or a personal computer. The unittounit link cable is included with the TI82 STATS. This chapter describes how to communicate with another calculator.
Linking Two
TI82 STATS calculators
You can transfer all variables and programs to another
TI82 STATS or backup the entire memory of a TI82 STATS.
The software that enables this communication is built into the
TI82 STATS. To transmit from one TI82 STATS to another, follow the steps on pages 19
.
6 and 19
.
7.
Linking a TI82 and a
TI82 STATS
You can transfer from a TI

82 to a TI82 STATS all variables and programs. Also, you can transfer from a TI82 STATS to a TI

82 lists
L
1
through
L
6
.
The software that enables this communication is built into the
TI82 STATS. To transmit data from a TI

82 to a TI82 STATS, follow the steps on pages 19
.
6 and 19
.
7.
•
You cannot perform a memory backup from a TI

82 to a
TI82 STATS.
•
The only data type you can transmit from a TI82 STATS to a TI

82 is list data stored in
L
1
through
L
6
. Use the
LINK
SEND
menu item
5:Lists to TI82
(page 19
.
8).
Connecting Two
Calculators with the Cable
1. Insert either end of the cable into the port very firmly.
2. Insert the other end of the cable into the other calculator’s port.
Linking to a CBR or the CBL
System
CBR and the CBL System are optional accessories that connect to a TI82 STATS with the unittounit link cable. With a CBR or a CBL and a TI82 STATS, you can collect and analyze realworld data.
Linking to a PC or Macintoshë
You can connect your TI82 STATS to a personal computer using TI Connect™ software and a TI Connectivity cable. The software is included on the CD in the TI82 STATS package.
When you connect to the TI Connect™ software, the TI82
STATS calculator will be identified by TI Connect™ as a TI83 calculator. Everything else should function as expected.
For more information, consult the TI Connect™ Help.
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Selecting Items to Send
LINK SEND Menu
To display the
LINK SEND
menu, press y [
LINK
].
SEND RECEIVE
1: All+...
2: AllN...
3: Prgm...
4: List...
5: Lists to TI82...
6: GDB...
7: Pic...
8: Matrix...
9: Real...
0: Complex...
A: YVars...
B: String...
C: Back Up...
Displays all items selected.
Displays all items deselected.
Displays all programs names.
Displays all list names.
Displays list names
L
1
through
L
6
.
Displays all graph databases.
Displays all picture data types.
Displays all matrix data types.
Displays all real variables.
Displays all complex variables.
Displays all
Y= variables.
Displays all string variables.
Selects all for backup to TI82 STATS.
When you select an item on the
LINK SEND
menu, the corresponding
SELECT
screen is displayed.
Note: Each
SELECT screen, except All+ SELECT, is displayed initially with no data selected.
Selecting Items to Send
To select items to send on the sending unit, follow these steps.
1. Press y [
LINK
] to display the
LINK SEND
menu.
2. Select the menu item that describes the data type to send.
The corresponding
SELECT
screen is displayed.
3. Press } and † to move the selection cursor (
4
) to an item you want to select or deselect.
4. Press Í to select or deselect the item. Selected names are marked with a
0
.
5. Repeat steps 3 and 4 to select or deselect additional items.
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Receiving Items
LINK RECEIVE
Menu
Receiving Unit
DuplicateName
Menu
Insufficient
Memory in
Receiving Unit
To display the
LINK RECEIVE
menu, press y [
LINK
] ~.
SEND RECEIVE
1: Receive
Sets unit to receive data transmission.
When you select
1:Receive
from the
LINK RECEIVE
menu on the receiving unit, the message
Waiting...
and the busy indicator are displayed. The receiving unit is ready to receive transmitted items. To exit the receive mode without receiving items, press
É, and then select
1:Quit
from the
Error in Xmit
menu.
To transmit, follow the steps on page 19
.
6.
When transmission is complete, the unit exits the receive mode.
You can select
1:Receive
again to receive more items. The receiving unit then displays a list of items received. Press y
[
QUIT
] to exit the receive mode.
During transmission, if a variable name is duplicated, the
DuplicateName
menu is displayed on the receiving unit.
DuplicateName
1: Rename
2: Overwrite
3: Omit
4: Quit
Prompts to rename receiving variable.
Overwrites data in receiving variable.
Skips transmission of sending variable.
Stops transmission at duplicate variable.
When you select
1:Rename
, the
Name=
prompt is displayed, and alphalock is on. Enter a new variable name, and then press
Í. Transmission resumes.
When you select
2:Overwrite
, the sending unit’s data overwrites the existing data stored on the receiving unit. Transmission resumes.
When you select
3:Omit
, the sending unit does not send the data in the duplicated variable name. Transmission resumes with the next item.
When you select
4:Quit
, transmission stops, and the receiving unit exits receive mode.
During transmission, if the receiving unit does not have sufficient memory to receive an item, the
Memory Full
menu is displayed on the receiving unit.
•
To skip this item for the current transmission, select
1:Omit
.
Transmission resumes with the next item.
•
To cancel the transmission and exit receive mode, select
2:Quit
.
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Transmitting Items
Transmitting
Items
To transmit selected items after you have selected items to send on the sending unit (page 19
.
4) and set the receiving unit to receive (page 19
.
5), follow these steps.
1. Press ~ on the sending unit to display the
TRANSMIT
menu.
2. Confirm that
Waiting...
is displayed on the receiving unit, which indicates it is set to receive (page 19
.
5).
3. Press Í to select
1:Transmit
. The name and type of each item are displayed line by line on the sending unit as the item is queued for transmission, and then on the receiving unit as each item is accepted.
Stopping a
Transmission
After all selected items have been transmitted, the message
Done
is displayed on both calculators. Press } and † to scroll through the names.
To stop a link transmission, press É. The
Error in Xmit
menu is displayed on both units. To leave the error menu, select
1:Quit
.
Error Conditions
A transmission error occurs after one or two seconds if:
•
A cable is not attached to the sending unit.
•
A cable is not attached to the receiving unit.
Note: If the cable is attached, push it in firmly and try again.
•
The receiving unit is not set to receive transmission.
•
You attempt a backup between a TI

82 and a TI82 STATS.
•
You attempt a data transfer from a TI82 STATS to a TI

82 with data other than lists
L
1
through
L
6
or without using menu item
5:Lists to TI82
.
Although a transmission error does not occur, these two conditions may prevent successful transmission.
•
You try to use
Get(
with a calculator instead of a CBL or
CBR.
•
You try to use
GetCalc(
with a TI

82 instead of a
TI82 STATS.
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Transmitting
Items to an
Additional
TI82 STATS
After sending or receiving data, you can repeat the same transmission to additional TI82 STATS units—from either the sending unit or the receiving unit—without having to reselect data to send. The current items remain selected.
Note: You cannot repeat transmission if you selected All+ or All ..
To transmit to an additional TI82 STATS, follow these steps.
1. Set the TI82 STATS to receive (page 19
.
5).
2. Do not select or deselect any new items to send. If you select or deselect an item, all selections or deselections from the previous transmission are cleared.
3. Disconnect the link cable from one TI82 STATS and connect it to the additional TI82 STATS.
4. Set the additional TI82 STATS to receive (page 19
.
5).
5. Press y [
LINK
] on the sending TI82 STATS to display the
LINK SEND
menu.
6. Select the menu item that you used for the last transmission.
The data from your last transmission is still selected.
7. Press ~ to display the
LINK TRANSMIT
menu.
8. Confirm that the receiving unit is set to receive (page 19
.
5).
9. Press Í to select
1:Transmit
and begin transmitting.
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Transmitting Lists to a TI

82
Transmitting
Lists to a TI82
The only data type you can transmit from a TI82 STATS to a
TI

82 is list data stored in
L
1
through
L
6
.
To transmit to a TI

82 the list data that is stored to
TI82 STATS lists
L
1
,
L
2
,
L
3
,
L
4
,
L
5
, or
L
6
, follow these steps.
1. Set the TI

82 to receive (page 19
.
5).
2. Press y [
LINK
]
5
on the sending TI82 STATS to select
5:Lists to TI82
. The
SELECT
screen is displayed.
3. Select each list to transmit.
4. Press ~ to display the
LINK TRANSMIT
menu.
5. Confirm that the receiving unit is set to receive (page 19
.
5).
6. Press Í to select
1:Transmit
and begin transmitting.
Note: If dimension > 99 for a TI82 STATS list that is selected to send, the receiving TI82 will truncate the list at the ninetyninth element during transmission.
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Transmitting from a TI

82 to a TI82 STATS
Resolved
Differences between the
TI82 and
TI82 STATS
Unresolved
Differences between the
TI82 and
TI82 STATS
Generally, you can transmit items to a TI82 STATS from a
TI

82, but differences between the two products may affect some transmitted data. This table shows differences for which the software built into the TI82 STATS automatically adjusts when a TI82 STATS receives TI

82 data.
TI.82
nMin
nStart
Un
Vn
UnStart
VnStart
TblMin
TI82 STATS u v
PlotStart
nMin u(nMin) v(nMin)
TblStart
For example, if you transmit from a TI

82 to a TI82 STATS a program that contains
nStart
on a command line and then display the program on the receiving TI82 STATS, you will see that
nMin
has automatically replaced
nStart
on the command line.
The software built into the TI82 STATS cannot resolve some differences between the TI

82 and TI82 STATS, which are described below. You must edit the data on the TI82 STATS after you transmit to account for these differences, or the
TI82 STATS will misinterpret the data.
The TI82 STATS reinterprets TI82 STATS prefix functions to include open parentheses, which may add extraneous parentheses to transmitted expressions.
For example, if you transmit
sin X+5
from a TI

82 to a
TI82 STATS, the TI82 STATS reinterprets it as
sin(X+5
.
Without a closing parenthesis after
X
, the TI82 STATS interprets this as
sin(X+5)
, not the sum of
5
and
sin(X)
.
If a TI

82 instruction that the TI82 STATS cannot translate is transmitted, the
ERR:INVALID
menu is displayed when the
TI82 STATS attempts to execute the instruction. For example, on the TI

82, the character group
U n1
is pasted to the cursor location when you press y [
UnN1
]. The TI82 STATS cannot directly translate
U n1
to the TI82 STATS syntax
u(nN1)
, so the
ERR:INVALID
menu is displayed.
Note: TI82 STATS implied multiplication rules differ from those of the
äääX,
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Backing Up Memory
Memory Backup
To copy the exact contents of memory in the sending
TI82 STATS to the memory of the receiving TI82 STATS, put the other unit in receive mode. Then, on the receiving unit, select
C:Back Up
from the
LINK SEND
menu.
•
Warning:
C:Back Up
overwrites the memory in the receiving unit; all information in the memory of the receiving unit is lost.
Note: If you do not want to do a backup, select
2:Quit to return to the LINK SEND menu.
•
Select
1:Transmit
to begin transmission.
Receiving Unit
As a safety check to prevent accidental loss of memory, the message
WARNING . Backup
is displayed when the receiving unit receives notice of a backup.
•
To continue with the backup process, select
1:Continue
. The backup transmission begins.
•
To prevent the backup, select
2:Quit
.
Note: If a transmission error is returned during a backup, the receiving unit is reset.
Memory Backup
Complete
When the backup is complete, both the sending calculator and receiving calculator display a confirmation screen.
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Contents
A
Tables and Reference
Information
Table of Functions and Instructions
............................................................
2
TI82 STATS Menu Map
..................................................................................
39
Variables
.......................................................................................................................
49
Statistics Formulas
.................................................................................................
50
Financial Formulas
................................................................................................
54
Tables and Reference Information A–1
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Table of Functions and Instructions
Functions return a value, list, or matrix. You can use functions in an expression.
Instructions initiate an action. Some functions and instructions have arguments. Optional arguments and accompanying commas are enclosed in brackets ( [ ] ). For details about an item, including argument descriptions and restrictions, turn to the page listed on the right side of the table.
From the
CATALOG
, you can paste any function or instruction to the home screen or to a command line in the program editor. However, some functions and instructions are not valid on the home screen. The items in this table appear in the same order as they appear in the
CATALOG
.
† indicates keystrokes that are valid in the program editor only. Some keystrokes display
menus that are available only in the program editor. Others paste mode, format, or tableset instructions only when you are in the program editor.
Function or Instruction/
Arguments
abs(
value
) abs(
complex value
)
valueA
and
valueB
angle(
value
)
ANOVA(
list1
,
list2
[
,
list3
,
...
,
list20]
)
Ans
Result
Returns the absolute value of a real number, expression, list, or matrix.
Returns the magnitude of a complex number or list.
Returns 1 if both valueA and
valueB are ƒ 0. valueA and
valueB can be real numbers, expressions, or lists.
Returns the polar angle of a complex number or list of complex numbers.
Performs a oneway analysis of variance for comparing the means of two to 20 populations.
Returns the last answer.
Key or Keys/
Menu or Screen/Item
NUM
1:abs(
213
1010
CPX
5:abs(
219 y [
TEST
]
LOGIC
1:and
226
CPX
4:angle(
219
…
TESTS
F:ANOVA(
1325 y [
ANS
] 118
A–2 Tables and Reference Information
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Function or Instruction/
Arguments Result
augment(
matrixA
,
matrixB
)
Returns a matrix, which is matrixB appended to matrixA as new columns.
augment(
listA
,
listB
)
Returns a list, which is listB concatenated to the end of listA.
AxesOff
AxesOn a+b
i
bal(
npmt[
,
roundvalue]
) binomcdf(
numtrials
,
p[
,
x]
) binompdf(
numtrials
,
p[
,
x]
) c
2 cdf(
lowerbound
,
upperbound
,
df
)
Turns off the graph axes.
Turns on the graph axes.
Sets the mode to rectangular complex number mode (a+bi).
Computes the balance at npmt for an amortization schedule using stored values for
PV
,
æ
, and
PMT
and rounds the computation to roundvalue.
Computes a cumulative probability at x for the discrete binomial distribution with the specified numtrials and probability p of success on each trial.
Computes a probability at x for the discrete binomial distribution with the specified numtrials and probability p of success on each trial.
Computes the c 2 distribution probability between lowerbound and upperbound for the specified degrees of freedom df.
Key or Keys/
Menu or Screen/Item
MATH
7:augment(
1014 y [
LIST
]
OPS
9:augment(
1115
† y [
FORMAT
]
AxesOff
† y [
FORMAT
]
AxesOn
† z
a+b
i
y [
FINANCE
]
CALC
9:bal(
314
314
112 y [
DISTR
]
DISTR
A:binomcdf(
y [
DISTR
]
DISTR
0:binompdf(
y [
DISTR
]
DISTR
7:c
2 cdf(
149
1333
1333
1331
Tables and Reference Information A–3
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Table of Functions and Instructions
(continued)
Function or Instruction/
Arguments
c
2 pdf(
x
,
df
) c
2
.Test(
observedmatrix
,
expectedmatrix
[
,
drawflag]
)
Circle(
X
,
Y
,
radius
)
Clear Entries
ClrAllLists
ClrDraw
ClrHome
ClrList
listname1
[
,
listname2
, ...,
listname n]
ClrTable conj(
value
)
Connected
Result
Computes the probability density function (pdf) for the c 2 distribution at a specified x value for the specified degrees of freedom df.
Performs a chisquare test.
drawflag=
1
draws results;
drawflag=
0
calculates results.
Draws a circle with center (X,Y) and radius.
Clears the contents of the Last
Entry storage area.
Sets to
0
the dimension of all lists in memory.
Clears all drawn elements from a graph or drawing.
Clears the home screen.
Sets to
0
the dimension of one or more listnames.
Clears all values from the table.
Returns the complex conjugate of a complex number or list of complex numbers.
Sets connected plotting mode; resets all Y= editor graphstyle settings to ç .
Key or Keys/
Menu or Screen/Item y [
DISTR
]
DISTR
6:c
2 pdf(
1331
† …
TESTS
C:c
2
.Test(
y [
DRAW
]
DRAW
9:Circle( y [
MEM
]
MEMORY
3:Clear Entries
y [
MEM
]
MEMORY
4:ClrAllLists
y [
DRAW
]
DRAW
1:ClrDraw
1322
811
184
184
84
†
I/O
8:ClrHome
1620
…
EDIT
4:ClrList
1220
†
I/O
9:ClrTable
1620
CPX
1:conj(
218
† z
Connected
111
A–4 Tables and Reference Information
826DEC~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09
PM Page 4 of 58
Function or Instruction/
Arguments
CoordOff
CoordOn cos(
value
) cos L1 (
value
) cosh(
value
) cosh
L1
(
value
)
CubicReg
[Xlistname
,
Ylistname
,
freqlist
,
regequ]
cumSum(
list
) cumSum(
matrix
) dbd(
date1
,
date2
)
value
4Dec
Result
Turns off cursor coordinate value display.
Turns on cursor coordinate value display.
Returns cosine of a real number, expression, or list.
Key or Keys/
Menu or Screen/Item
† y [
FORMAT
]
CoordOff
† y [
FORMAT
]
CoordOn
™
314
314
Returns arccosine of a real number, expression, or list.
Returns hyperbolic cosine of a real number, expression, or list.
Returns hyperbolic arccosine of a real number, expression, or list.
Fits a cubic regression model to
Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ.
23 y [
COS
L1
]
23 y [
CATALOG
]
cosh(
1510 y [
CATALOG
]
cosh
L1
(
1510
…
CALC
6:CubicReg
1226
Returns a list of the cumulative sums of the elements in list, starting with the first element.
Returns a matrix of the cumulative sums of matrix elements. Each element in the returned matrix is a cumulative sum of a matrix column from top to bottom.
Calculates the number of days between date1 and date2 using the actualdaycount method.
Displays a real or complex number, expression, list, or matrix in decimal format.
y [
LIST
]
OPS
6:cumSum(
MATH
0:cumSum(
y [
FINANCE
]
CALC
D:dbd(
MATH
2:4Dec
1112
1015
1413
25
Tables and Reference Information A–5
826DEC~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09
PM Page 5 of 58
Table of Functions and Instructions
(continued)
Function or Instruction/
Arguments
Degree
DelVar
variable
DependAsk
DependAuto det(
matrix
)
DiagnosticOff
DiagnosticOn dim(
listname
) dim(
matrixname
)
length
!
listname
)
{
rows
,
columns
}
!
dim(
matrixname
)
Disp
Disp
[valueA
,
valueB
,
valueC
,
...
,
value n]
Result
Sets degree angle mode.
Deletes from memory the contents of variable.
Sets table to ask for dependentvariable values.
Sets table to generate dependentvariable values automatically.
Returns determinant of matrix.
Sets diagnosticsoff mode;
r
,
r
2
and
R
2
are not displayed as regression model results.
,
Sets diagnosticson mode;
r
,
r
2
, and
R
2
are displayed as regression model results.
Returns the dimension of
listname.
Returns the dimension of
matrixname as a list.
Assigns a new dimension (length) to a new or existing listname.
Assigns new dimensions to a new or existing matrixname.
Displays the home screen.
Displays each value.
Key or Keys/
Menu or Screen/Item
† z
Degree
†
CTL
G:DelVar
†
I/O
3:Disp
111
1615
† y [
TBLSET
]
Depend: Ask
73
† y [
TBLSET
]
Depend: Auto
73
MATH
1:det(
y [
CATALOG
]
DiagnosticOff
1012
1223 y [
CATALOG
]
DiagnosticOn
1223 y [
LIST
]
OPS
3:dim(
MATH
3:dim(
y [
LIST
]
OPS
3:dim(
MATH
3:dim(
1111
1012
1111
1013
†
I/O
3:Disp
1618
1618
A–6 Tables and Reference Information
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PM Page 6 of 58
Function or Instruction/
Arguments
DispGraph
DispTable
value
4DMS
Dot
DrawF
expression
DrawInv
expression
:DS<(
:
variable
,
value
)
commandA
:
commands
e^(
power
) e^(
list
)
Exponent:
value
E
exponent
Exponent:
list
E
exponent
Exponent:
matrix
E
exponent
4Eff(
nominal rate
,
compounding periods
)
Else
See
If:Then:Else
Result
Displays the graph.
Displays the table.
Displays value in DMS format.
Sets dot plotting mode; resets all
Y=
editor graphstyle settings to í .
Draws expression (in terms of
X
) on the graph.
Draws the inverse of expression by plotting
X
values on the yaxis and
Y
values on the xaxis.
Decrements variable by 1; skips
commandA if variable < value.
Returns
e
raised to power.
Returns a list of
e
raised to a list of powers.
Returns value times 10 to the
exponent.
Returns list elements times 10 to the exponent.
Returns matrix elements times 10 to the exponent.
Computes the effective interest rate.
Key or Keys/
Menu or Screen/Item
†
I/O
4:DispGraph
1619
†
I/O
5:DispTable
1619 y [
ANGLE
]
ANGLE
4:4DMS
224
† z
Dot
111 y [
DRAW
]
DRAW
6:DrawF
y [
DRAW
]
DRAW
8:DrawInv
89
89
†
CTL
B:DS<(
y [ e
x
]
1614
24 y [ e
x
]
24 y [
EE
]
17 y [
EE
]
17 y [
EE
]
17 y [
FINANCE
]
CALC
C:4Eff(
1412
Tables and Reference Information A–7
826DEC~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09
PM Page 7 of 58
Table of Functions and Instructions
(continued)
Function or Instruction/
Arguments
End
Eng
Equ4String(Y=
var
,Str
n
) expr(
string
)
ExpReg
[Xlistname
,
Ylistname
,
freqlist
,
regequ]
ExprOff
ExprOn
lowerbound
,
upperbound
,
numerator df
,
denominator df
)
Fill(
value
,
matrixname
)
Fill(
value
,
listname
)
Fix
#
Float
Result
Identifies end of
For(
,
If

Then

Else
,
Repeat
, or
While
loop.
Sets engineering display mode.
Converts the contents of a Y=
var
to a string and stores it in
Str
n.
Converts string to an expression and executes it.
Fits an exponential regression model to Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ.
Turns off the expression display during TRACE .
Turns on the expression display during TRACE .
Computes the Û distribution probability between lowerbound and upperbound for the specified
numerator df (degrees of freedom) and denominator df.
Key or Keys/
Menu or Screen/Item
†
CTL
7:End
† z
Eng
y [
CATALOG
]
Equ4String(
1612
110
157 y [
CATALOG
]
expr(
…
CALC
0:ExpReg
157
† y [
FORMAT
]
ExprOff
† y [
FORMAT
]
ExprOn
y [
DISTR
]
DISTR
9:
ÛÛ
cdf(
1226
314
314
Stores value to each element in
matrixname.
Stores value to each element in
listname.
Sets fixeddecimal mode for # of decimal places.
Sets floating decimal mode.
1332
MATH
4:Fill(
y [
LIST
]
OPS
4:Fill(
1013
† z
Float
1111
† z
0123456789
(select one) 110
110
A–8 Tables and Reference Information
826DEC~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09
PM Page 8 of 58
Function or Instruction/
Arguments
fMax(
expression
,
variable
,
lower
,
upper[
,
tolerance]
) fMin(
expression
,
variable
,
lower
,
upper[
,
tolerance]
) fnInt(
expression
,
variable
,
lower
,
upper[
,
tolerance]
)
FnOff
[function#
,
function#
,...,
function n]
FnOn
[function#
,
function#
,...,
function n]
:For(
variable
,
begin
,
end
:
[
,
increment]
)
commands
:End
:
commands
fPart(
value
)
x
,
numerator df
,
denominator df
)
Result
Returns the value of variable where the local maximum of
expression occurs, between lower and upper, with specified
tolerance.
Returns the value of variable where the local minimum of
expression occurs, between lower and upper, with specified
tolerance.
Returns the function integral of
expression with respect to
variable, between lower and
upper, with specified tolerance.
Key or Keys/
Menu or Screen/Item
MATH
7:fMax(
MATH
6:fMin(
MATH
9:fnInt(
26
26
27
Deselects all Y= functions or specified
Y= functions.
Selects all
Y= functions or specified Y= functions.
Executes commands through
End
, incrementing variable from
begin by increment until
variable>end.
YVARS On/Off
2:FnOff
YVARS On/Off
1:FnOn
†
CTL
4:For(
38
38
1610
Returns the fractional part or parts of a real or complex number, expression, list, or matrix.
NUM
4:fPart(
214
1011
Computes the Û distribution probability between lowerbound and upperbound for the specified
numerator df (degrees of freedom) and denominator df.
y [
DISTR
]
DISTR
8:
ÛÛ
1332
Tables and Reference Information A–9
826DEC~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09
PM Page 9 of 58
Table of Functions and Instructions
(continued)
Function or Instruction/
Arguments
value
4Frac
Full
Func gcd(
valueA,valueB
) geometcdf(
p
,
x
) geometpdf(
p
,
x
)
Get(
variable
)
GetCalc(
variable
) getKey
Goto
label
Result
Displays a real or complex number, expression, list, or matrix as a fraction simplified to its simplest terms.
Sets full screen mode.
Sets function graphing mode.
Returns the greatest common divisor of valueA and valueB, which can be real numbers or lists.
Computes a cumulative probability at x, the number of the trial on which the first success occurs, for the discrete geometric distribution with the specified probability of success p.
Key or Keys/
Menu or Screen/Item
MATH
1:4Frac
25
† z
Full
112
† z
Func
NUM
9:gcd(
111
215 y [
DISTR
]
DISTR
E:geometcdf(
Computes a probability at x, the number of the trial on which the first success occurs, for the discrete geometric distribution with the specified probability of success p. y [
DISTR
]
DISTR
D:geometpdf(
Gets data from the CBL System or
CBR and stores it in variable.
Gets contents of variable on another TI82 STATS and stores it to variable on the receiving
TI82 STATS.
Returns the key code for the current keystroke, or
0
, if no key is pressed.
Transfers control to label.
1334
†
I/O
A:Get(
1621
†
I/O
0:GetCalc(
1621
†
I/O
7:getKey
†
CTL
0:Goto
1334
1620
1613
A–10 Tables and Reference Information
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PM Page 10 of 58
Function or Instruction/
Arguments
GraphStyle(
function#
,
graphstyle#
)
GridOff
GridOn
GT
Horiz
Horizontal
y
identity(
dimension
)
:
:
:If
condition commandA commands
:If
condition
:Then
:
commands
:End
:
commands
:If
condition
:Then
:
commands
:Else
:
commands
:End
:
commands
imag(
value
)
Result
Sets a graphstyle for function#.
Turns off grid format.
Turns on grid format.
Sets graphtable vertical splitscreen mode.
Sets horizontal splitscreen mode.
Draws a horizontal line at y.
Returns the identity matrix of
dimension rows × dimension columns.
If condition = 0 (false), skips
commandA.
Executes commands from
Then
to
End
if condition = 1 (true).
Key or Keys/
Menu or Screen/Item
†
CTL
H:GraphStyle(
1615
† y [
FORMAT
]
GridOff
314
† y [
FORMAT
]
GridOn
† z
GT
† z
Horiz
y [
DRAW
]
DRAW
3:Horizontal
MATH
5:identity(
314
112
112
86
1013
†
CTL
1:If
†
CTL
2:Then
169
169
Executes commands from
Then
to
Else
if condition = 1 (true); from
Else
to
End
if condition = 0
(false).
†
CTL
3:Else
1610
Returns the imaginary (nonreal) part of a complex number or list of complex numbers.
CPX
3:imag(
218
Tables and Reference Information A–11
826DEC~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09
PM Page 11 of 58
Table of Functions and Instructions
(continued)
Function or Instruction/
Arguments
IndpntAsk
IndpntAuto
Input
Input
[variable]
Input
[
"
text
",
variable]
Input [
Str
n
,
variable]
inString(
string
,
substring
[
,
start]
) int(
value
)
GInt(
pmt1
,
pmt2
[
,
roundvalue]
) invNorm(
area[
,
m
,
s]
) iPart(
value
)
Result
Sets table to ask for independentvariable values.
Sets table to generate independentvariable values automatically.
Displays graph.
Prompts for value to store to
variable.
Displays
Str
n and stores entered value to variable.
Returns the character position in
string of the first character of
substring beginning at start.
Returns the largest integer a real or complex number, expression, list, or matrix.
Computes the sum, rounded to
roundvalue, of the interest amount between pmt1 and pmt2 for an amortization schedule.
Key or Keys/
Menu or Screen/Item
† y [
TBLSET
]
Indpnt: Ask
† y [
TBLSET
]
Indpnt: Auto
73
73
†
I/O
1:Input
†
I/O
1:Input
†
I/O
1:Input
y [
CATALOG
]
inString(
1616
1617
1617
157
NUM
5:int(
214
1011 y [
FINANCE
]
CALC
A:GInt(
149
Computes the inverse cumulative normal distribution function for a given area under the normal distribution curve specified by and s
.
m
Returns the integer part of a real or complex number, expression, list, or matrix.
y [
DISTR
]
DISTR
3:invNorm(
NUM
3:iPart(
1330
214
1011
A–12 Tables and Reference Information
826DEC~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09
PM Page 12 of 58
Function or Instruction/
Arguments
irr(
CF0
,
CFList[
,
CFFreq]
)
:IS>(
variable
,
value
)
:
commandA
:
commands
ÙÙÙÙ
listname
LabelOff
LabelOn
Lbl
label
lcm(
valueA,valueB
) length(
string
)
Line(
X1
,
Y1
,
X2
,
Y2
)
Line(
X1
,
Y1
,
X2
,
Y2
,0)
Result
Returns the interest rate at which the net present value of the cash flows is equal to zero.
Increments variable by 1; skips commandA if
variable>value.
Identifies the next one to five characters as a usercreated list name.
Turns off axes labels.
Turns on axes labels.
Creates a label of one or two characters.
Returns the least common multiple of valueA and valueB, which can be real numbers or lists.
Returns the number of characters in string.
Draws a line from (X1,Y1) to
(X2,Y2).
Erases a line from (X1,Y1) to
(X2,Y2).
Key or Keys/
Menu or Screen/Item y [
FINANCE
]
CALC
8:irr(
148
†
CTL
A:IS>(
1613 y [
LIST
]
OPS
B:
ÙÙÙÙ
† y [
FORMAT
]
LabelOff
† y [
FORMAT
]
LabelOn
†
CTL
9:Lbl
NUM
8:lcm(
1116
314
314
1613
215 y [
CATALOG
]
length(
y [
DRAW
]
DRAW
2:Line(
y [
DRAW
]
DRAW
2:Line(
158
85
85
Tables and Reference Information A–13
826DEC~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09
PM Page 13 of 58
Table of Functions and Instructions
(continued)
Function or Instruction/
Arguments
LinReg(a+bx)
[Xlistname
,
Ylistname
,
freqlist
,
regequ]
LinReg(ax+b)
[Xlistname
,
Ylistname
,
freqlist
,
regequ]
LinRegTTest
[Xlistname
,
Ylistname
,
freqlist
,
alternative
,
regequ]
@List(
list
)
List
4 matr(
listname1
,
...
,
listname n
,
matrixname
) ln(
value
)
LnReg
[Xlistname
,
Ylistname
,
freqlist
,
regequ]
log(
value
)
Result
Fits a linear regression model to
Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ.
Key or Keys/
Menu or Screen/Item
…
CALC
8:LinReg(a+bx)
…
CALC
4:LinReg(ax+b)
1226
Fits a linear regression model to
Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ.
Performs a linear regression and a
ttest. alternative=
L1
is <;
alternative=
0
is ƒ; alternative=
1
is >.
Returns a list containing the differences between consecutive elements in list.
Fills matrixname column by column with the elements from each specified listname.
Returns the natural logarithm of a real or complex number, expression, or list.
Fits a logarithmic regression model to Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ.
1225
† …
TESTS
E:LinRegTTest
1324 y [
LIST
]
OPS
1112
7:@List(
y [
LIST
]
OPS
0:List
4 matr(
1014
1115
µ
…
CALC
9:LnReg
24
1226
Returns logarithm of a real or complex number, expression, or list.
«
24
A–14 Tables and Reference Information
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PM Page 14 of 58
Function or Instruction/
Arguments
Logistic
[Xlistname
,
Ylistname
,
freqlist
,
regequ]
Matr
4 list(
matrix
,
listnameA
,
...
,
listname n
)
Matr
4 list(
matrix
,
column#
,
listname
) max(
valueA
,
valueB
) max(
list
) max(
listA
,
listB
) max(
value,list
) mean(
list[
,
freqlist]
) median(
list[
,
freqlist]
)
MedMed
[Xlistname
,
Ylistname
,
freqlist
,
regequ]
Menu("
title
","
text1
",
label1
[
,
...
,"
text7
",
label7]
)
Result
Fits a logistic regression model to
Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ.
Key or Keys/
Menu or Screen/Item
…
CALC
B:Logistic
1227
Fills each listname with elements from each column in matrix.
Fills a listname with elements from a specified column# in matrix.
Returns the larger of valueA and
valueB.
Returns largest real or complex element in list.
Returns a real or complex list of the larger of each pair of elements in listA and listB.
y [
LIST
]
OPS
A:Matr
4 list(
y [
LIST
]
OPS
A:Matr
4 list(
NUM
7:max(
y [
LIST
]
MATH
2:max(
y [
LIST
]
MATH
2:max(
1014
1116
1014
1116
215
1116
1116
Returns a real or complex list of the larger of value or each list element.
Returns the mean of list with frequency freqlist.
Returns the median of list with frequency freqlist.
Fits a medianmedian model to
Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ.
y [
LIST
ä
MATH
2:max(
y [
LIST
]
MATH
3:mean(
y [
LIST
]
MATH
4:median(
…
CALC
3:MedMed
1116
1116
1116
1225
Generates a menu of up to seven items during program execution.
†
CTL
C:Menu(
1614
Tables and Reference Information A–15
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PM Page 15 of 58
Table of Functions and Instructions
(continued)
Function or Instruction/
Arguments
min(
valueA
,
valueB
) min(
list
) min(
listA
,
listB
) min(
value,list
)
valueA
nCr
valueB
value
nCr
list
list
nCr
value
listA
nCr
listB
nDeriv(
expression
,
variable
,
value[
,
H]
)
4Nom(
effective rate
,
compounding periods
)
Normal
Result
Returns smaller of valueA and
valueB.
Returns smallest real or complex element in list.
Returns real or complex list of the smaller of each pair of elements in listA and listB.
Returns a real or complex list of the smaller of value or each list element.
Returns the number of combinations of valueA taken
valueB at a time.
Returns a list of the combinations of value taken each element in list at a time.
Returns a list of the combinations of each element in list taken value at a time.
Returns a list of the combinations of each element in listA taken each element in listB at a time.
Returns approximate numerical derivative of expression with respect to variable at value, with specified H.
PRB
3:nCr
PRB
3:nCr
PRB
3:nCr
Key or Keys/
Menu or Screen/Item
NUM
6:min(
215 y [
LIST
]
MATH
1:min(
y [
LIST
]
MATH
1:min(
y [
LIST
]
MATH
1:min(
1116
1116
1116
221
221
221
PRB
3:nCr
221
MATH
8:nDeriv(
27
Computes the nominal interest rate.
Sets normal display mode.
y [
FINANCE
]
CALC
B:4Nom(
† z
Normal
1412
110
A–16 Tables and Reference Information
826DEC~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09
PM Page 16 of 58
Function or Instruction/
Arguments
normalcdf(
lowerbound
,
upperbound[
,
m
,
s]
) normalpdf(
x[
,
m
,
s]
) not(
value
)
valueA
nPr
valueB
value
nPr
list
list
nPr
value
listA
nPr
listB
npv(
interest rate
,
CF0
,
CFList[
,
CFFreq]
)
valueA
or
valueB
Result
Computes the normal distribution probability between lowerbound and upperbound for the specified m
and s
.
Key or Keys/
Menu or Screen/Item y [
DISTR
]
DISTR
2:normalcdf(
1327
Computes the probability density function for the normal distribution at a specified x value for the specified m
and s
.
Returns
0
if value is ƒ 0. value can be a real number, expression, or list.
Returns the number of permutations of valueA taken
valueB at a time.
Returns a list of the permutations of value taken each element in list at a time.
Returns a list of the permutations of each element in list taken value at a time.
Returns a list of the permutations of each element in listA taken each element in listB at a time.
y [
DISTR
]
DISTR
1:normalpdf(
y [
TEST
]
LOGIC
4:not(
PRB
2:nPr
PRB
2:nPr
PRB
2:nPr
PRB
2:nPr
1329
226
221
221
221
221
Computes the sum of the present values for cash inflows and outflows.
Returns 1 if valueA or valueB is ƒ
0. valueA and valueB can be real numbers, expressions, or lists.
y [
FINANCE
]
CALC
7:npv(
y [
TEST
]
LOGIC
2:or
148
226
Tables and Reference Information A–17
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PM Page 17 of 58
Table of Functions and Instructions
(continued)
Function or Instruction/
Arguments Result
Output(
row
,
column
,"
text
")
Displays text beginning at specified row and column.
Output(
row
,
column
,
value
)
Param
Pause
Pause
[value]
Plot
#
(
type
,
Xlistname
,
Ylistname
,
mark
)
Plot
#
(
type
,
Xlistname
,
freqlist
)
Plot
#
(
type
,
Xlistname
,
freqlist
,
mark
)
Plot
#
(
type
,
datalistname
,
data axis
,
mark
)
PlotsOff
[
1,2,3
]
PlotsOn
[
1,2,3
]
Displays value beginning at specified row and column.
Sets parametric graphing mode.
Suspends program execution until you press Í.
Displays value; suspends program execution until you press Í.
Defines
Plot
# (
1
,
2
, or
3
) of type
Scatter
or
xyLine
for Xlistname and Ylistname using mark.
Defines
Plot
# (
1
,
2
, or
3
) of type
Histogram
or
Boxplot
for
Xlistname with frequency freqlist.
Defines
Plot
# (
1
,
2
, or
3
) of type
ModBoxplot
for Xlistname with frequency freqlist using mark.
Defines
Plot
# (
1
,
2
, or
3
) of type
NormProbPlot
for datalistname on data axis using mark. data
axis can be
X
or
Y
.
Deselects all stat plots or one or more specified stat plots (
1
,
2
, or
3
).
Selects all stat plots or one or more specified stat plots (
1
,
2
, or
3
).
Key or Keys/
Menu or Screen/Item
†
I/O
6:Output(
†
I/O
6:Output(
† z
Par
1619
1619
111
†
CTL
8:Pause
†
CTL
8:Pause
1612
1612
† y [
STAT PLOT
]
PLOTS
1:Plot1(
2:Plot2(
3:Plot3(
1237
† y [
STAT PLOT
]
PLOTS
1:Plot1(
2:Plot2(
3:Plot3(
1237
† y [
STAT PLOT
]
PLOTS
1:Plot1(
2:Plot2(
3:Plot3(
1237
† y [
STAT PLOT
]
PLOTS
1:Plot1(
2:Plot2(
3:Plot3(
y [
STAT PLOT
]
1237
STAT PLOTS
4:PlotsOff
1235 y [
STAT PLOT
]
STAT PLOTS
5:PlotsOn
1235
A–18 Tables and Reference Information
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PM Page 18 of 58
Function or Instruction/
Arguments
Pmt_Bgn
Pmt_End poissoncdf(
m
,
x
) poissonpdf(
m
,
x
)
Polar
complex value
4Polar
PolarGC prgm
name
GPrn(
pmt1
,
pmt2
[
,
roundvalue]
) prod(
list[
,
start
,
end]
)
Prompt
variableA
[
,
variableB
,
...
,
variable n
]
Result
Specifies an annuity due, where payments occur at the beginning of each payment period.
Specifies an ordinary annuity, where payments occur at the end of each payment period.
Computes a cumulative probability at x for the discrete
Poisson distribution with specified mean m.
Computes a probability at x for the discrete Poisson distribution with the specified mean m.
Sets polar graphing mode.
Displays complex value in polar format.
Sets polar graphing coordinates format.
Executes the program name.
Computes the sum, rounded to
roundvalue, of the principal amount between pmt1 and pmt2 for an amortization schedule.
Key or Keys/
Menu or Screen/Item y [
FINANCE
]
CALC
F:Pmt_Bgn
1413 y [
FINANCE
]
CALC
E:Pmt_End
y [
DISTR
]
DISTR
C:poissoncdf(
1413
1334 y [
DISTR
]
DISTR
B:poissonpdf(
1333
† z
Pol
CPX
7:4Polar
† y [
FORMAT
]
PolarGC
†
CTRL
D:prgm
y [
FINANCE
]
CALC
0:GPrn(
111
219
313
1615
149
Returns product of list elements between start and end.
Prompts for value for variableA, then variableB, and so on.
y [
LIST
]
MATH
6:prod(
†
I/O
2:Prompt
1118
1618
Tables and Reference Information A–19
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PM Page 19 of 58
Table of Functions and Instructions
(continued)
Function or Instruction/
Arguments
1.PropZInt(
x
,
n
[
,
confidence level]
)
2.PropZInt(
x1
,
n1
,
x2
,
n2
[
,
confidence level]
)
1.PropZTest(
p0
,
x
,
n
[
,
alternative
,
drawflag]
)
2.PropZTest(
x1
,
n1
,
x2
,
n2
[
,
alternative
,
drawflag]
)
Pt.Change(
x
,
y
)
Pt.Off(
x
,
y[
,
mark]
)
Pt.On(
x
,
y[
,
mark]
)
PwrReg
[Xlistname
,
Ylistname
,
freqlist
,
regequ]
Result
Computes a oneproportion
z confidence interval.
Computes a twoproportion
z confidence interval.
Key or Keys/
Menu or Screen/Item
† …
TESTS
A:1.PropZInt(
1320
† …
TESTS
B:2.PropZInt(
1321
† …
TESTS
5:1.PropZTest(
Computes a oneproportion z test.
alternative=
L1
is <; alternative=
0
is ƒ; alternative=
1
is >.
drawflag=
1
draws results;
drawflag=
0
calculates results.
Computes a twoproportion z test.
alternative=
L1
is <; alternative=
0
is ƒ; alternative=
1
is >.
drawflag=
1
draws results;
drawflag=
0
calculates results.
1314
† …
TESTS
6:2.PropZTest(
1315
Reverses a point at (x,y).
Erases a point at (x,y) using mark.
Draws a point at (x,y) using mark.
Fits a power regression model to
Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ.
y [
DRAW
]
POINTS
3:Pt.Change(
y [
DRAW
]
POINTS
2:Pt.Off(
y [
DRAW
]
POINTS
1:Pt.On(
…
CALC
A:PwrReg
815
815
814
1227
A–20 Tables and Reference Information
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PM Page 20 of 58
Function or Instruction/
Arguments
Pxl.Change(
row
,
column
)
Pxl.Off(
row
,
column
)
Pxl.On(
row
,
column
) pxl.Test(
row
,
column
)
P4Rx(
r
,
P4Ry(
r
,
q
)
q
)
QuadReg
[Xlistname
,
Ylistname
,
freqlist
,
regequ]
QuartReg
[Xlistname
,
Ylistname
,
freqlist
,
regequ]
Radian rand
[
(
numtrials
)
]
randBin(
numtrials
,
prob
[
,
numsimulations]
)
Result
Reverses pixel at (row,column);
0 row 62 and
0 column 94.
Erases pixel at (row,column);
0 row 62 and
0 column 94.
Draws pixel at (row,column);
0 row 62 and
0 column 94.
Returns 1 if pixel (row, column) is on, 0 if it is off; 0 row 62 and 0 column 94.
Returns
X
, given polar coordinates r and q or a list of polar coordinates.
Returns
Y
, given polar coordinates r and q or a list of polar coordinates.
Fits a quadratic regression model to Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ.
Key or Keys/
Menu or Screen/Item y [
DRAW ä
POINTS
6:Pxl.Change(
y [
DRAW
]
POINTS
5:Pxl.Off(
y [
DRAW
]
POINTS
4:Pxl.On(
y [
DRAW
]
POINTS
7:pxl.Test(
816
816
816
816 y [
ANGLE
]
ANGLE
7:P4Rx(
y [
ANGLE
]
ANGLE
8:P4Ry(
…
CALC
5:QuadReg
224
224
1225
Fits a quartic regression model to
Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ.
…
CALC
7:QuartReg
1226
Sets radian angle mode.
Returns a random number between 0 and 1 for a specified number of trials numtrials.
† z
Radian
PRB
1:rand
111
220
Generates and displays a random real number from a specified
Binomial distribution.
PRB
7:randBin(
222
Tables and Reference Information A–21
826DEC~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09
PM Page 21 of 58
Table of Functions and Instructions
(continued)
Function or Instruction/
Arguments
randInt(
lower,upper
[,numtrials]
)
Result
Generates and displays a random integer within a range specified by lower and upper integer bounds for a specified number of trials numtrials.
Returns a random matrix of rows
(
1
–
99
) × columns (
1
–
99
).
Key or Keys/
Menu or Screen/Item
PRB
5:randInt(
222
randM(
rows
,
columns
) randNorm(
m
,
s
[
,
numtrials]
)
Generates and displays a random real number from a specified
Normal distribution specified by m and s for a specified number of trials numtrials.
r
e
^q
i
Real real(
value
)
RecallGDB
n
RecallPic
n
complex value
4Rect
RectGC ref(
matrix
)
Sets the mode to polar complex number mode (
r
e
^q
i).
Sets mode to display complex results only when you enter complex numbers.
Returns the real part of a complex number or list of complex numbers.
Restores all settings stored in the graph database variable
GDB
n.
Displays the graph and adds the picture stored in
Pic
n.
Displays complex value or list in rectangular format.
Sets rectangular graphing coordinates format.
Returns the rowechelon form of a matrix.
MATH
6:randM(
PRB
6:randNorm(
1013
222
† z
r
e
^q
i
112
† z
Real
CPX
2:real(
y [
DRAW
]
STO
4:RecallGDB
y [
DRAW
]
STO
2:RecallPic
CPX
6:4Rect
112
218
820
818
219
† y [
FORMAT
]
RectGC
MATH
A:ref(
313
1015
A–22 Tables and Reference Information
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PM Page 22 of 58
Function or Instruction/
Arguments
:Repeat
condition
:
commands
:End
:
commands
Return round(
value[
,
#decimals]
)
äääärow(
value
,
matrix
,
row
) row+(
matrix
,
rowA
,
rowB
)
äääärow+(
value
,
matrix
,
rowA
,
rowB
) rowSwap(
matrix
,
rowA
,
rowB
) rref(
matrix
)
R4Pr(
x
,
y
)
R4Pq(
x
,
y
)
Result
Executes commands until
condition is true.
Key or Keys/
Menu or Screen/Item
†
CTL
6:Repeat
1611
Returns to the calling program.
Returns a number, expression, list, or matrix rounded to
#decimals ( 9).
Returns a matrix with row of
matrix multiplied by value and stored in row.
Returns a matrix with rowA of
matrix added to rowB and stored in rowB.
Returns a matrix with rowA of
matrix multiplied by value, added to rowB, and stored in rowB.
†
CTL
E:Return
NUM
2:round(
MATH
E:
äääärow(
MATH
D:row+(
MATH
F:
äääärow+(
Returns a matrix with rowA of
matrix swapped with rowB.
Returns the reduced rowechelon form of a matrix.
Returns
R
, given rectangular coordinates x and y or a list of rectangular coordinates.
Returns
q
, given rectangular coordinates x and y or a list of rectangular coordinates.
MATH
C:rowSwap(
MATH
B:rref(
y [
ANGLE
]
ANGLE
5:R4Pr(
y [
ANGLE
]
ANGLE
6:R4Pq(
1615
213
1016
1016
1016
1016
1015
224
224
Tables and Reference Information A–23
826DEC~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09
PM Page 23 of 58
Table of Functions and Instructions
(continued)
Function or Instruction/
Arguments
[listname1
,
listname2
,
freqlist1
,
freqlist2
,
alternative
,
drawflag]
(Data list input)
Sx1
,
n1
,
Sx2
,
n2[
,
alternative
,
drawflag]
(Summary stats input)
2.SampTInt
[listname1
,
listname2
,
freqlist1
,
freqlist2
,
confidence level
,
pooled]
(Data list input)
2.SampTInt
v
1
,
Sx1
,
n1
,
v
2
,
Sx2
,
n2
[
,
confidence level
,
pooled]
(Summary stats input)
2.SampTTest
[listname1
,
listname2
,
freqlist1
,
freqlist2
,
alternative
,
pooled
,
drawflag]
(Data list input)
Result
Performs a twosample Û test.
alternative=
L1
is
<
; alternative=
0
is
ƒ
; alternative=
1
is
>
.
drawflag=
1
draws results;
drawflag=
0
calculates results.
Key or Keys/
Menu or Screen/Item
† …
TESTS
D:2.SampÛ
1323
Performs a twosample Û test.
alternative=
L1
is
<
; alternative=
0
is
ƒ
; alternative=
1
is
>
.
drawflag=
1
draws results;
drawflag=
0
calculates results.
† …
TESTS
D:2.SampÛ
† …
TESTS
0:2.SampTInt
1323
Computes a twosample t confidence interval. pooled=
1
pools variances; pooled=
0
does not pool variances.
Computes a twosample t confidence interval. pooled=
1
pools variances; pooled=
0
does not pool variances.
Computes a twosample t test.
alternative=
L1
is
<
; alternative=
0
is
ƒ
; alternative=
1
is
>
. pooled=
1
pools variances; pooled=
0
does not pool variances. drawflag=
1
draws results; drawflag=
0
calculates results.
1319
† …
TESTS
0:2.SampTInt
1319
† …
TESTS
4:2.SampTTest
1313
A–24 Tables and Reference Information
826DEC~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09
PM Page 24 of 58
Function or Instruction/
Arguments
2.SampTTest
v
1
,
Sx1
,
n1
,
v
2
,
Sx2
,
n2[
,
alternative
,
pooled
,
drawflag]
(Summary stats input)
2.SampZInt(
s v
1
,
n1
,
v
2
,
n2
1
,
s
freqlist1
,
freqlist2
,
confidence level]
)
(Data list input)
2
[
,
listname1
,
listname2
,
2.SampZInt(
s
1
,
s
2
,
v
1
,
n1
,
v
2
,
n2
[
,
confidence level]
)
(Summary stats input)
2.SampZTest(
s 1, s
freqlist1
,
freqlist2
,
alternative
,
drawflag]
)
(Data list input)
2
[
,
listname1
,
listname2
,
2.SampZTest(
s
1, s
2
,
[
,
alternative
,
drawflag]
)
(Summary stats input)
Sci
Select(
Xlistname
,
Ylistname
)
Result
Computes a twosample t test.
alternative=
L1
is
<
; alternative=
0
is
ƒ
; alternative=
1
is
>
. pooled=
1
pools variances; pooled=
0
does not pool variances. drawflag=
1
draws results; drawflag=
0
calculates results.
Computes a twosample z confidence interval.
Key or Keys/
Menu or Screen/Item
† …
TESTS
4:2.SampTTest
† …
TESTS
9:2.SampZInt(
1313
Computes a twosample z confidence interval.
Computes a twosample z test.
alternative=
L1
is
<
; alternative=
0
is
ƒ
; alternative=
1
is
>
.
drawflag=
1
draws results;
drawflag=
0
calculates results.
Computes a twosample z test.
alternative=
L1
is
<
; alternative=
0
is
ƒ
; alternative=
1
is
>
.
drawflag=
1
draws results;
drawflag=
0
calculates results.
† …
TESTS
1318
† …
TESTS
9:2.SampZInt(
1318
3:2.SampZTest(
1312
† …
TESTS
3:2.SampZTest(
1312
Sets scientific notation display mode.
Selects one or more specific data points from a scatter plot or xyLine plot (only), and then stores the selected data points to two new lists, Xlistname and
Ylistname.
† z
Sci
y [
LIST
]
OPS
8:Select(
110
1112
Tables and Reference Information A–25
826DEC~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09
PM Page 25 of 58
Table of Functions and Instructions
(continued)
Function or Instruction/
Arguments
Send(
variable
) seq(
expression
,
variable
,
begin
,
end[
,
increment]
)
Seq
Sequential
SetUpEditor
SetUpEditor
listname1
[
,
listname2
,
...
,
listname20]
Shade(
lowerfunc
,
upperfunc[
,
Xleft
,
Xright
,
pattern
,
patres]
)
Shadec
2
(
lowerbound
,
upperbound
,
df
)
Result
Sends contents of variable to the
CBL System or CBR.
Returns list created by evaluating
expression with regard to
variable, from begin to end by
increment.
Sets sequence graphing mode.
Sets mode to graph functions sequentially.
Removes all list names from the stat list editor, and then restores list names
L
1
through
L
6
to columns
1
through
6
.
Removes all list names from the stat list editor, then sets it up to display one or more listnames in the specified order, starting with column
1
.
Draws lowerfunc and upperfunc in terms of
X
on the current graph and uses pattern and patres to shade the area bounded by
lowerfunc, upperfunc, Xleft, and
Xright.
Draws the density function for the c
2 distribution specified by degrees of freedom df and shades the area between lowerbound and
upperbound.
y [
DRAW
]
DRAW
7:Shade(
y [
DISTR
]
DRAW
3:Shadec
2
(
Key or Keys/
Menu or Screen/Item
†
I/O
B:Send(
y [
LIST
]
OPS
5:seq(
1621
1111
† z
Seq
† z
Sequential
…
EDIT
5:SetUpEditor
111
112
1221
…
EDIT
5:SetUpEditor
1221
810
1336
A–26 Tables and Reference Information
826DEC~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09
PM Page 26 of 58
Function or Instruction/
Arguments
Shade
Ü(
lowerbound
,
upperbound
,
numerator df
,
denominator df
)
ShadeNorm(
lowerbound
,
upperbound[
,
m
,
s]
)
Shade_t(
lowerbound
,
upperbound
,
df
)
Simul sin(
value
) sin
L1
(
value
) sinh(
value
) sinh
L1
(
value
)
Result
Draws the density function for the
Û distribution specified by
numerator df and denominator df and shades the area between
lowerbound and upperbound.
Key or Keys/
Menu or Screen/Item y [
DISTR
]
DRAW
4:Shade
Ü
Draws the normal density function specified by m and s and shades the area between
lowerbound and upperbound.
Draws the density function for the
Studentt distribution specified by degrees of freedom df, and shades the area between lowerbound and
upperbound.
y [
DISTR
]
DRAW
1:ShadeNorm(
1336
1335 y [
DISTR
]
DRAW
2:Shade_t(
Sets mode to graph functions simultaneously.
Returns the sine of a real number, expression, or list.
Returns the arcsine of a real number, expression, or list.
Returns the hyperbolic sine of a real number, expression, or list.
Returns the hyperbolic arcsine of a real number, expression, or list.
1336
† z
Simul
˜
112
23 y [
SIN
L1 ]
23 y [
CATALOG
]
sinh(
1510 y [
CATALOG
]
sinh L1 (
1510
Tables and Reference Information A–27
826DEC~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09
PM Page 27 of 58
Table of Functions and Instructions
(continued)
Function or Instruction/
Arguments
SinReg
[iterations
,
Xlistname
,
Ylistname
,
period
,
regequ]
solve(
expression
,
variable
,
guess
,{
lower
,
upper
})
SortA(
listname
)
SortA(
keylistname
,
dependlist1[
,
dependlist2
,
...,
dependlist n]
)
SortD(
listname
)
SortD(
keylistname
,
dependlist1[
,
dependlist2
,
...
,
dependlist n]
) stdDev(
list[
,
freqlist]
)
Stop
Store: value
!
variable
StoreGDB
n
Result
Attempts iterations times to fit a sinusoidal regression model to
Xlistname and Ylistname using a
period guess, and stores the regression equation to regequ.
Solves expression for variable, given an initial guess and lower and upper bounds within which the solution is sought.
Sorts elements of listname in ascending order.
Sorts elements of keylistname in ascending order, then sorts each
dependlist as a dependent list.
Key or Keys/
Menu or Screen/Item
…
CALC
C:SinReg
1227
†
MATH
0:solve(
212 y [
LIST
]
OPS
1:SortA(
y [
LIST
]
OPS
1:SortA(
1110
1220
1110
1220
Sorts elements of listname in descending order.
Sorts elements of keylistname in descending order, then sorts each
dependlist as a dependent list.
y [
LIST
]
OPS
2:SortD(
y [
LIST
]
OPS
2:SortD(
1110
1220
1110
1220
Returns the standard deviation of the elements in list with frequency freqlist.
Ends program execution; returns to home screen.
Stores value in variable.
Stores current graph in database
GDB
n.
y [
LIST
]
MATH
7:stdDev(
†
CTL
F:Stop
¿ y [
DRAW
]
STO
3:StoreGDB
1118
1615
114
819
A–28 Tables and Reference Information
826DEC~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09
PM Page 28 of 58
Function or Instruction/
Arguments
StorePic
n
String4Equ(
string
,Y=
var
) sub(
string
,
begin
,
length
) sum(
list[
,
start
,
end]
) tan(
value
) tan
L1
(
value
)
Tangent(
expression
,
value
) tanh(
value
) tanh
L1
(
value
) tcdf(
lowerbound
,
upperbound
,
df
)
Text(
row
,
column
,
text1
,
text2
,
...
,
text n
)
Result
Stores current picture in picture
Pic
n.
Converts string into an equation and stores it in
Y=
var.
Returns a string that is a subset of another string, from begin to
length.
Returns the sum of elements of
list from start to end.
Returns the tangent of a real number, expression, or list.
Returns the arctangent of a real number, expression, or list.
Key or Keys/
Menu or Screen/Item y [
DRAW
]
STO
1:StorePic
y [
CATALOG
]
String4Equ(
817
158 y [
CATALOG
]
sub(
159 y [
LIST
]
MATH
5:sum(
1118
š y [
TAN
L1
]
23
Draws a line tangent to
expression at
X
=value.
Returns hyperbolic tangent of a real number, expression, or list.
Returns the hyperbolic arctangent of a real number, expression, or list.
23 y [
DRAW ä
DRAW
5:Tangent(
y [
CATALOG
]
tanh(
y [
CATALOG
]
tanh
L1
(
88
1510
1510
Computes the Studentt distribution probability between
lowerbound and upperbound for the specified degrees of freedom
df.
Writes text on graph beginning at pixel (row,column), where
0 row 57 and
0 column 94.
y [
DISTR
]
DISTR
5:tcdf(
y [
DRAW
]
DRAW
0:Text(
1331
812
Then
See
If:Then
Tables and Reference Information A–29
826DEC~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09
PM Page 29 of 58
Table of Functions and Instructions
(continued)
Function or Instruction/
Arguments
Time
TInterval
[listname
,
freqlist
,
confidence level]
(Data list input)
TInterval
v
,
Sx
,
n
[
,
confidence level]
(Summary stats input)
tpdf(
x
,
df
)
Trace
TTest
m
0[
,
listname
freqlist
,
alternative
,
drawflag]
(Data list input)
,
TTest
m
0
,
v
,
Sx
,
n
[
,
alternative
,
drawflag]
(Summary stats input)
Result
Sets sequence graphs to plot with respect to time.
Computes a t confidence interval.
Computes a t confidence interval.
Key or Keys/
Menu or Screen/Item
† y [
FORMAT
]
Time
68
† …
TESTS
8:TInterval
1317
† …
TESTS
8:TInterval
1317 y [
DISTR
]
DISTR
4:tpdf(
Computes the probability density function (pdf) for the Studentt distribution at a specified x value with specified degrees of freedom
df.
Displays the graph and enters
TRACE
mode.
Performs a t test with frequency
freqlist. alternative=
L1
is
<
;
alternative=
0
is
ƒ
; alternative=
1
is
>
. drawflag=
1
draws results;
drawflag=
0
calculates results.
r
† …
TESTS
2:TTest
1330
318
1311
Performs a t test with frequency
freqlist. alternative=
L1
is < ;
alternative=
0
is ƒ ; alternative=
1
is >. drawflag=
1
draws results;
drawflag=
0
calculates results.
† …
TESTS
2:TTest
1311
A–30 Tables and Reference Information
826DEC~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09
PM Page 30 of 58
Function or Instruction/
Arguments
tvm_FV
[
(
Ú
P/Y
,
C/Y
)
]
,
æ
,
PV
,
PMT
, tvm_
æ
[
(
Ú
P/Y
,
C/Y
)
]
,
PV
,
PMT
,
FV
, tvm_
Ú
[
(
æ
P/Y
,
C/Y
)
]
,
PV
,
PMT
,
FV
, tvm_Pmt
[
(
P/Y
,
C/Y
)
]
Ú
,
æ
,
PV
,
FV
, tvm_PV
[
(
Ú
P/Y
,
C/Y
)
]
,
æ
,
PMT
,
FV
, uvAxes uwAxes
1Var Stats
[Xlistname
,
freqlist]
2Var Stats
[Xlistname
,
Ylistname
,
freqlist]
variance(
list[
,
freqlist]
)
Vertical
x
vwAxes
Web
Result
Computes the future value.
Computes the annual interest rate.
Computes the number of payment periods.
Computes the amount of each payment.
Computes the present value.
Sets sequence graphs to plot
u(n)
on the xaxis and
v(n)
on the yaxis.
Sets sequence graphs to plot
u(n)
on the xaxis and
w(n)
on the yaxis.
Performs onevariable analysis on the data in Xlistname with frequency freqlist.
Performs twovariable analysis on the data in Xlistname and
Ylistname with frequency freqlist.
Returns the variance of the elements in list with frequency
freqlist.
Draws a vertical line at x.
Sets sequence graphs to plot
v(n)
on the xaxis and
w(n)
on the yaxis.
Sets sequence graphs to trace as webs.
Key or Keys/
Menu or Screen/Item y [
FINANCE
]
CALC
6:tvm_FV
147 y [
FINANCE
]
CALC
3:tvm_
æ y [
FINANCE
]
CALC
5:tvm_
Ú y [
FINANCE
]
CALC
2:tvm_Pmt
147
147
146 y [
FINANCE
]
CALC
4:tvm_PV
147
† y [
FORMAT
]
uv
68
† y [
FORMAT
]
uw
68
…
CALC
1:1Var Stats
…
CALC
2:2Var Stats
1225
1225 y [
LIST
]
MATH
8:variance(
y [
DRAW
]
DRAW
4:Vertical
1118
86
† y [
FORMAT
]
vw
68
† y [
FORMAT
]
Web
68
Tables and Reference Information A–31
826DEC~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09
PM Page 31 of 58
Table of Functions and Instructions
(continued)
Function or Instruction/
Arguments
:While
condition
:
commands
:End
:
command
valueA
xor
valueB
ZBox
ZDecimal
ZInteger
ZInterval
s
[
,
listname
(Data list input)
,
freqlist
,
confidence level]
ZInterval
s
,
v
,
n
[
,
confidence level]
(Summary stats input)
Zoom In
Zoom Out
Result
Executes commands while
condition is true.
Key or Keys/
Menu or Screen/Item
†
CTL
5:While
1611
Returns 1 if only valueA or
valueB = 0. valueA and valueB can be real numbers, expressions, or lists.
Displays a graph, lets you draw a box that defines a new viewing window, and updates the window.
y [
TEST
]
LOGIC
3:xor
† q
ZOOM
1:ZBox
226
320
Adjusts the viewing window so that
@
X=0.1
and
@Y=0.1
, and displays the graph screen with the origin centered on the screen.
† q
ZOOM
4:ZDecimal
Redefines the viewing window using these dimensions:
@X=1
Xscl=10
@Y=1
Yscl=10
Computes a z confidence interval.
Computes a z confidence interval.
Magnifies the part of the graph that surrounds the cursor location.
Displays a greater portion of the graph, centered on the cursor location.
321
† q
ZOOM
8:ZInteger
322
† …
TESTS
7:ZInterval
1316
† …
TESTS
7:ZInterval
1316
† q
ZOOM
2:Zoom In
321
† q
ZOOM
3:Zoom Out
321
A–32 Tables and Reference Information
826DEC~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09
PM Page 32 of 58
Function or Instruction/
Arguments
ZoomFit
ZoomRcl
ZoomStat
ZoomSto
ZPrevious
ZSquare
ZStandard
Result
Recalculates
Ymin
and
Ymax
to include the minimum and maximum
Y
values, between
Xmin
and
Xmax
, of the selected functions and replots the functions.
Graphs the selected functions in a userdefined viewing window.
Redefines the viewing window so that all statistical data points are displayed.
Immediately stores the current viewing window.
Replots the graph using the window variables of the graph that was displayed before you executed the last
ZOOM instruction.
Adjusts the
X
or
Y
window settings so that each pixel represents an equal width and height in the coordinate system, and updates the viewing window.
Key or Keys/
Menu or Screen/Item
† q
ZOOM
0:ZoomFit
322
† q
MEMORY
3:ZoomRcl
323
† q
ZOOM
9:ZoomStat
322
† q
MEMORY
2:ZoomSto
323
† q
MEMORY
1:ZPrevious
† q
ZOOM
5:ZSquare
323
321
Replots the functions immediately, updating the window variables to the default values.
† q
ZOOM
6:ZStandard
322
Tables and Reference Information A–33
826DEC~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09
PM Page 33 of 58
Table of Functions and Instructions
(continued)
Function or Instruction/
Arguments
ZNTest(
m
0
,s [
,
listname
freqlist
,
alternative
,
drawflag]
)
(Data list input)
,
ZNTest(
m
0
,s,v,
n
[
,
alternative
,
drawflag]
)
(Summary stats input)
ZTrig
Factorial: value
!
Factorial: list
!
Degrees notation: value
¡
Radian: angle
r
Transpose: matrix
T
Result
Performs a z test with frequency
freqlist. alternative=
L1
is
<
;
alternative=
0
is
ƒ
; alternative=
1
is
>
. drawflag=
1
draws results;
drawflag=
0
calculates results.
Key or Keys/
Menu or Screen/Item
† …
TESTS
1:Z.Test(
1310
Performs a z test. alternative=
L1
is
<
; alternative=
0
is
ƒ
;
alternative=
1
is
>
. drawflag=
1
draws results; drawflag=
0
calculates results.
† …
TESTS
1:Z.Test(
1310
Replots the functions immediately, updating the window variables to preset values for plotting trig functions.
† q
ZOOM
7:ZTrig
322
Returns factorial of value.
Returns factorial of list elements.
Interprets value as degrees; designates degrees in DMS format.
Interprets angle as radians.
Returns a matrix in which each element (row, column) is swapped with the corresponding element
(column, row) of matrix.
PRB
4:!
PRB
4:!
y [
ANGLE
]
ANGLE
1:¡
y [
ANGLE
]
ANGLE
3: r
MATH
2:
T
221
221
223
224
1012
A–34 Tables and Reference Information
826DEC~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09
PM Page 34 of 58
Function or Instruction/
Arguments
x th root
x
‡
value x th root
x
‡
list list
x
‡
value listA
x
‡
listB
Cube: value
3
Cube root:
3
‡(
value
)
Equal: valueA
=
valueB
Not equal: valueA
ƒ
valueB
Less than: valueA
<
valueB
Result
Returns x
th
root of value.
Returns x
th
root of list elements.
Returns list roots of value.
Returns listA roots of listB.
Returns the cube of a real or complex number, expression, list, or square matrix.
Returns the cube root of a real or complex number, expression, or list.
Returns 1 if valueA = valueB.
Returns 0 if valueA ƒ valueB.
valueA and valueB can be real or complex numbers, expressions, lists, or matrices.
Returns 1 if valueA ƒ valueB.
Returns 0 if valueA = valueB.
valueA and valueB can be real or complex numbers, expressions, lists, or matrices.
Returns 1 if valueA < valueB.
Returns 0 if valueA ‚ valueB.
valueA and valueB can be real or complex numbers, expressions, or lists.
Key or Keys/
Menu or Screen/Item
MATH
5: x
‡
MATH
5: x
‡
MATH
5: x
‡
MATH
5: x
‡
MATH
3:
3
26
26
26
26
26
1010
MATH
4:
3
‡(
y [
TEST
]
TEST
1:=
26
225
1011 y [
TEST
]
TEST
2:ƒ
225
1011 y [
TEST
]
TEST
5:<
225
Tables and Reference Information A–35
826DEC~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09
PM Page 35 of 58
Table of Functions and Instructions
(continued)
Function or Instruction/
Arguments
Greater than:
valueA
>
valueB
Less than or equal:
valueA
valueB
Greater than or equal:
valueA
‚
valueB
Inverse: value
L1
Inverse: list
L1
Inverse: matrix
L1
Square: value
2
Square: list
2
Square: matrix
2
Powers: value
^
power
Powers: list
^
power
Powers: value
^
list
Result
Returns 1 if valueA > valueB.
Returns 0 if valueA valueB.
valueA and valueB can be real or complex numbers, expressions, or lists.
Returns 1 if valueA valueB.
Returns 0 if valueA > valueB.
valueA and valueB can be real or complex numbers, expressions, or lists.
Returns 1 if valueA
‚
valueB.
Returns 0 if valueA < valueB.
valueA and valueB can be real or complex numbers, expressions, or lists.
Returns 1 divided by a real or complex number or expression.
Key or Keys/
Menu or Screen/Item y [
TEST
]
TEST
3:>
y [
TEST
]
TEST
6:
y [
TEST
]
TEST
4:‚
—
225
225
225
23
Returns 1 divided by list elements.
Returns matrix inverted.
Returns value multiplied by itself.
value can be a real or complex number or expression.
—
—
¡
23
1010
23
Returns list elements squared.
¡
23
¡
Returns matrix multiplied by itself.
Returns value raised to power.
value can be a real or complex number or expression.
Returns list elements raised to
power.
Returns value raised to list elements.
›
›
›
1010
23
23
23
A–36 Tables and Reference Information
826DEC~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09
PM Page 36 of 58
Function or Instruction/
Arguments
Powers: matrix
^
power
Negation:
L
value
Power of ten:
10
^(
value
)
Power of ten:
10
^(
list
)
Square root:
‡(
value
)
Multiplication:
valueA
ääää
valueB
Multiplication:
value
ääää
list
Multiplication:
list
ääää
value
Multiplication:
listA
ääää
listB
Multiplication:
value
ääää
matrix
Multiplication:
matrixA
ääää
matrixB
Division: valueA
à
valueB
Division: list
à
value
Division: value
à
list
Division: listA
à
listB
Result
Returns matrix elements raised to
power.
Returns the negative of a real or complex number, expression, list, or matrix.
Returns 10 raised to the value power. value can be a real or complex number or expression.
Key or Keys/
Menu or Screen/Item
›
1010
Ì
24
109 y [
10
x]
24 y [
10
x]
Returns a list of 10 raised to the
list power.
Returns square root of a real or complex number, expression, or list.
Returns valueA times valueB.
y [
¯
‡
]
24
23
23
¯
Returns value times each list element.
Returns each list element times
value.
Returns listA elements times listB elements.
Returns value times matrix elements.
Returns matrixA times matrixB.
¯
¯
¯
¯
23
23
23
109
109
¥
Returns valueA divided by
valueB.
Returns list elements divided by value.
Returns value divided by list elements.
Returns listA elements divided by
listB elements.
¥
¥
¥
23
23
23
23
Tables and Reference Information A–37
826DEC~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09
PM Page 37 of 58
Table of Functions and Instructions
(continued)
Function or Instruction/
Arguments
Addition: valueA
+
valueB
Addition: list
+
value
Addition: listA
+
listB
Addition:
matrixA
+
matrixB
Concatenation:
string1
+
string2
Subtraction:
valueA
N
valueB
Subtraction:
value
N
list
Subtraction:
list
N
value
Subtraction:
listA
N
listB
Subtraction:
matrixA
N
matrixB
Minutes notation:
degrees
¡
minutes
'
seconds
"
Seconds notation:
degrees
¡
minutes
'
seconds
"
Result
Returns valueA plus valueB.
Returns list in which value is added to each list element.
Returns listA elements plus listB elements.
Returns matrixA elements plus
matrixB elements.
Concatenates two or more strings.
Subtracts valueB from valueA.
Subtracts list elements from
value.
Subtracts value from list elements.
Subtracts listB elements from
listA elements.
Subtracts matrixB elements from
matrixA elements.
Interprets minutes angle measurement as minutes.
Interprets seconds angle measurement as seconds.
Key or Keys/
Menu or Screen/Item
Ã
Ã
23
23
Ã
23
Ã
109
Ã
156
¹
23
¹
23
¹
23
¹
23
¹
109 y [
ANGLE
]
ANGLE
2:'
ƒ [
ã
]
223
223
A–38 Tables and Reference Information
826DEC~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09
PM Page 38 of 58
TI82 STATS Menu Map
The TI82 STATS Menu Map begins at the topleft corner of the keyboard and follows the keyboard layout from left to right. Default values and settings are shown.
o
¸¿¶¶¶¶¶¶¶¶¶¶¶¶¶¶¾¶¶¶¶¶¶¶¶¶¶¶¶¶¶¾¶¶¶¶¶¶¶¶¶¶¶¶¶¶¹
(Func mode) (Par mode) (Pol mode) (Seq mode)
Plot1 Plot2 Plot3
ççççY1=
ççççY2=
ççççY3=
ççççY4=
...
ççççY9=
ççççY0=
Plot1 Plot2 Plot3
ççççX1T=
Y1T=
ççççX2T=
Y2T=
...
ççççX6T=
Y6T=
Plot1 Plot2 Plot3
ççççr1=
ççççr2=
ççççr3=
ççççr4=
ççççr5=
ççççr6=
Plot1 Plot2 Plot3
nMin=1
í
u(nMin)=
í
v(nMin)=
í
w(nMin)=
y [
STAT PLOT
]
¸¶¶¶¶¶»
STAT PLOTS
1:Plot1…Off
"
›
2:Plot2…Off
"
›
3:Plot3…Off
"
›
4:PlotsOff
5:PlotsOn
y [
STAT PLOT
]
¸¶¶¶¶¶¿¶¶¶¶¶¶¶¾¶¶¶¶¶¶¶¶¶¶¶¶¹
(PRGM editor) (PRGM editor) (PRGM editor)
PLOTS
1:Plot1(
2:Plot2(
3:Plot3(
4:PlotsOff
5:PlotsOn
TYPE
1:Scatter
2:xyLine
3:Histogram
4:ModBoxplot
5:Boxplot
6:NormProbPlot
MARK
1:
›
2:+
3:¦
p
¸¿¶¶¶¶¶¶¶¶¶¶¶¶¶¶¾¶¶¶¶¶¶¶¶¶¶¶¶¶¶¾¶¶¶¶¶¶¶¶¶¶¶¶¶¶¹
(Func mode) (Par mode) (Pol mode) (Seq mode)
WINDOW
Xmin=10
Xmax=10
Xscl=1
Ymin=10
Ymax=10
Yscl=1
Xres=1
WINDOW
Tmin=0
Tmax=pä2
Tstep=pà24
Xmin=10
Xmax=10
Xscl=1
Ymin=10
Ymax=10
Yscl=1
WINDOW
qmin=0
qmax=pä2
qstep=pà24
Xmin=10
Xmax=10
Xscl=1
Ymin=10
Ymax=10
Yscl=1
WINDOW
nMin=1
nMax=10
PlotStart=1
PlotStep=1
Xmin=10
Xmax=10
Xscl=1
Ymin=10
Ymax=10
Yscl=1
y [
TBLSET
]
¸¶¶¶»
TABLE SETUP
TblStart=0
@Tbl=1
Indpnt:Auto Ask
Depend:Auto Ask
y [
TBLSET
]
¸¶¶¶¶»
(PRGM editor)
TABLE SETUP
Indpnt:Auto Ask
Depend:Auto Ask
Tables and Reference Information A–39
826DEC~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09
PM Page 39 of 58
TI82 STATS Menu Map
(continued)
q
¸¿¶¶¶¶¶¶¶¶¶¶¶¶¶¶¹
ZOOM MEMORY
1:ZBox
2:Zoom In
3:Zoom Out
4:ZDecimal
5:ZSquare
6:ZStandard
7:ZTrig
8:ZInteger
9:ZoomStat
0:ZoomFit
1:ZPrevious
2:ZoomSto
3:ZoomRcl
4:SetFactors…
MEMORY
(Set Factors...)
ZOOM FACTORS
XFact=4
YFact=4
y [
FORMAT
]
¸¿¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¹
(Func/Par/Pol modes) (Seq mode)
RectGC PolarGC
CoordOn CoordOff
GridOff GridOn
AxesOn AxesOff
LabelOff LabelOn
ExprOn ExprOff
Time Web uv vw uw
RectGC PolarGC
CoordOn CoordOff
GridOff GridOn
AxesOn AxesOff
LabelOff LabelOn
ExprOn ExprOff
y [
CALC
]
¸¶¶¶¿¶¶¶¶¶¶¶¶¶¶¶¾¶¶¶¶¶¶¶¶¶¶¶¶¶¶¾¶¶¶¶¶¶¶¶¶¶¶¶¶¶¹
(Func mode)
CALCULATE
1:value
2:zero
3:minimum
4:maximum
5:intersect
6:dy/dx
7:‰f(x)dx
(Par mode)
CALCULATE
1:value
2:dy/dx
3:dy/dt
4:dx/dt
(Pol mode)
CALCULATE
1:value
2:dy/dx
3:dr/dq
(Seq mode)
CALCULATE
1:value
z
¸»
Normal Sci Eng
Float 0123456789
Radian Degree
Func Par Pol Seq
Connected Dot
Sequential Simul
Real a+b
×××× re^q××××
Full Horiz GT
A–40 Tables and Reference Information
826DEC~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09
PM Page 40 of 58
y [
LINK
]
¸¿¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¹
SEND RECEIVE
1:Receive 1:All+…
2:AllN…
3:Prgm…
4:List…
5:Lists to TI82…
6:GDB…
7:Pic…
8:Matrix…
9:Real…
0:Complex…
A:YVars…
B:String…
C:Back Up…
…
¸¿¶¶¶¶¶¶¶¶¶¶¶¶¶¾¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¹
EDIT
1:Edit…
2:SortA(
3:SortD(
4:ClrList
5:SetUpEditor
CALC
1:1Var Stats
2:2Var Stats
3:MedMed
4:LinReg(ax+b)
5:QuadReg
6:CubicReg
7:QuartReg
8:LinReg(a+bx)
9:LnReg
0:ExpReg
A:PwrReg
B:Logistic
C:SinReg
TESTS
1:ZTest…
2:TTest…
3:2SampZTest…
4:2SampTTest…
5:1PropZTest…
6:2PropZTest…
7:ZInterval…
8:TInterval…
9:2SampZInt…
0:2SampTInt…
A:1PropZInt…
B:2PropZInt…
C:c 2 Test…
ÛTest…
E:LinRegTTest…
F:ANOVA(
Tables and Reference Information A–41
826DEC~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09
PM Page 41 of 58
TI82 STATS Menu Map
(continued)
y [
LIST
]
¸¶¶¿¶¶¶¶¶¶¶¶¶¾¶¶¶¶¶¶¶¶¶¶¶¶¹
NAMES
1:listname
OPS
1:SortA(
MATH
1:min(
2:listname
3:listname
...
2:SortD(
3:dim(
4:Fill(
5:seq(
6:cumSum(
7:@List(
8:Select(
9:augment(
0:List4matr(
A:Matr4list(
2:max(
3:mean(
4:median(
5:sum(
6:prod(
7:stdDev(
8:variance(
¸¿¶¶¶¶¶¶¶¶¶¶¶¶¾¶¶¶¶¶¶¶¶¶¶¶¾¶¶¶¶¶¶¶¶¶¶¶¶¹
MATH NUM CPX PRB
1:4Frac
2:4Dec
3:
3
4:
3
‡(
5:x‡
6:fMin(
7:fMax(
8:nDeriv(
9:fnInt(
0:Solver…
1:abs(
2:round(
3:iPart(
4:fPart(
5:int(
6:min(
7:max(
8:lcm(
9:gcd(
1:conj(
2:real(
3:imag(
4:angle(
5:abs(
6:4Rect
7:4Polar
1:rand
2:nPr
3:nCr
4:!
5:randInt(
6:randNorm(
7:randBin(
y [
TEST
]
¸¶¶¶¶¿¶¶¶¶¶¶¶¶¹
TEST LOGIC
1:=
2:ƒ
3:>
4:‚
5:<
6:
1:and
2:or
3:xor
4:not(
A–42 Tables and Reference Information
826DEC~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09
PM Page 42 of 58
¸¿¶¶¶¶¶¶¶¶¶¶¶¶¾¶¶¶¶¶¶¶¶¶¶¶¶¹
NAMES MATH EDIT
1:[A]
2:[B]
3:[C]
4:[D]
5:[E]
6:[F]
7:[G]
8:[H]
9:[I]
0:[J]
1:det(
2:
T
3:dim(
4:Fill(
5:identity(
6:randM(
7:augment(
8:Matr4list(
9:List4matr(
0:cumSum(
A:ref(
B:rref(
C:rowSwap(
D:row+(
E:…row(
F:…row+(
1:[A]
2:[B]
3:[C]
4:[D]
5:[E]
6:[F]
7:[G]
8:[H]
9:[I]
0:[J]
¸¿¶¶¶¶¶¶¶¶¶¶¶¶¶¾¶¶¶¶¶¶¶¶¶¶¶¶¶¹
EXEC EDIT NEW
1:name
2:name
...
1:name
2:name
...
1:Create New
¸¿¶¶¶¶¶¶¶¶¶¶¶¶¶¾¶¶¶¶¶¶¶¶¶¶¶¶¶¶¹
(PRGM editor)
CTL
1:If
2:Then
3:Else
4:For(
5:While
6:Repeat
7:End
8:Pause
9:Lbl
0:Goto
A:IS>(
B:DS<(
C:Menu(
D:prgm
E:Return
F:Stop
G:DelVar
H:GraphStyle(
(PRGM editor)
I/O
1:Input
2:Prompt
3:Disp
4:DispGraph
5:DispTable
6:Output(
7:getKey
8:ClrHome
9:ClrTable
0:GetCalc(
A:Get(
B:Send(
(PRGM editor)
EXEC
1:name
2:name
...
y [
ANGLE
]
¸¶¶¶¶»
ANGLE
1:¡
2:'
3:r
4:4DMS
5:R4Pr(
6:R4Pq(
7:P4Rx(
8:P4Ry(
Tables and Reference Information A–43
826DEC~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09
PM Page 43 of 58
TI82 STATS Menu Map
(continued)
y [
DRAW
]
¸¶¶¶¶¶¿¶¶¶¶¶¶¶¶¾¶¶¶¶¶¶¶¶¶¶¶¶¶¹
DRAW POINTS STO
1:ClrDraw
2:Line(
3:Horizontal
4:Vertical
5:Tangent(
6:DrawF
7:Shade(
8:DrawInv
9:Circle(
0:Text(
A:Pen
1:PtOn(
2:PtOff(
3:PtChange(
4:PxlOn(
5:PxlOff(
6:PxlChange(
7:pxlTest(
1:StorePic
2:RecallPic
3:StoreGDB
4:RecallGDB
¸¿¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¹
VARS
1:Window…
YVARS
1:Function…
2:Zoom…
3:GDB…
4:Picture…
5:Statistics…
6:Table…
7:String…
2:Parametric…
3:Polar…
4:On/Off…
VARS
¸¿¶¶¶¶¶¶¶¶¶¶¶¶¶¾¶¶¶¶¶¶¶¶¶¶¶¶¾
(Window…)
X/Y
1:Xmin
2:Xmax
3:Xscl
4:Ymin
5:Ymax
6:Yscl
7:Xres
8:
@
X
9:
@
Y
0:XFact
A:YFact
(Window…)
T/q
1:Tmin
2:Tmax
3:Tstep
4:qmin
5:qmax
6:qstep
(Window…)
U/V/W
1:u(nMin)
2:v(nMin)
3:w(nMin)
4:nMin
5:nMax
6:PlotStart
7:PlotStep
A–44 Tables and Reference Information
826DEC~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09
PM Page 44 of 58
VARS
¶¶¶¶¶¶¶¶¶¶¶¾¶¶¶¶¶¶¶¶¶¶¶¶¾
(Zoom…)
ZX/ZY
1:ZXmin
2:ZXmax
3:ZXscl
4:ZYmin
5:ZYmax
6:ZYscl
7:ZXres
(Zoom…)
ZT/Zq
1:ZTmin
2:ZTmax
3:ZTstep
4:Zqmin
5:Zqmax
6:Zqstep
(Zoom…)
ZU
1:Zu(nMin)
2:Zv(nMin)
3:Zw(nMin)
4:ZnMin
5:ZnMax
6:ZPlotStart
7:ZPlotStep
VARS
¶¶¾¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¾
(GDB…) (Picture…)
GRAPH DATABASE
1:GDB1
2:GDB2
...
9:GDB9
0:GDB0
PICTURE
1:Pic1
2:Pic2
...
9:Pic9
0:Pic0
VARS
¶¶¶¶¾¶¶¶¶¶¶¶¶¶¶¾¶¶¶¶¶¶¶¶¶¶¶¶¾¶¶¶¶¶¶¶¶¶¶¶¶¾¶¶¶¶¶¶¶¶¶¶¶¾
(Statistics…)
XY
1:n
2:v
3:Sx
4:sx
5:w
6:Sy
7:sy
8:minX
9:maxX
0:minY
A:maxY
(Statistics…)
G
1:Gx
2:Gx
2
3:Gy
4:Gy
2
5:Gxy
(Statistics…)
EQ
1:RegEQ
2:a
3:b
4:c
5:d
6:e
7:r
8:r
2
9:R
2
(Statistics…)
TEST
1:p
2:z
3:t
4:c
Û
2
6:df
7:Ç
Ç1
9:Ç
0:s
A:ü
(Statistics…)
PTS
1:x1
2:y1
3:x2
4:y2
5:x3
6:y3
7:Q 1
8:Med
9:Q 3
C:Sx1
D:Sx2
E:Sxp
F:n1
G:n2
H:lower
I:upper
Tables and Reference Information A–45
826DEC~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09
PM Page 45 of 58
TI82 STATS Menu Map
(continued)
VARS
¶¶¾¶¶¶¶¶¶¶¶¶¶¶¶¶¶¹
(Table…)
TABLE
1:TblStart
2:
@
Tbl
3:TblInput
(String…)
STRING
1:Str1
2:Str2
3:Str3
4:Str4
...
9:Str9
0:Str0
YVARS
¸¶¿¶¶¶¶¶¶¶¶¶¶¶¾¶¶¶¶¶¶¶¶¶¶¶¶¶¾¶¶¶¶¶¶¶¶¶¹
(Function…)
FUNCTION
(Parametric…)
PARAMETRIC
(Polar…)
POLAR
(On/Off…)
ON/OFF
1:Y
1
2:Y
2
3:Y
3
4:Y
4
...
9:Y
9
0:Y
0
1:X
1T
2:Y
1T
3:X
2T
4:Y
2T
...
A:X
6T
B:Y
6T
1:r
1
2:r
2
3:r
3
4:r
4
5:r
5
6:r
6
1:FnOn
2:FnOff
A–46 Tables and Reference Information
826DEC~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09
PM Page 46 of 58
y [
DISTR
]
¸¶¶¶¿¶¶¶¶¶¶¶¶¶¶¶¶¶¹
DISTR
1:normalpdf(
DRAW
1:ShadeNorm(
2:normalcdf(
3:invNorm(
4:tpdf(
5:tcdf(
6:c
2 pdf(
7:c
ÛÛ
2 cdf(
Ûpdf(
2:Shade_t(
3:Shadec
2
Û(
(
0:binompdf(
A:binomcdf(
B:poissonpdf(
C:poissoncdf(
D:geometpdf(
E:geometcdf(
y [
FINANCE
]
¸¶¶¶¿¶¶¶¶¶¶¶¶¶¶¶¶¶¹
CALC VARS
1:TVM Solver…
2:tvm_Pmt
3:tvm_æ
4:tvm_PV
5:tvm_Ú
6:tvm_FV
7:npv(
8:irr(
9:bal(
0:GPrn(
A:GInt(
B:4Nom(
C:4Eff(
D:dbd(
E:Pmt_End
F:Pmt_Bgn
1:Ú
2:æ
3:PV
4:PMT
5:FV
6:P/Y
7:C/Y
Tables and Reference Information A–47
826DEC~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09
PM Page 47 of 58
TI82 STATS Menu Map
(continued)
y [
MEM
]
¸¶¶»
MEMORY
1:Check RAM…
2:Delete…
3:Clear Entries
4:ClrAllLists
5:Reset…
MEMORY
¸¶¶¶¿¶¶¶¶¶¶¶¶¶¶¶¶¶¾¶¶¶¶¶¶¶¶¶¶¶¶¶¹
(Check RAM…) (Delete…) (Reset…)
MEM FREE 27225
Real 15
Complex 0
List 0
Matrix 0
YVars 240
Prgm 14
Pic 0
GDB 0
String 0
DELETE FROM…
1:All…
2:Real…
3:Complex…
4:List…
5:Matrix…
6:YVars…
7:Prgm…
8:Pic…
9:GDB…
0:String…
RESET
1:All Memory…
2:Defaults…
MEMORY (Reset...)
¸¶¿¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¹
(All Memory…)
RESET MEMORY
(Defaults…)
RESET DEFAULTS
1:No
2:Reset
1:No
2:Reset
Resetting memory erases all data and programs.
y [
CATALOG
]
¸¶¶»
CATALOG cosh( cosh
L1
(
...
Equ4String( expr(
...
inString(
...
length(
...
sinh( sinh
L1
(
...
String4Equ( sub(
...
tanh( tanh
L1
(
A–48 Tables and Reference Information
826DEC~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09
PM Page 48 of 58
Variables
User Variables
The TI82 STATS uses the variables listed below in various ways. Some variables are restricted to specific data types.
The variables
A
through
Z
and
q
are defined as real or complex numbers. You may store to them. The TI82 STATS can update
X
,
Y
,
R
,
q
, and
T
during graphing, so you may want to avoid using these variables to store nongraphing data.
The variables (list names)
L
1
through
L
6
are restricted to lists; you cannot store another type of data to them.
The variables (matrix names)
[A]
through
[J]
are restricted to matrices; you cannot store another type of data to them.
The variables
Pic1
through
Pic9
and
Pic0
are restricted to pictures; you cannot store another type of data to them.
The variables
GDB1
through
GDB9
and
GDB0
are restricted to graph databases; you cannot store another type of data to them.
The variables
Str1
through
Str9
and
Str0
are restricted to strings; you cannot store another type of data to them.
You can store any string of characters, functions, instructions, or variables to the functions
Y
n, (
1
through
9
, and
0
),
X
n
T
/
Y
n
T
(
1
through
6
),
r
n (
1
through
6
),
u(n)
,
v(n)
, and
w(n)
directly or through the
Y=
editor. The validity of the string is determined when the function is evaluated.
System Variables
The variables below must be real numbers. You may store to them. Since the TI82 STATS can update some of them, as the result of a
ZOOM
, for example, you may want to avoid using these variables to store nongraphing data.
•
Xmin
,
Xmax
,
Xscl
,
@X
,
XFact
,
Tstep
,
PlotStart
,
nMin
, and other window variables.
•
ZXmin
,
ZXmax
,
ZXscl
,
ZTstep
,
ZPlotStart
,
Zu(nMin)
, and other
ZOOM
variables.
The variables below are reserved for use by the TI82 STATS.
You cannot store to them.
n
,
v
,
Sx
,
sx
,
minX
,
maxX
,
Gy
,
Gy y1
,
z
,
t
,
F
,
c
2
,
Ç
,
v1
statistical variables.
,
Sx1
,
n1
,
2
,
Gxy
,
a
,
b
,
c
,
RegEQ
,
x
1
,
x
2,
lower
,
upper
,
r
2
,
R
2
and other
Tables and Reference Information A–49
826DEC~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09
PM Page 49 of 58
Statistics Formulas
This section contains statistics formulas for the
Logistic
and
SinReg
regressions,
ANOVA
,
2.SampÜ
, and
2.SampTTest
.
Logistic
The logistic regression algorithm applies nonlinear recursive leastsquares techniques to optimize the following cost function:
J
=
i
N
∑
=
1
1
+
c ae
−
bx i
−
y i
2 which is the sum of the squares of the residual errors, where: x = the independent variable list
y = the dependent variable list
N = the dimension of the lists
This technique attempts to estimate the constants a, b, and c recursively to make J as small as possible.
SinReg
The sine regression algorithm applies nonlinear recursive leastsquares techniques to optimize the following cost function:
J
=
i
N
∑
[
a
sin( )
i
]
2
=
1
bx i
+ + − which is the sum of the squares of the residual errors, where: x = the independent variable list
y = the dependent variable list
N = the dimension of the lists
This technique attempts to recursively estimate the constants a,
b, c, and d to make J as small as possible.
A–50 Tables and Reference Information
826DEC~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09
PM Page 50 of 58
ANOVA(
The
ANOVA
Û statistic is:
Û
=
Factor MS
Error MS
The mean squares (MS) that make up Û are:
Factor MS
=
Factor SS
Factor df
Error MS
=
Error SS
Error df
The sum of squares (SS) that make up the mean squares are:
Factor SS
=
i
I
∑
=
1
(
i
−
x
)
2
Error SS
=
i
I
∑
=
1
(
n i
−
1 )
Sx i
2
The degrees of freedom df that make up the mean squares are:
Factor df I
1 numerator
df
for Û
=
i
I
∑
=
1
n i
1
df
for
Û where:
x i
I = number of populations
= the mean of each list
Sxi = the standard deviation of each list
ni = the length of each list
x
= the mean of all lists
Tables and Reference Information A–51
826DEC~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09
PM Page 51 of 58
Statistics Formulas
(continued)
Below is the definition for the
2
.
Samp
Ü .
Sx1, Sx2 = Sample standard deviations having n
1
1 and n
2
1 degrees of freedom df, respectively.
Û = Ûstatistic =
Sx
Sx
1
2
2
df(x, n
1
1, n
2
1)
= Ûpdf( ) with degrees of freedom
df, n
1
1, and n
2
1
p = reported p value
2
.
Samp
Ü
p
=
F
∞
∫
(
for the alternative hypothesis s
1
> s
2
.
1
−
1
, n
2
−
1 )
dx
2
.
Samp
Ü
p
=
0
F
∫
(
for the alternative hypothesis s
1
< s
2
.
1
−
1
, n
2
−
1 )
dx
2
.
Samp
Ü
for the alternative hypothesis s must satisfy the following:
1
ƒ s
2
. Limits
p
2
=
∫
0
L bnd
,
1
−
1
, n
2
−
1 )
dx
=
∫
∞
U bnd
,
1
−
1
, n
2
−
1 )
dx
where: [Lbnd,Ubnd] = lower and upper limits
The Ûstatistic is used as the bound producing the smallest integral. The remaining bound is selected to achieve the preceding integral’s equality relationship.
A–52 Tables and Reference Information
826DEC~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09
PM Page 52 of 58
2.SampTTest
The following is the definition for the
2.SampTTest
. The twosample t statistic with degrees of freedom df is:
t
=
x
1
−
x
S
2 where the computation of S and df are dependent on whether the variances are pooled. If the variances are not pooled:
S
=
Sx
1
2
n
1
+
Sx n
2
2
2
df
=
n
1
1
−
1
Sx n
Sx
1
2
n
1
2
1
1
2
+
+
Sx n
2
2
2
2
n
2
1
−
1
Sx n
2
2
2
2 otherwise:
Sx p
=
(
n
1
−
1 )
Sx
1
2 +
df
(
n
2
−
1 )
Sx
2
2
S
=
n
1
1
+
n
1
2
Sx p df
=
n
1
+
n
2
−
2 and Sxp is the pooled variance.
Tables and Reference Information A–53
826DEC~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09
PM Page 53 of 58
Financial Formulas
This section contains financial formulas for computing time value of money, amortization, cash flow, interestrate conversions, and days between dates.
Time Value of
Money
i
=
[
e
(
y
×
ln
(
x
+
1 ))
]
−
1 where: PMT ƒ 0
y = C/Y
÷
P/Y
x = (.01
×
I%)
÷
C/Y
C/Y = compounding periods per year
P/Y = payment periods per year
I% = interest rate per year
i
=
(
−
FV
÷
PV
)
( 1
÷
N
) −
1 where: PMT = 0
The iteration used to compute i:
0
=
PV
+
PMT
×
G i
1 ( 1
i i
)
−
N
+
FV
(
i
)
−
N
I %
=
1100
×
C Y
×
[
e
(
y
× ln(
x
+
1 ))
−
1
] where:
x = i
y = P/Y
÷
C/Y
G i
where: k = 0 for endofperiod payments
k = 1 for beginningofperiod payments
N
=
ln
PMT
×
G i
−
FV
×
i
PMT
×
ln( 1
G
+
i i
+
)
PV
×
i
where: i ƒ 0
N
=
−
(
PV
+
FV
)
÷
PMT
where: i = 0
A–54 Tables and Reference Information
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PM Page 54 of 58
Time Value of
Money
(Continued)
PMT
=
−
G i i
×
PV
+
(
PV
+
FV
1
+
i
)
N
−
1
where: i ƒ 0
PMT
=
−
(
PV
+
FV
)
÷
N
where: i = 0
PV
=
i i
−
FV
×
( 1
+
1
i
)
N
− where: i ƒ 0
PV
=
−
(
FV
+
PMT
×
N
) where: i = 0
FV
=
i
×
i
−
(
1
+
i )
N
×
PV
+ where: i ƒ 0
FV
=
−
(
PV
+
PMT
×
N
) where: i = 0
i
×
i i
×
i
Tables and Reference Information A–55
826DEC~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09
PM Page 55 of 58
Financial Formulas
(continued)
Amortization
If computing bal( ), pmt2 = npmt
Let bal(0) = RND(PV)
Iterate from m = 1 to pmt2
I m
=
RND RND
( )
=
(
12
1 )
(
−
I m
+
(
−
1 ))]
) then:
bal
( )
=
Σ
Pr n
( )
=
Σ
Int
2 )
2 )
−
pm t
2
−
pm t
1 1 )
1 )
)
− Σ
Pr n
( ) where: RND = round the display to the number of decimal places selected
RND12 = round to 12 decimal places
Balance, principal, and interest are dependent on the values of
PMT
,
PV
,
æ
, and pmt1 and pmt2.
A–56 Tables and Reference Information
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PM Page 56 of 58
Cash Flow
Interest Rate
Conversions
npv
( )
=
CF
0
+
j
N
∑
=
1
CF j
( 1
+
i
)
−
S j
−
1
( 1 ( 1
i i
)
−
n j
) where: S
j
=
∑
i
=
j
1
0
n i j j
≥
1
=
0
Net present value is dependent on the values of the initial cash flow (CF
0
), subsequent cash flows (CFj), frequency of each cash flow (nj), and the specified interest rate (i).
irr( ) = 100
×
i, where i satisfies npv( ) = 0
Internal rate of return is dependent on the values of the initial cash flow (CF
0
) and subsequent cash flows (CFj).
i = I%
÷
100
4
Eff
( )
=
100
×
(
e
CP
×
ln
(
x
+
1 ) −
1 ) where:
4
Nom
( )
=
100
x = .01
×
NOM
÷
CP
×
CP
×
[
e
1
÷
CP
×
ln
(
x
+
1 ) −
1
] where: x = .01
×
EFF
EFF = effective rate
CP = compounding periods
NOM = nominal rate
Tables and Reference Information A–57
826DEC~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09
PM Page 57 of 58
Financial Formulas
(continued)
Days between
Dates
With the
dbd(
function, you can enter or compute a date within the range Jan. 1, 1950, through Dec. 31, 2049.
Actual/actual daycount method
(assumes actual number of days per month and actual number of days per year):
dbd( (days between dates) =
Number of Days II  Number of Days I
Number of Days I = (Y1

YB)
×
365
+ (number of days MB to M1)
+ DT1
+
(
Y
1
−
YB
4
)
Number of Days II = (Y2

YB)
×
365
+ (number of days MB to M2)
+ DT2
+
(
Y
2
−
YB
4
) where: M1 = month of first date
DT1 = day of first date
Y1 = year of first date
M2 = month of second date
DT2 = day of second date
Y2 = year of second date
MB = base month (January)
DB = base day (1)
YB = base year (first year after leap year)
A–58 Tables and Reference Information
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PM Page 58 of 58
Contents
B
General Information
Battery Information ................................................................2
In Case of Difficulty...............................................................4
Error Conditions.....................................................................5
Accuracy Information...........................................................10
Texas Instruments Support and Service................................12
General Information B–1
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3:16 PM Page 1 of 12
Battery Information
When to Replace the Batteries
The TI82 STATS uses five batteries: four AAA alkaline batteries and one lithium battery. The lithium battery provides auxiliary power to retain memory while you replace the AAA batteries.
When the battery voltage level drops below a usable level, the
TI82 STATS displays this message when you turn on the unit.
Effects of
Replacing the
Batteries
Battery
Precautions
After this message is first displayed, you can expect the batteries to function for about one or two weeks, depending on usage. (This oneweek to twoweek period is based on tests with alkaline batteries; the performance of other kinds of batteries may vary.)
The lowbattery message continues to be displayed each time you turn on the unit until you replace the batteries. If you do not replace the batteries within about two weeks, the calculator may turn off by itself or fail to turn on until you install new batteries.
Replace the lithium battery every three or four years.
Do not remove both types of batteries (AAA and lithium
auxiliary) at the same time. Do not allow the batteries to lose power completely. If you follow these guidelines and the steps for replacing batteries on page B
.
3, you can replace either type of battery without losing any information in memory.
Take these precautions when replacing batteries.
•
Do not mix new and used batteries. Do not mix brands (or types within brands) of batteries.
•
Do not mix rechargeable and nonrechargeable batteries.
•
Install batteries according to polarity (+ and N) diagrams.
•
Do not place nonrechargeable batteries in a battery recharger.
•
Properly dispose of used batteries immediately. Do not leave them within the reach of children.
•
Do not incinerate batteries.
B–2 General Information
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3:16 PM Page 2 of 12
Replacing the
Batteries
To replace the batteries, follow these steps.
1. Turn off the calculator. Replace the slide cover over the keyboard to avoid inadvertently turning on the calculator.
Turn the back of the calculator toward you.
2. Hold the calculator upright. Place your thumb on the oval indentation on the battery cover. Push down and toward you to slide the cover about ¼ inch (6 mm). Lift off the cover to expose the battery compartment.
Note: To avoid loss of information stored in memory, you must turn off the calculator. Do not remove the AAA batteries and the lithium battery simultaneously.
3. Replace all four AAA alkaline batteries at the same time. Or, replace the lithium battery.
•
To replace the AAA alkaline batteries, remove all four discharged AAA batteries and install new ones according to the polarity (+ and N) diagrams in the battery compartment.
•
To remove the lithium battery, place your index finger on the battery. Insert the tip of a ballpoint pen (or similar instrument) under the battery at the small opening provided in the battery compartment. Carefully pry the battery upward, holding it with your thumb and finger.
(There is a spring that pushes against the underside of the battery.)
•
Install the new battery, + side up, by inserting the battery and gently snapping it in with your finger. Use a CR1616 or CR1620 (or equivalent) lithium battery.
4. Replace the battery compartment cover. Turn the calculator on and adjust the display contrast, if necessary (step 1; page
B
.
4).
General Information B–3
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3:16 PM Page 3 of 12
In Case of Difficulty
Handling a
Difficulty
To handle a difficulty, follow these steps.
1. If you cannot see anything on the screen, the contrast may need to be adjusted.
To darken the screen, press and release y, and then press and hold } until the display is sufficiently dark.
To lighten the screen, press and release y, and then press and hold † until the display is sufficiently light.
2. If an error menu is displayed, follow the steps in Chapter 1.
Refer to pages B
.
5 through B
.
9 for details about specific errors, if necessary.
3. If a checkerboard cursor ( # ) is displayed, then either you have entered the maximum number of characters in a prompt, or memory is full. If memory is full, press y
[
MEM
]
2
to select
2:Delete
, and then delete some items from memory (Chapter 18).
4. If the busy indicator (dotted line) is displayed, a graph or program has been paused; the TI82 STATS is waiting for input. Press Í to continue or press É to break.
5. If the calculator does not seem to work at all, be sure the batteries are fresh and that they are installed properly. Refer to battery information on pages B
.
2 and B
.
3.
B–4 General Information
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3:16 PM Page 4 of 12
Error Conditions
When the TI82 STATS detects an error, it displays
ERR:
message and an error menu.
Chapter 1 describes the general steps for correcting errors. This table contains each error type, possible causes, and suggestions for correction.
Error Type
ARCHIVED VAR
ARGUMENT
BAD GUESS
BOUND
BREAK
DATA TYPE
DIM MISMATCH
DIVIDE BY 0
Possible Causes and Suggested Remedies
A function or instruction is archived and therefore cannot be executed or edited. Use the unarchive command to unarchive the variable before using it.
A function or instruction does not have the correct number of arguments. See Appendix A and the appropriate chapter.
¦ In a CALC operation, you specified a
Guess
that is not between
Left Bound
and
Right Bound
.
¦ For the
solve(
function or the equation solver, you specified a
guess that is not between lower and upper.
¦ Your guess and several points around it are undefined.
Examine a graph of the function. If the equation has a solution, change the bounds and/or the initial guess.
¦ In a CALC operation or with
Select(, you defined
Left Bound
>
Right Bound
.
¦ In
fMin(
,
fMax(
,
solve(
, or the equation solver, you entered
lower ‚ upper.
You pressed the É key to break execution of a program, to halt a
DRAW
instruction, or to stop evaluation of an expression.
You entered a value or variable that is the wrong data type.
¦ For a function (including implied multiplication) or an instruction, you entered an argument that is an invalid data type, such as a complex number where a real number is required. See Appendix A and the appropriate chapter.
¦ In an editor, you entered a type that is not allowed, such as a matrix entered as an element in the stat list editor. See the appropriate chapter.
¦ You attempted to store to an incorrect data type, such as a matrix, to a list.
You attempted to perform an operation that references more than one list or matrix, but the dimensions do not match.
¦ You attempted to divide by zero. This error is not returned during graphing. The TI82 STATS allows for undefined values on a graph.
¦ You attempted a linear regression with a vertical line.
General Information B–5
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3:16 PM Page 5 of 12
Error Conditions
(continued)
Error Type
DOMAIN
Duplicate Name
Error in Xmit
ILLEGAL NEST
INCREMENT
INVALID
Possible Causes and Suggested Remedies
¦ You specified an argument to a function or instruction outside the valid range. This error is not returned during graphing. The TI82 STATS allows for undefined values on a graph. See Appendix A and the appropriate chapter.
¦ You attempted a logarithmic or power regression with a
LX
or an exponential or power regression with a
LY
.
¦ You attempted to compute
GPrn(
or
GInt(
with pmt2 < pmt1.
A variable you attempted to transmit cannot be transmitted because a variable with that name already exists in the receiving unit.
¦ The TI82 STATS was unable to transmit an item. Check to see that the cable is firmly connected to both units and that the receiving unit is in receive mode.
¦ You pressed É to break during transmission.
¦ You attempted to perform a backup from a TI
.
82 to a
TI82 STATS.
¦ You attempted to transfer data (other than
L
1
through
L
6
) from a TI82 STATS to a TI
.
82.
¦ You attempted to transfer
L
1
through
L
6
from a TI82 STATS to a TI
.
82 without using
5:Lists to TI82
on the
LINK SEND menu.
You attempted to use an invalid function in an argument to a function, such as
seq(
within expression for
seq(
.
¦ The increment in
seq(
is 0 or has the wrong sign. This error is not returned during graphing. The TI82 STATS allows for undefined values on a graph.
¦ The increment in a
For(
loop is 0.
¦ You attempted to reference a variable or use a function where it is not valid. For example,
Y
n cannot reference
Y
,
Xmin
,
@X
, or
TblStart
.
¦ You attempted to reference a variable or function that was transferred from the TI
.
82 and is not valid for the
TI82 STATS. For example, you may have transferred
UnN1
to the TI82 STATS from the TI
.
82 and then tried to reference it.
¦ In
Seq
mode, you attempted to graph a phase plot without defining both equations of the phase plot.
B–6 General Information
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3:16 PM Page 6 of 12
Error Type
INVALID (cont.)
INVALID DIM
ITERATIONS
LABEL
MEMORY
Possible Causes and Suggested Remedies
¦ In
Seq
mode, you attempted to graph a recursive sequence without having input the correct number of initial conditions.
¦ In
Seq
mode, you attempted to reference terms other than
(nN1)
or
(nN2)
.
¦ You attempted to designate a graph style that is invalid within the current graph mode.
¦ You attempted to use
Select(
without having selected (turned on) at least one xyLine or scatter plot.
¦ You specified dimensions for an argument that are not appropriate for the operation.
¦ You specified a list dimension as something other than an integer between 1 and 999.
¦ You specified a matrix dimension as something other than an integer between 1 and 99.
¦ You attempted to invert a matrix that is not square.
¦ The
solve(
function or the equation solver has exceeded the maximum number of permitted iterations. Examine a graph of the function. If the equation has a solution, change the bounds, or the initial guess, or both.
¦
irr(
has exceeded the maximum number of permitted iterations.
¦ When computing
æ , the maximum number of iterations was exceeded.
The label in the
Goto
instruction is not defined with a
Lbl
instruction in the program.
Memory is insufficient to perform the instruction or function.
You must delete items from memory (Chapter 18) before executing the instruction or function.
Recursive problems return this error; for example, graphing the equation
Y
1
=Y
1
.
Branching out of an
If
/
Then
,
For(
,
While
, or
Repeat
loop with a
Goto
also can return this error because the
End
statement that terminates the loop is never reached.
General Information B–7
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3:16 PM Page 7 of 12
Error Conditions
(continued)
Error Type
MemoryFull
MODE
NO SIGN CHNG
NONREAL ANS
OVERFLOW
RESERVED
SINGULAR MAT
Possible Causes and Suggested Remedies
¦ You are unable to transmit an item because the receiving unit’s available memory is insufficient. You may skip the item or exit receive mode.
¦ During a memory backup, the receiving unit’s available memory is insufficient to receive all items in the sending unit’s memory. A message indicates the number of bytes the sending unit must delete to do the memory backup. Delete items and try again.
You attempted to store to a window variable in another graphing mode or to perform an instruction while in the wrong mode; for example,
DrawInv
in a graphing mode other than
Func
.
¦ The
solve(
function or the equation solver did not detect a sign change.
¦ You attempted to compute all ‚ 0, or when
FV
, ( Ú
æ
ÚääääPMT when
FV
, (
Ú
), and
PV
are
), and
PV
are all 0.
¦ You attempted to compute
irr(
when neither CFList nor CFO is > 0, or when neither CFList nor CFO is < 0.
In
Real
mode, the result of a calculation yielded a complex result.
This error is not returned during graphing. The TI82 STATS allows for undefined values on a graph.
You attempted to enter, or you have calculated, a number that is beyond the range of the calculator. This error is not returned during graphing. The TI82 STATS allows for undefined values on a graph.
You attempted to use a system variable inappropriately. See
Appendix A.
¦ A singular matrix (determinant = 0) is not valid as the argument for
L1
.
¦ The
SinReg
instruction or a polynomial regression generated a singular matrix (determinant = 0) because it could not find a solution, or a solution does not exist.
This error is not returned during graphing. The TI82 STATS allows for undefined values on a graph.
B–8 General Information
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3:16 PM Page 8 of 12
Error Type
SINGULARITY
STAT
STAT PLOT
SYNTAX
TOL NOT MET
UNDEFINED
WINDOW RANGE
ZOOM
Possible Causes and Suggested Remedies
expression in the
solve(
function or the equation solver contains a singularity (a point at which the function is not defined).
Examine a graph of the function. If the equation has a solution, change the bounds or the initial guess or both.
You attempted a stat calculation with lists that are not appropriate.
¦ Statistical analyses must have at least two data points.
¦
Med.Med
must have at least three points in each partition.
¦ When you use a frequency list, its elements must be ‚ 0.
¦ (
Xmax
N
Xmin
) à
Xscl
must be 47 for a histogram.
You attempted to display a graph when a stat plot that uses an undefined list is turned on.
The command contains a syntax error. Look for misplaced functions, arguments, parentheses, or commas. See Appendix A and the appropriate chapter.
You requested a tolerance to which the algorithm cannot return an accurate result.
You referenced a variable that is not currently defined. For example, you referenced a stat variable when there is no current calculation because a list has been edited, or you referenced a variable when the variable is not valid for the current calculation, such as
a
after
Med.Med
.
A problem exists with the window variables.
¦ You defined
Xmax
Xmin
or
Ymax
Ymin
.
¦ You defined
qmax
qmin
and
qstep
>
0
(or vice versa).
¦ You attempted to define
Tstep=0
.
¦ You defined
Tmax
Tmin
and
Tstep
>
0
(or vice versa).
¦ Window variables are too small or too large to graph correctly.
You may have attempted to zoom in or zoom out to a point that exceeds the TI82 STATS numerical range.
¦ A point or a line, instead of a box, is defined in
ZBox.
¦ A ZOOM
operation returned a math error.
General Information B–9
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3:16 PM Page 9 of 12
Accuracy Information
Computational
Accuracy
Graphing
Accuracy
To maximize accuracy, the TI82 STATS carries more digits internally than it displays. Values are stored in memory using up to 14 digits with a twodigit exponent.
•
You can store a value in the window variables using up to 10 digits (12 for
Xscl
,
Yscl
,
Tstep
, and
qstep
).
•
Displayed values are rounded as specified by the mode setting with a maximum of 10 digits and a twodigit exponent.
•
RegEQ
displays up to 14 digits in
Float
mode. Using a fixeddecimal setting other than
Float
causes
RegEQ
results to be rounded and stored with the specified number of decimal places.
Xmin
is the center of the leftmost pixel,
Xmax
is the center of the nexttotherightmost pixel. (The rightmost pixel is reserved for the busy indicator.)
@X
is the distance between the centers of two adjacent pixels.
•
In
Full
screen mode,
@X
is calculated as
(
Xmax
N
Xmin
) à 94. In
G.T
splitscreen mode,
@X
is calculated as (
Xmax
N
Xmin
) à 46.
•
If you enter a value for
@X
from the home screen or a program in
Full
screen mode,
Xmax
is calculated as
Xmin
+
@X
… 94. In
G.T
splitscreen mode,
Xmax
is calculated as
Xmin
+
@X
… 46.
Ymin
is the center of the nexttothebottom pixel;
Ymax
is the center of the top pixel.
@Y
is the distance between the centers of two adjacent pixels.
•
In
Full
screen mode,
@Y
is calculated as
(
Ymax
N
Ymin
) à 62. In
Horiz
splitscreen mode,
@Y
is calculated as (
Ymax
N
Ymin
) à 30. In
G.T
splitscreen mode,
@Y
is calculated as (
Ymax
N
Ymin
) à 50.
•
If you enter a value for
@Y
from the home screen or a program in
Full
screen mode,
Ymax
is calculated as
Ymin
+
@Y
… 62. In
Horiz
splitscreen mode,
Ymax
is calculated as
Ymin
+
@Y
… 30. In
G.T
splitscreen mode,
Ymax
is calculated as
Ymin
+
@Y
… 50.
B–10 General Information
826FEC~1.DOC TI83 Intl English, Appendix B Bob Fedorisko Revised: 10/27/05 3:16 PM Printed: 10/27/05
3:16 PM Page 10 of 12
Graphing
Accuracy
(continued)
Cursor coordinates are displayed as eightcharacter numbers
(which may include a negative sign, decimal point, and exponent) when
Float
mode is selected.
X
and
Y
are updated with a maximum accuracy of eight digits.
minimum
and
maximum
on the
CALCULATE
menu are calculated with a tolerance of 1
EL
5;
‰f(x)dx
is calculated at 1
EL
3.
Therefore, the result displayed may not be accurate to all eight displayed digits. For most functions, at least five accurate digits exist. For
fMin(
,
fMax(
, and
fnInt(
on the
MATH
menu and
solve(
in the
CATALOG
, the tolerance can be specified.
Function Limits
Function Range of Input Values sin
x,
cos
x,
tan
x
sin L1 ln e
x
x,
log
x
10
x
x,
cos L1
x
sinh
x,
cosh
x
tanh
x
sinh
L1 cosh
L1
x x
0 x < 10
12
(radian or degree)
L1 x 1
10 L100 < x < 10 100
L10
L10
100
100
< x 230.25850929940
< x < 100
x 230.25850929940
x < 10
100
x < 5 × 10
99
1 x < 5 × 10
99
tanh
L1
x
‡
x (real mode)
L1 < x < 1
0 x < 10 100
‡
x (complex mode) x < 10 100
x
!
L.5 x 69, where x is a multiple of .5
Function Results
Function sin
L1 cos
L1
x,
tan
L1
x x
Range of Result
L90¡ to 90¡ or Lpà2 to pà2 (radians)
0¡ to 180¡ or 0 to p (radians)
General Information B–11
826FEC~1.DOC TI83 Intl English, Appendix B Bob Fedorisko Revised: 10/27/05 3:16 PM Printed: 10/27/05
3:16 PM Page 11 of 12
Texas Instruments Support and Service
For General
Information
Service and warranty information
For more information about TI products and services, contact TI by email or visit the TI Internet address.
Email inquiries:
Home Page:
[email protected]
education.ti.com
For information about the length and terms of the warranty or about product service, refer to the warranty statement enclosed with this product or contact your local Texas Instruments retailer/distributor.
B–12 General Information
826FEC~1.DOC TI83 Intl English, Appendix B Bob Fedorisko Revised: 10/27/05 3:16 PM Printed: 10/27/05
3:16 PM Page 12 of 12
Index
!
ìììì
íííí
çççç
>
‚
L1
'
ääää
à
=
¦
Ö
Ò
Õ
Ô
M
+
3
:
+ c
2 c
2 c
2
(addition), 2 .
3, A .
38
cdf(
(chisquare cdf), 13
pdf(
(chisquare pdf), 13
.
31, A .
3
.
.Test
(chisquare test), 13
31, A .
4
.
22, A .
4
(colon), 6, 16 .
5
(concatenation), 15 .
6, A .
38
3
‡(
(cube), 2 .
6, A
.
35
(cube root), 2 .
6, A
.
35
¡
<
{ }
[ ]
ƒ
( ) p
›
+
^
(degrees notation), 2 .
3, A .
34
(division), 2 .
3, A
.
37
(equalto relational test), 2 .
25, A
.
35
(factorial), 2
.
21, A
.
34
(graph style, animate), 3
.
9
(graph style, dot), 3
.
9
(graph style, line), 3
.
9
(greater than), 2
.
25, A
.
35
(greater than or equal to), 2
.
25, A
.
35
(inverse), 2
.
3, 8
.
9, 10
.
10, A
.
36
(less than), 2
.
25, A
.
35
(less than or equal to), 2
.
25, A
.
36
(list indicator), 11
.
4
(matrix indicator), 10
.
7
(minutes notation), 2
.
23, A
.
38
(multiplication), 2
.
3, A
.
37
(negation), 1
.
23, 2
.
4, A
.
37
(not equal to), 2
.
25, A
.
35
(parentheses), 1
.
23
(pi), 2
.
4
(pixel mark), 8
.
15, 12
.
34
(pixel mark), 8
.
15, 12
.
34
(pixel mark), 8
.
15, 12
.
34
(plot type, box), 12
.
33
(plot type, histogram), 12 .
32
(plot type, modified box), 12 .
32
(plot type, normal probability), 12 .
33
(power), 2 .
3, A .
36, A .
37
"
2
10 x
‡
^(
‡(
!
" "
N
(power of ten), 2
(root), 2 .
6, A
.
35
(square) , 2 .
3 , A
(square root) , 2 .
.
4, A .
37
(seconds notation), 2
.
36
.
23, A
.
38
3 , A
.
Store, 1 .
14, A
.
28
(string indicator), 15 .
3
(subtraction), 2 .
3, A
.
38
37
. A .
a+b
i (rectangular complex mode), 1 .
12,
2
.
16, A .
3
above graph style(
éééé
), 3
.
9
abs(
(absolute value), 2 .
13, 2 .
19, 10 .
10,
A
.
2
accuracy information computational and graphing, B .
10
graphing, 3 .
17
function limits and results, B .
11
addition (
+
), 2 .
3, A .
38
alpha cursor, 1 .
5
alpha key, 3 alphalock, 1 .
8
alternative hypothesis, 13 .
7
amortization
bal(
(amortization balance), 14
.
9, A
.
3
calculating schedules, 14
.
9
formula, A
.
56
GInt(
(sum of interest),14
.
9, A
.
12
(sum of principal), 14
GPrn( and
(Boolean operator), 2
.
9, A
.
19
.
26, A
.
2
angle(
, 2
.
19, A
.
2
ANGLE
menu, 2
.
23
angle modes, 1
.
11
animate graph style (
ìììì
), 3
.
9
ANOVA(
(oneway variance analysis),
13
.
25, A
.
2
formula, A
.
51
Ans
(last answer), 1
.
18, A
.
2
APDé (Automatic Power Down™), 1
.
2
applications. See examples, applications arccosine (
cos
M1
(
), 2
.
3
arcsine (
sin
M1
(
), 2
.
3
arctangent (
tan
M1
(
), 2
.
3
augment(
, 10
.
14, 11
.
15, A
.
3
Automatic Power Down™ (APDé), 1 .
2
automatic regression equation, 12 .
22
automatic residual list ( RESID ), 12 .
22
axes format, sequence graphing, 6 .
8
axes, displaying (
AxesOn
,
AxesOff
),
3
.
14, A .
3
AxesOff
, 3 .
14, A .
3
AxesOn
, 3 .
14, A .
3
. B .
backing up calculator memory, 19 .
4,
19
.
10
bal(
(amortization balance), 14 .
9, A .
3
batteries, 1 .
2, B .
2
below graph style (
ê
), 3 .
9
binomcdf(
, 13 .
33, A .
3
binompdf(
, 13
.
33, A
.
3
Index1
825915~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 2:25 PM Printed: 10/27/05 3:22
PM Page 1 of 16
Index (continued)
Boolean logic, 2 .
26
box pixel mark (
›
), 8
Boxplot
.
15, 12
plot type (
Ö
), 12
.
.
34
33
busy indicator, 1 .
4
. C .
CALCULATE menu, 3 .
25
Calculate
output option, 13 .
6, 13
.
8
cash flow calculating, 14 .
8
formula, A .
57
irr(
(internal rate of return), 14 .
8, A .
13
npv(
(net present value), 14 .
8, A .
17
CATALOG , 15 .
2
CBLé System, 16
.
21, 19
.
3, A
.
10
CBRé, 16
.
21, 19
.
3, A
.
10
Check RAM (memory screen), 18 chisquare cdf (
c
chisquare pdf ( chisquare test (
c c
2
2
2 cdf( pdf(
), 13
), 13
.Test
), 13
.
2
.
31, A
.
3
.
31, A
.
4
.
22, A
.
4
Circle(
(draw circle), 8
Clear Entries
, 18 clearing
.
11, A
.
4
.
4, A
.
4
entries (
Clear Entries
), 18 all lists (
ClrAllLists
), 18
.
4, A
.
4
.
4, A
.
4
drawing (
ClrDraw
), 8
.
4, A
.
4
home screen (
ClrHome
), 16
.
20, A
.
4
list (
ClrList
), 12
.
20, A
.
4
table (
ClrTable
), 16
.
20, A
.
4
ClrAllLists
(clear all lists), 18
.
4, A
.
4
ClrDraw
(clear drawing), 8
.
4, A
.
4
ClrHome
(clear home screen), 16
.
20, A
.
4
ClrList
(clear list), 12
.
20, A
.
4
ClrTable
(clear table), 16
.
20, A coefficients of determination (
r
2
.
4
,
R
2
),
12
.
23
colon separator (
:
), 6, 16 combinations (
nCr
), 2 .
.
5
21, A .
16
. C (continued) .
complex modes (
a+b
i,
r
e
^q
i), 1 .
12, 2
.
16, A .
3,
A
.
22
numbers, 1 .
12, 2 .
16, 2 .
18, A .
22
compoundingperiodsperyear variable
(
C/Y
), 14 .
4, 14
.
14
concatenation (
+
), 15 .
6, A .
38
confidence intervals, 13 .
8, 13
.
16
N
13
.
21
conj(
(conjugate), 2 .
18, A .
4
Index2
Connected
(plotting mode), 1 .
11, A .
4
contrast (display), 1 .
3
convergence, sequence graphing, 6 conversions
.
12
4Dec
(to decimal), 2 .
5, A .
5
4DMS
(to degrees/minutes/ seconds),
4Eff
2
.
24, A
.
7
(to effective interest rate), 14 .
12,
A
.
7
Equ4String(
(equationtostring conversion), 157, A .
8
4Frac
(to fraction conversion), 2
.
5,
A
.
10
List4matr(
(listtomatrix conversion),
10
.
14, 11
.
15, A
.
14
Matr4list(
(matrixtolist conversion),
10
4Nom
.
14, 11
.
16, A
.
15
(to nominal interest rate conversion), 14
4Polar
.
12, A
.
16
(to polar conversion), 2
.
19,
A
.
19
P4Rx(
,
P4Ry(
(polartorectangular conversion), 2
4Rect
.
24, A
.
21
(to rectangular conversion), 2
.
19,
A
.
22
R4Pr(
,
R4Pq(
(rectangulartopolar conversion), 2
.
24, A
.
23
String4Equ(
(stringtoequation conversion), 15
.
8, A
.
29
CoordOff
, 3
CoordOn
, 3
.
14, A
.
5
.
14, A
.
5
correlation coefficient (
r
), 12
.
23, 12
.
25
N
12
.
27
cos(
(cosine), 2 .
3, A
cos
M1
(
(arccosine), 2
.
.
5
3, A
.
5
cosh(
(hyperbolic cosine), 15 .
10, A
.
5
. D (continued) .
cosh
M1
(
(hyperbolic arccosine), 15 .
10, A
.
5
cosine (
cos(
), 2 .
3, A
.
5
cross pixel mark (
+
), 8 cube (
3
) , 2 cube root (
.
6, A
3
‡(
.
), 2
35
.
6, A
.
15, 12
.
34
.
35
CubicReg
(cubic regression), 12 .
26, A
.
5
cubic regression (
CubicReg
), 12 .
26, A
.
5
cumulative sum (
cumSum(
), 10 .
15,
11
.
12, A
.
5
cumSum(
(cumulative sum), 10 .
15,
11
.
12, A
.
5
825915~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 2:25 PM Printed: 10/27/05 3:22
PM Page 2 of 16
cursors, 1 .
5, 1 .
8
C/Y
(compoundingperiodsperyear variable), 14 .
4, 14
.
14
. D .
Data input option, 13 .
6, 13
.
7
days between dates (
dbd(
), 14 .
13, A
.
5,
A
.
58
dbd(
(days between dates), 14 .
13, A
.
5,
A
.
58
4Dec
(to decimal conversion), 2 .
5, A
.
5
decimal mode (float or fixed), 1 .
10
decrement and skip (
DS<(
), 16 .
14, A
.
7
definite integral, 2 .
7, 3
.
28, 4
.
8, 5
.
6
Degree
angle mode, 1 degrees notation (
¡
) , 2
.
11, 2
.
23, A
.
6
.
3, A
.
34
DELETE FROM menu, 18
.
3
delete variable contents (
DelVar
), 16
.
15,
A
.
6
DelVar
(delete variable contents), 16
.
15,
A
.
6
DependAsk
, 7
.
3, 7
.
5, A
.
6
DependAuto
, 7
.
3, 7
.
5, A
.
6
derivative. See numerical derivative
det(
(determinant), 10 determinant (
det(
), 10
DiagnosticOff
, 12
.
12, A
.
6
.
12, A
.
6
.
23, A
.
6
DiagnosticOn
, 12
.
23, A
.
6
diagnostics display mode(
r
,
r
2
,
R
2
differentiation, 2
.
8, 3
.
28, 4
.
8, 5
.
6
), 12
.
23
. D (continued) .
dimensioning a list or matrix, 10
.
12,
dim(
!
10
.
13, 11
.
11, A
.
6
(dimension), 10
.
12, 11
.
(assign dimension), 10
11, A
.
.
6
13, 11
.
11,
A
.
6
Disp
(display), 16
.
18, A
.
6
DispGraph
(display graph), 16 .
19, A
.
7
display contrast, 1 .
3
display cursors, 1 .
5
DispTable
(display table), 16 .
19, A
.
7
DISTR (distributions menu), 13 .
29
DISTR DRAW (distributions drawing menu), 13 .
35
distribution functions
binomcdf(
, 13 .
33, A
.
3
binompdf(
, 13
c
2 cdf(
, 13 .
.
31, A
33, A
.
3
.
3
c
ÛÛ
2 pdf(
Ûcdf(
, 13
, 13
.
31, A
.
4
.
32, A
.
8
, 13 .
32, A
.
9
geometcdf(
, 13 .
34, A
.
10
geometpdf(
, 13 .
34, A
.
11
invNorm(
, 13 .
30, A
.
12
normalcdf(
, 13 .
30, A
.
17
normalpdf(
, 13 .
29, A
.
17
poissoncdf(
, 13 .
34, A
.
99
poissonpdf(
, 13 .
33, A
.
19
tcdf(
, 13 .
31, A
.
29
tpdf(
, 13
.
30, A
.
29
distribution shading instructions
Shadec
Shade
Û
2
(
, 13
, 13
.
.
36, A
36, A
.
.
26
27
ShadeNorm(
, 13
.
35, A
.
27
Shade_t(
, 13 division (
à
) , 2
.
36, A
.
27
.
3, A
.
37
DMS (degrees/minutes/seconds entry notation), 2
.
23, A
.
38
4DMS
(to degrees/minutes/seconds), 2
.
24,
A
.
7
dot graph style (
íííí
), 3 dot pixel mark (
¦
), 8
.
9
.
15, 12
.
34
Dot
(plotting mode), 1
.
11, A
DrawF
(draw a function), 8
.
7
.
9, A
.
7
Index3
825915~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 2:25 PM Printed: 10/27/05 3:22
PM Page 3 of 16
Index (continued)
. D (continued) .
drawing on a graph circles (
Circle(
), 8
.
11
functions and inverses (
DrawF
,
DrawInv
), 8
.
9
lines (
Horizontal
,
Line(
,
Vertical
),
8
.
6, 8
.
7
line segments (
Line(
), 8
.
5
pixels (
Pxl.Change
,
Pxl.Off
,
Pxl.On
,
pxl.Test
), 8
.
16
points (
Pt.Change
,
Pt.Off
,
Pt.On
),
8
.
14
tangents (
Tangent
), 8
.
8
text (
Text
), 8
.
12
using
Pen
, 8
.
13
DrawInv
(draw inverse), 8
.
9, A
.
7
DRAW menu, 8 .
3
DRAW instructions, 8 .
3
N
8
.
16
Draw output option, 13 .
6
N
13
.
8
DRAW POINTS menu, 8 .
14
DRAW STO (draw store menu), 8 .
17
dr/dq
operation on a graph, 5 .
6
DS<(
(decrement and skip), 16 .
14, A
.
7
DuplicateName menu, 19 .
5
dx/dt
operation on a graph, 3 .
28, 4
.
8
dy/dx
operation on a graph, 3 .
28, 4
.
8, 5
.
6
. E .
e (constant), 2 .
4
e^(
(exponential), 2 .
4, A
.
7
åååå
(exponent), 1 .
7, 1
.
10, A
.
7
edit keys table, 1 .
8
4Eff(
(to effective interest rate), 14
.
12, A
.
7
Else
, 16
End
, 16
.
10
.
12, A
.
8
Eng
(engineering notation mode), 1
.
10,
A
.
8
entry cursor, 1
.
5
ENTRY
(last entry key), 1
.
16
EOSé (Equation Operating System), 1
.
22
eqn
(equation variable), 2
.
8, 2
.
12
equalto relational test (
=
), 2
.
25, A
.
35
Equation Operating System (EOSé), 1
.
22
Equation Solver
, 2
.
8
equations with multiple roots, 2
.
12
. E (continued) .
Equ4String(
(equationtostring conversion), 15
.
7, A
.
8
Index4
errors diagnosing and correcting, 1 .
24
messages, B .
5
examples—applications area between curves, 17 .
11
areas of regular nsided polygons,
17
.
16
box plots, 17 .
2
cobweb attractors, 17 .
8
fundamental theorem of calculus, 17 .
14
guess the coefficients, 17 .
9
inequalities, 17
.
5
mortgage payments 17
.
18
parametric equations: ferris wheel problem, 17
.
12
piecewise functions, 17
Sierpinski triangle, 17
.
7
.
4
solving a system of nonlinear equations,
17
.
6
unit circle and trig curves, 17
.
10
examples—Getting Started box with lid 9 – 16 defining a, 9 defining a table of values, 10 finding calculated maximum, 16 setting the viewing window, 12 tracing the graph, 13 zooming in on the graph, 15 zooming in on the table, 11 coin flip, 2
.
2
compound interest, 14
.
3
drawing a tangent line, 8
.
2
financing a car, 14 .
2
forest and trees, 6 .
2
generating a sequence, 11 .
2
graphing a circle, 3 .
2
mean height of a population, 13 .
2
path of a ball, 4 .
2
pendulum lengths and periods, 12 .
2
polar rose, 5 .
2
825915~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 2:25 PM Printed: 10/27/05 3:22
PM Page 4 of 16
. E (continued) .
examples—Getting Started (continued) quadratic formula converting to a fraction, 7 displaying complex results, 8 entering a calculation, 6 roots of a, 7
.
2
sending variables, 19
.
2
solving a system of linear equations,
10
.
2
unit circle, 9
.
2
volume of a cylinder, 16
.
2
examples—miscellaneous convergence, 6
.
12
daylight hours in Alaska, 12
.
28
calculating outstanding loan balances,
14
.
10
predatorprey model, 6 .
13
exponential regression (
ExpReg
), 12 .
26,
A
.
8
expr(
(stringtoexpression conversion),
15
.
7, A
.
8
ExpReg
(exponential regression), 12 .
26,
A
.
8
expression, 1 .
6
converting from string (
expr(
), 15 .
7,
A
.
8
turning on and off (
ExprOn
,
ExprOff
),
3
.
14, A
.
8
ExprOff
(expression off), 3
ExprOn
(expression on), 3
.
14, A
.
8
.
14, A
.
8
. F .
‰f(x)dx
operation on a graph, 3
.
28
factorial (
!
), 2
.
21, A
.
34
family of curves, 3
.
16
, 13
.
32, A
.
8
Fill(
, 10
.
13, A
.
8
FINANCE CALC
menu, 14
FINANCE VARS
menu, 14
.
5
.
14
financial functions amortization schedules, 14
.
9
cash flows, 14
.
8
days between dates, 14
.
13
interest rate conversions, 14
.
12
payment method, 14
.
13
time value of money (
TVM
), 14
.
6
. F (continued) .
Fix
(fixeddecimal mode), 1
.
10, A
.
8
fixeddecimal mode (
Fix
), 1
.
10, A
.
8
Float
(floatingdecimal mode), 1 floatingdecimal mode (
Float
), 1
fMax(
(function maximum), 2
.
10, A
.
8
.
10, A
.
8
.
6, A
.
9
fMin(
(function minimum), 2
fnInt(
(function integral), 2
.
6, A
.
9
.
7, A
.
9
FnOff
(function off), 3
FnOn
(function on), 3
.
8, A
.
9
.
8, A
.
9
For(
, 16
.
10, A
.
9
format settings, 3
.
13, 6
.
8
formulas amortization, A
.
56
ANOVA
, A
.
51
cash flow, A
.
57
days between dates, A .
58
factorial, 2 .
21
interest rate conversions, A .
57
logistic regression, A sine regression, A .
50
.
50
time value of money, A .
54
twosample ÛTest, A twosample t test, A .
.
53
52
fPart(
(fractional part), 2 .
14, 10 .
11, A
.
9
, 13 .
32, A
.
9
4Frac
(to fraction), 2 .
5, A
.
10
freemoving cursor, 3 .
17
frequency, 12 .
24
Full
(fullscreen mode), 1
.
12, A
.
10
fullscreen mode (
Full
), 1
.
12, A
.
10
Func
(function graphing mode), 1
.
11,
A
.
10
function, definition of, 1
.
7
function graphing, 3
.
1 – 3
.
28
accuracy, 3
.
17
CALC
(calculate menu), 3 defining and displaying, 3
.
25
.
3
defining in the Y= editor, 3
.
5
defining on the home screen, in a program, 3
.
6
deselecting, 3 displaying, 3
.
7
.
3, 3
.
11, 3
.
15
evaluating, 3
.
6
family of curves, 3 format settings, 3
.
16
.
13
. F (continued) .
Function graphing (continued)
Index5
825915~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 2:25 PM Printed: 10/27/05 3:22
PM Page 5 of 16
Index (continued)
freemoving cursor, 3 .
17
graph styles, 3 .
9
maximum of (
fMax(
), 2.6, A.9
minimum of (
fMin(
), 2.6, A.9
modes, 1 .
11, 3 .
4, A .
10
moving the cursor to a value, 3 .
19
overlaying functions on a graph, 3 .
16
panning, 3 .
19
pausing or stopping a graph, 3 .
15
Quick Zoom, 3 .
19
selecting, 3 .
7, 3 .
8, A
.
9
shading, 3
.
10
Smart Graph, 3
.
15
tracing, 3
.
18
window variables, 3
.
11, 3
.
12
Y= editor, 3
.
5
viewing window, 3
.
11
@X
and
@Y
window variables, 3
.
12
ZOOM
menu, 3
.
20
ZOOM MEMORY
menu, 3 function integral (
fnInt(
), 2
.
23
.
7, A
.
9
functions and instructions table, A
.
2 – A
.
2
future value, 14
.
5, 14
.
7, 14
.
14
present value, 14
.
5, 14
.
7, 14
.
14
FV
(futurevalue variable), 14
.
4, 14
.
14
.G .
gcd(
(greatest common divisor), 2
.
15,
A
.
10
GDB
(graph database), 8
geometcdf(
, 13
.
19
.
34, A
.
10
geometpdf(
, 13
.
34, A
.
10
Get(
(get data from CBL or CBR), 16
.
21,
A
.
10
GetCalc(
(get data from TI82 STATS),
16
.
21, A
.
10
getKey
, 16 .
20, A
.
10
Getting Started, 1 – 18. See also examples,
Getting Started
Goto
, 16 .
13, A
.
10
. G (continued) .
graph database (
GDB
), 8
.
19
graphing modes, 1
.
11
graphingorder modes, 1
.
12
GraphStyle(
, 16
.
15, A
.
11
graph styles, 3
.
9
graphtable splitscreen mode (
G.T
), 1
9
.
5, A
.
11
greater than (
>
), 2
.
25, A
.
35
greater than or equal to (
‚
), 2
.
12,
.
25, A
.
35
greatest common divisor (
gcd(
), 2
.
15,
A
.
10
greatest integer (
int(
), 2
.
14, 10
.
11, A
.
12
GridOff
, 3
GridOn
, 3
.
14, A
.
11
.
14, A
.
11
G.T
(graphtable splitscreen mode), 1
.
12,
9
.
5, A
.
11
. H .
Histogram
plot type (
Ò
), 12 .
32
home screen, 1 .
4
Horiz
(horizontal splitscreen mode), 1 .
12,
9
.
4, A
.
11
hyperbolic functions, 15 .
10
Horizontal
(draw line), 8 .
6
N
8
.
7, A
.
11
hypothesis tests, 13 .
10
N
13
.
15
. I .
i (complex number constant), 2 .
17
(annual interest rate variable), 14 .
4,
14
.
14
identity(
, 10
If
instructions
If
, 16
.
13, A
.
9, A
.
11
.
11
IfThen
, 16 .
9, A
.
11
IfThenElse
, 16
.
10, A
.
11
imag(
(imaginary part), 2
.
18, A
.
11
imaginary part (
imag(
), 2
.
18, A
.
11
implied multiplication, 1
.
23
increment and skip (
IS>(
), 16
.
13, A
.
13
IndpntAsk
, 7
.
3, A
.
12
IndpntAuto
, 7
.
3, A
.
12
independent variable, 7
.
3, A
.
12
inferential stat editors, 13
.
6
Index6
825915~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 2:25 PM Printed: 10/27/05 3:22
PM Page 6 of 16
. I (continued) .
inferential statistics. See also stat tests; confidence intervals alternative hypotheses, 13
.
7
bypassing editors, 13
.
8
calculating test results (
Calculate
),
13
.
8
confidence interval calculations, 13
.
8,
13
.
16
N
13
.
21
data input or stats input, 13
.
7
entering argument values, 13
.
7
graphing test results (
Draw
), 13
.
8
input descriptions table, 13
.
26
pooled option, 13
.
8
STAT TESTS
menu, 13
.
9
test and interval output variables, 13
.
28
Input
, 16 .
16, 16
.
17, A
.
12
insert cursor, 1 .
5
inString(
(in string), 15 .
7, A
.
12
instruction, definition of, 1 .
7
int(
(greatest integer), 2 .
14, 10 .
11, A
.
12
GInt(
(sum of interest), 14 .
9, A
.
12
integer part (
iPart(
), 2 .
14, 10 .
11, A
.
12
integral. See numerical integral interest rate conversions calculating, 14 .
12
4Eff(
(compute effective interest rate),
14
.
12, A
.
7
formula, A .
57
4Nom(
(compute nominal interest rate),
14
.
12, A
.
16
internal rate of return (
irr(
), 14
.
8, A
.
13
intersect
operation on a graph, 3 inverse (
L1
), 2
.
3, 8
.
9, 10
.
10, A
.
36
.
27
inverse cumulative normal distribution
(
invNorm(
), 13
.
30, A
.
12
inverse trig functions, 2
.
3
invNorm(
(inverse cumulative normal distribution), 13
.
30, A
.
12
iPart(
(integer part), 2
.
14, 10
.
11, A
.
12
irr(
(internal rate of return), 14
.
8, A
.
13
IS>(
(increment and skip), 16
.
13, A
.
13
. K .
keyboard layout, 2, 3 math operations, 2
.
3
keycode diagram, 16
.
20
. L .
L
(usercreated list name symbol), 11
.
16,
A
.
13
LabelOff
, 3
LabelOn
, 3 labels
.
14, A
.
13
.
14, A
.
13
graph, 3
.
14, A
.
13
program, 16
Last Entry, 1
.
13, A
.
13
.
16
Lbl
(label), 16
.
13, A
.
13
lcm(
(least common multiple), 2 least common multiple (
lcm(
), 2
length(
of string, 15
.
8, A
.
13
.
15, A
.
13
.
15, A
.
13
less than (
<
), 2 .
25, A
.
35
less than or equal to (
), 2 line graph style (
çççç
), 3 .
9
.
25, A
.
36
Line(
(draw line), 8 .
5, A
.
13
line segments, drawing, 8 .
5
lines, drawing, 8 .
6, 8
.
7
linking receiving items, 19 .
5
to a CBL System or CBR, 19 .
3
to a PC or Macintosh, 19 .
3
to a TI.82, 19 .
3, 19
.
8
transmitting items, 19 .
6
two TI82 STATS units, 19 .
3
LINK RECEIVE
LINK SEND
menu, 19
.
5
menu, 19
.
4
LinReg(a+bx)
(linear regression), 12
.
26,
A
.
14
LinReg(ax+b)
(linear regression), 12
.
25,
A
.
14
LinRegTTest
(linear regression t test),
13
.
24, A
.
14
@List(
, 11
.
12, A
.
14
LIST MATH
menu, 11
.
17
List4matr(
(liststomatrix conversion),
10
.
14, 11
LIST NAMES
.
15, A
menu, 11
LIST OPS
menu, 11
.
14
.
10
.
6
. L (continued) .
lists, 11
.
1 – 11
.
18
Index7
825915~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 2:25 PM Printed: 10/27/05 3:22
PM Page 7 of 16
Index (continued)
accessing an element, 11 .
5
attaching formulas, 11 .
7, 12
.
14
clearing all elements, 12 .
12, 12
.
20
copying, 11 .
5
creating, 11 .
3, 12
.
12
deleting from memory, 11 .
5, 18
.
3
detaching formulas, 11 .
8, 12
.
16
dimension, 11 .
4, 11
.
11
entering list names, 11 .
6, 12
.
11
indicator (
{ }
), 11 .
4
naming lists, 11 .
3
storing and displaying, 11
.
4
transmitting to and from TI.82, 19
.
4
using in expressions, 11
.
9
using to graph a family of curves, 3
.
16,
11
.
5
using to select data points from a plot,
11
.
13
using with math functions, 11
.
9
using with math operations, 2
.
3
ln(
, 2
.
4, A
.
14
LnReg
(logarithmic regression), 12
.
26,
A
.
14
log(
, 2
.
4, A
.
14
logic (Boolean) operators, 2
Logistic
(regression), 12
.
26
.
27, A
.
15
logistic regression formula, A
.
50
. M .
MATH CPX
(complex menu), 2
.
18
MATH
menu, 2
.
5
MATH NUM
(number menu), 2 math operations, keyboard, 2
.
3
.
13
MATH PRB
(probability menu), 2
.
20
Matr4list(
(matrixtolist conversion),
10
.
14, 11 .
16, A
.
15
matrices, 10 .
1 – 10 .
16
accessing elements, 10 .
8
copying, 10 .
8
defined, 10 .
3
deleting from memory, 10 .
4
dimensions, 10 .
3, 10
.
12, 10
.
13
displaying a matrix, 10 .
8
displaying matrix elements, 10 .
4
editing matrix elements, 10 .
6
. M (continued) .
matrices, (continued) indicator (
[ ]
), 10 .
7
Index8
inverse (
L1
), 10 .
10
math functions, 10 .
9 – 10 .
11
matrix math functions (
det(
,
T
,
dim(
,
Fill(
,
identity(
,
randM(
,
augment(
,
Matr4list(
,
List4matr(
,
cumSum(
),
10
.
12 – 10 .
16
referencing in expressions, 10 .
7
relational operations, 10 .
11
row operations(
ref(
,
rref(
,
rowSwap(
,
row+(
,
†row(
,
†row+(
), 10 .
15
selecting, 10 .
3
viewing, 10
MATRX EDIT
.
5
menu, 10
.
3
MATRX MATH menu, 10
.
12
MATRX NAMES
menu, 10
max(
(maximum), 2
.
7
.
15, 11
.
17, A
.
15
maximum of a function (
fMax(
), 2
.
6, A
.
9
maximum
operation on a graph, 3
.
27
mean(
, 11
.
17, A
.
15
median(
, 11
.
17, A
.
15
Med.Med
memory
(medianmedian), 12
.
25, A
.
15
backing up, 19
.
10
checking available, 18
.
2
clearing all list elements from, 18
.
4
clearing entries from, 18 deleting items from, 18
.
3
.
4
insufficient during transmission, 19
.
5
resetting defaults, 18
.
6
resetting memory, 18
.
5
MEMORY
menu, 18
.
2
Menu(
(define menu), 16
.
14, A
.
15
menus, 4, 1 .
19
defining (
Menu(
), 16 .
14, A
.
15
map, A .
39
scrolling, 1 .
19
min(
(minimum), 2 .
15, 11 .
17, A
.
minimum
operation on a graph, 3
16
.
27
minimum of a function (
fMin(
), 2 .
6, A
.
9
minutes notation (
'
) , 2
ModBoxplot
.
23, A
plot type (
Õ
.
38
), 12 .
32
. M (continued) .
modified box plot type (
Õ
), 12 .
32
mode settings, 1 .
9
a+b
i (complex rectangular), 1 .
12, 2
.
16,
A
.
3
r
e
^q
i (complex polar), 1 .
12, 2
.
16, A
.
22
Connected
(plotting), 1
.
11, A
.
4
825915~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 2:25 PM Printed: 10/27/05 3:22
PM Page 8 of 16
Degree
(angle), 1 .
11, 2 .
24, A
.
6
Dot
(plotting), 1 .
11, A
.
7
Eng
(notation), 1 .
10, A
.
8
Fix
(decimal), 1 .
10, A
.
8
Float
(decimal), 1 .
10, A
.
8
Full
(screen), 1 .
12, A
.
10
Func
(graphing), 1 .
11, A
.
10
G.T
(screen), 1 .
12, A
.
11
Horiz
(screen), 1 .
12, A
.
11
Normal
(notation), 1 .
10, A
.
16
Par
/
Param
(graphing), 1 .
11, A
.
18
Pol
/
Polar
(graphing), 1
Radian
(angle), 1
.
11, A
.
19
.
11, 2
.
24, A
.
21
Real
, 1
.
12, A
.
22
Sci
(notation), 1
.
10, A
.
25
Seq
(graphing), 1
.
11, A
.
26
Sequential
(graphing order), 1
.
12,
A
.
26
Simul
(graphing order), 1 modified box plot type (
Õ
), 12 multiple entries on a line, 1 multiplication (
ääää
), 2
.
3, A
multiplicative inverse, 2
.
.
3
.
6
37
.
12, A
.
27
.
32
. N .
(number of payment periods variable),
14
.
4, 14
.
14
nCr
(number of combinations), 2
nDeriv(
(numerical derivative), 2
.
21, A
.
16
.
7, A
.
16
negation (
M
), 1
.
23, 2
.
4, A
.
37
4Nom(
(to nominal interest rate), 14
.
12,
A
.
16
nonrecursive sequences, 6
.
5
normal distribution probability
(
normalcdf(
), 13
.
30, A
.
17
Normal
notation mode, 1 .
10, A
.
16
normal probability plot type (
Ô
), 12 .
33
. N (continued) .
normalcdf(
(normal distribution probability), 13 .
30, A
.
17
normalpdf(
(probability density function),
13
.
29, A
.
17
NormProbPlot
plot type (
Ô
), 12 .
33
not(
(Boolean operator), 2 .
26, A
.
17
not equal to (
ƒ
), 2 .
25, A
.
35
nPr
(permutations), 2 .
21, A
.
17
npv(
(net present value), 14 .
8, A
.
17
numerical derivative, 2 .
7, 3
.
28, 4
.
8, 5
.
6
numerical integral, 2 .
7, 3
.
28
. O .
oneproportion z confidence interval
(
1.PropZInt
), 13 .
20, A
.
20
oneproportion z test (
1.PropZTest
),
13
.
14, A
.
20
onesample t confidence interval
(
TInterval
), 13 .
17, A
.
30
onevariable statistics (
1.Var Stats
),
12
.
25, A .
31
or
(Boolean) operator, 2 .
26, A
.
17
order of evaluating equations, 1 .
22
Output(
, 9 .
6, 16 .
19, A
.
18
. P .
panning, 3 .
19
Par
/
Param
(parametric graphing mode),
1
.
9, 1
.
11, A
.
18
parametric equations, 4
.
5
parametric graphing
CALC
(calculate operations on a graph),
4
.
8
defining and editing, 4
.
4
freemoving cursor, 4
.
7
graph format, 4 graph styles, 4
.
6
.
4
moving the cursor to a value, 4
.
8
selecting and deselecting, 4 setting parametric mode, 4
.
.
4
5
tracing, 4
.
7
window variables, 4
.
5
Y=
editor, 4
.
4
zoom operations, 4 parentheses, 1
.
23
path (
ëëëë
) graph style, 3
.
8
.
9
. P (continued) .
Pause
, 16
.
12, A
.
18
pausing a graph, 3
.
15
Pen
, 8
.
13
permutations (
nPr
), 2 .
21, A
.
17
phase plots, 6 .
13
Pi (
p
), 2 .
4
Pic (pictures), 8 .
17, 8
.
18
pictures ( Pic ), 8 .
17, 8
.
18
pixel, 8 .
16
pixels in
Horiz
/
G.T
modes, 8 .
16, 9
.
6
Plot1(
, 12 .
34, A
.
18
Index9
825915~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 2:25 PM Printed: 10/27/05 3:22
PM Page 9 of 16
Index (continued)
Plot2(
, 12 .
34, A
.
18
Plot3(
, 12 .
34, A
.
18
PlotsOff
, 12 .
35, A
.
18
PlotsOn
, 12 .
35, A
.
18
plotting modes, 1 .
11
plotting stat data, 12 .
31
PMT
(payment amount variable), 14 .
4,
14
.
14
Pmt_Bgn
(payment beginning variable),
14
.
13, A .
19
Pmt_End
(payment end variable), 14 .
13,
A
.
19
poissoncdf(
, 13
poissonpdf(
, 13
.
34, A
.
19
.
33, A
.
19
Pol
/
Polar
(polar graphing mode), 1
.
9,
1
.
11, A
.
19
polar equations, 5
.
4
polar form, complex numbers, 2
.
17
4Polar
(to polar), 2
.
19, A
.
19
polar graphing
CALC
(calculate operations on a graph),
5
.
6
defining and displaying, 5
.
3
equations, 5
.
4
freemoving cursor, 5
.
6
graph format, 5
.
5
graph styles, 5
.
3
moving the cursor to a value, 5
.
6
selecting and deselecting, 5
.
4
mode (
Pol
/
Polar
), 1
.
9, 1
.
11, 5
.
3, A
.
19
tracing, 5
.
6
window variables, 5
.
4
Y= editor, 5 .
3
ZOOM operations, 5 .
6
PolarGC
(polar graphing coordinates),
3
.
13, A .
19
. P (continued) .
pooled option, 13 .
6, 13
.
8
power (
^
), 2 .
3, A .
36, A .
37
power of ten (
10
^(
), 2 .
4, A .
37
present value, 14 .
5, 14 .
7, 14
.
14
previous entry (Last Entry), 1 .
16
PRGM CTL (program control menu), 16 .
8
PRGM EDIT menu, 16 .
7
PRGM EXEC menu, 16 .
7
PRGM I/O (Input/Output menu), 16 .
16
prgm
(program name), 16 .
15, A .
19
PRGM NEW menu, 16
.
4
Index10
GPrn(
(sum of principal), 14 .
9, A .
19
probability, 2 .
20
probability density function (
normalpdf(
),
13
.
29, A
.
17
prod(
(product), 11 .
18, A .
19
programming copying and renaming, 16 .
7
creating new, 16 .
4
defined, 16 .
4
deleting, 16 .
4
deleting command lines, 16 .
6
editing, 16
.
6
entering command lines, 16
.
5
executing, 16
.
5
instructions, 16
.
9
N
16
.
21
inserting command lines, 16
.
6
name (
prgm
), 16
.
15, A
.
19
renaming, 16 stopping, 16
.
7
.
5
subroutines, 16
.
22
Prompt
, 16
.
18, A
.
19
1.PropZInt
(oneproportion z confidence interval), 13
1.PropZTest
13
.
14, A
.
20
.
20, A
.
20
(oneproportion z test),
2.PropZInt
(twoproportion z confidence interval), 13
2.PropZTest
13
.
15, A
.
20
.
21, A
.
20
(twoproportion z test),
P4Rx(
,
P4Ry(
(polartorectangular conversions), 2
Pt.Change(
, 8
.
24, A
.
21
.
15, A
.
20
Pt.Off(
, 8 .
15, A
.
20
Pt.On(
, 8 .
14, A
.
20
. P (continued) .
PV
(present value variable), 14 .
4, 14
.
14
pvalue, 13 .
28
PwrReg
(power regression), 12 .
27, A
.
20
Pxl.Change(
, 8 .
16, A
.
21
Pxl.Off(
, 8 .
16, A
.
21
Pxl.On(
, 8 .
16, A
.
21
pxl.Test(
P/Y
, 8 .
16, A
.
21
(numberofpaymentperiodsperyear variable), 14 .
4, 14
.
14
. Q .
QuadReg
(quadratic regression), 12 .
25,
A
.
21
825915~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 2:25 PM Printed: 10/27/05 3:22
PM Page 10 of 16
QuartReg
(quartic regression), 12 .
26
Quick Zoom, 3 .
19, A
.
21
. R .
r
(radian notation), 2 .
24, A
.
34
r r
(correlation coefficient), 12
2
,
R
2
.
23
(coefficients of determination),
12
.
23
Radian
angle mode, 1 radian notation (
r
), 2
.
11, 2 .
24, A
.
21
.
24, A
.
34
rand
(random number), 2 .
20, A
.
21
randBin(
(random binomial), 2 .
22, A
.
21
randInt(
(random integer), 2 .
22, A
.
22
randM(
(random matrix), 10 .
13, A
.
22
randNorm(
(random Normal), 2
.
22, A
.
22
random seed, 2
.
20, 2
.
22
RCL
(recall), 1
.
15, 11
.
9
r
e
^q
i (polar complex mode), 1
A
.
22
Real
mode, 1
.
12, A
real(
(real part), 2
.
22
.
18, A
.
22
.
12, 2
.
16,
RecallGDB
, 8
RecallPic
, 8
.
20, A
.
22
.
18, A
.
22
4Rect
(to rectangular), 2
.
19, A
.
22
rectangular form, complex numbers, 2
.
17
RectGC
(rectangular graphing coordinates), 3
.
13, A
.
22
recursive sequences, 6
.
6
ref(
(rowechelon form), 10
.
15, A
.
22
. R (continued) .
RegEQ
(regression equation variable),
12
.
22, 12
.
29
regression model automatic regression equation, 12
.
22
automatic residual list feature, 12
.
22
diagnostics display mode, 12
.
23
models, 12
.
25
relational operations, 2 .
25, 10 .
11
Repeat
, 16 .
11, A
.
23
RESET menu, 18 .
5
resetting defaults, 18 .
6
memory, 5, 18 .
5
residual list ( RESID ), 12 .
22
Return
, 16 root (
x
‡
), 2
.
15, A
.
23
.
6, A
.
35
root of a function, 3 .
26
round(
, 2 .
13, 10 .
10, A
.
23
row+(
, 10 .
16, A
.
23
…row(
, 10 .
…row+(
, 10
16, A
.
.
16, A
23
.
23
rowSwap(
, 10 .
16, A
.
23
R4Pr(
,
R4Pq(
(rectangulartopolar conversions), 2 .
24, A
.
23
rref(
(reducedrowechelon form), 10 .
15,
A
.
23
. S .
(twosample ÛTest),
13
.
23, A
.
24
2.SampTInt
(twosample t confidence interval), 13 .
19, A
.
24
2.SampTTest
(twosample t test), 13
.
13,
A
.
24, A
.
25
2.SampZInt
(twosample z confidence interval), 13
.
18, A
.
25
2.SampZTest
(twosample z test), 13
Scatter
A
.
25
plot type (
"
), 12
.
12,
.
31
Sci
(scientific notation mode), 1
.
10, A
.
25
scientific notation, 1
.
7,1
.
10
screen modes, 1
.
12
second cursor (
2nd
), 1
.
5
second key (
2nd
), 3
. S (continued) .
seconds DMS notation (
"
) , 2
.
23
Select(
, 11
.
12, A
.
25
selecting data points from a plot, 11
.
13
functions from the home screen or a program, 3
.
8
functions in the
Y=
editor, 3
.
7
items from menus, 4 stat plots from the
Y=
editor, 3
.
7
Send(
(send to CBL or CBR), 16
.
21, A
.
26
sending. See transmitting
Seq
(sequence graphing mode), 1 .
11,
A
.
26
seq(
(sequence), 11 .
12, A
.
26
sequence graphing axes format, 6 .
8
CALC (calculate menu), 6 defining and displaying, 6
.
10
.
3
evaluating, 6 .
10
freemoving cursor, 6 .
9
graph format, 6 .
8
Index11
825915~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 2:25 PM Printed: 10/27/05 3:22
PM Page 11 of 16
Index (continued)
graph styles, 6 .
4
moving the cursor to a value, 6 .
9
nonrecursive sequences, 6 .
5
phase plots, 6 .
13
recursive sequences, 6 .
6
setting sequence mode, 6 .
3
selecting and deselecting, 6 .
4
TI82 STATS versus TI.82 table, 6 .
15
tracing, 6 .
9
web plots, 6 .
11
window variables, 6 .
7
Y= editor, 6
.
4
ZOOM (zoom menu), 6
.
10
Sequential
(graphing order mode), 1
.
12,
service information, B
.
12
setting
A
.
26
display contrast, 1
.
3
graph styles, 3
.
9
graph styles from a program, 3
.
10
modes, 1
.
9
modes from a program, 1
.
9
splitscreen modes, 9
.
3
splitscreen modes from a program, 9
.
6
tables from a program, 7
.
3
. S (continued) .
SetUpEditor
, 12
.
21, A
.
26
shade above (
éééé
) graph style, 3 shade below (
ê
) graph style, 3
.
9
.
10
Shade(
Shade
Û
, 8
Shadec
2
(
.
9, A
, 13
, 13
.
26
.
36, A
.
26
.
36, A
.
27
ShadeNorm(
, 13
.
35, A
.
27
Shade_t(
, 13
.
36, A
.
27
shading graph areas, 3 .
10, 8
.
10
Simul
(simultaneous graphing order mode), 1 .
12, A
.
27
sin(
(sine), 2 .
3, A
sin
M1
(
(arcsine), 2 .
.
27
3, A
.
27
sine (
sin(
), 2 .
3, A
.
27
sine regression formula, A .
50
sinh(
(hyperbolic sine), 15 .
10, A
.
27
sinh M1 (
(hyperbolic arcsine), 15 .
10, A
.
27
SinReg
(sinusoidal regression), 12 .
27,
A
.
28
Smart Graph, 3 .
15
solve(
, 2 .
12, A
.
28
Solver
, 2
.
8
Index12
solving for variables in the equation solver,
2
.
10, 2 .
11
SortA(
(sort ascending), 11 .
10, 12 .
20,
A
.
28
SortD(
(sort descending), 11 .
10, 12 .
20,
A
.
28
splitscreen modes
G.T
(graphtable) mode, 9 .
5
Horiz
(horizontal) mode, 9 .
4
setting, 9 .
3, 9 .
6
splitscreen values, 8 square (
2
) , 2
.
3 , A
square root (
‡(
) , 2
.
.
12, 8
36
.
3 , A
.
37
STAT CALC menu, 12
.
24
STAT EDIT
menu, 12
.
20
stat list editor
.
16, 9
.
6
attaching formulas to list names, 12 clearing elements from lists, 12
.
12
creating list names, 12
.
12
detaching formulas from list names,
.
14
12
.
16
displaying, 12
.
10
editelements context, 12
.
18
. S (continued) .
stat list editor (continued) editing elements of formulagenerated lists, 12
.
16
editing list elements, 12
.
13
enternames context, 12 entering list names, 12
.
19
.
11
formulagenerated list names, 12
.
15
removing lists, 12
.
12
restoring list names
L
1
–
L
6
, 12
.
12,
12
.
21
switching contexts, 12 .
17
viewelements context, 12 .
18
viewnames context, 12 .
19
STAT PLOTS menu, 12 .
34
stat tests and confidence intervals
ANOVA(
(oneway analysis of variance), 13
c
²
.Test
.
25
(chisquare test), 13 .
22
LinRegTTest
(linear regression t test),
13
.
24
1.PropZInt
(oneproportion
z confidence interval), 13 .
20
1.PropZTest
(oneproportion z test),
13
.
14
825915~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 2:25 PM Printed: 10/27/05 3:22
PM Page 12 of 16
2.PropZInt
(twoproportion
z confidence interval), 13 .
21
2.PropZTest
(twoproportion z test),
13
.
15
(twosample Û.Test),
13
.
23
2.SampTInt
(twosample t confidence interval), 13 .
19
2.SampTTest
(twosample t test),
13
.
13
2.SampZInt
(twosample z confidence interval), 13
.
18
2.SampZTest
(twosample z test),
13
.
12
TInterval
(onesample t confidence interval), 13
.
17
T.Test
(onesample t test), 13
.
11
ZInterval
(onesample z confidence interval), 13
.
16
Z.Test
(onesample z test), 13
Stats input option, 13
.
6, 13
STAT TESTS
menu, 13
.
9
.
7
.
10
statistical distribution functions. See distribution functions
. S (continued) .
statistical plotting, 12
.
31
Boxplot
(regular box plot), 12
.
33
defining, 12
.
34
from a program, 12
Histogram
.
37
, 12
.
32
ModBoxplot
(modified box plot),
12
.
32
NormProbPlot
(normal probability plot), 12
.
33
Scatter
, 12 tracing, 12
.
31
.
36
turning on/off stat plots, 3
.
7, 12
.
35
viewing window, 12
.
36
xyLine
, 12
.
31
statistical variables table, 12
.
29
stdDev(
(standard deviation), 11 .
18, A
.
28
Stop
, 16 .
15, A
Store (
!
), 1 .
.
28
14, A
.
28
StoreGDB
, 8 .
19, A
.
28
StorePic
, 8 .
17, A
.
29
storing graph databases ( GDB s), 8 .
19
graph pictures, 8 .
17
variable values, 1 .
14
String4Equ(
(stringtoequation conversions), 15 .
8, A
.
29
strings, 15 .
3 – 15 .
9
concatenation (
+
), 15 .
6, A .
38
converting, 15
.
7, 15
.
8
defined, 15
.
3
displaying contents, 15
.
5
entering, 15
.
3
functions in
CATALOG
, 15
.
6
indicator (
"
), 15
.
3
length (
length(
), 15
.
8, A
.
13
storing, 15
.
5
variables, 15
.
4
studentt distribution probability (
tcdf(
), 13
.
31, A
.
29
probability density function (
tpdf(
),
13
.
30, A
.
30
sub(
(substring), 15 subroutines, 16
.
9, A
.
29
.
15, 16
.
22
subtraction (
N
), 2
.
3, A
.
38
sum(
(summation), 11 system variables, A
.
49
.
18, A
.
29
Index13
825915~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 2:25 PM Printed: 10/27/05 3:22
PM Page 13 of 16
Index (continued)
. T .
TABLE SETUP
screen, 7
.
3
tables, 7
.
1 – 7
.
6
description, 7
.
5
variables, 7
.
3 – 7
.
5
tan(
(tangent), 2
.
3, A
.
29
tan
M1
(
(arctangent), 2
.
3, A
.
29
tangent (
tan(
), 2
.
3, A
.
29
Tangent(
(draw line), 8 tangent lines, drawing, 8
.
8, A
.
29
.
8
tanh(
(hyperbolic tangent), 15
.
10, A
.
29
tanh
M1
(
(hyperbolic arctangent), 15
.
10,
A
.
29
@Tbl
(table step variable), 7
.
3
TblStart
(table start variable), 7
.
3
tcdf(
(studentt distribution probability),
13
.
31, A
.
29
technical support, B .
12
TEST (relational menu), 2 .
25
TEST LOGIC (Boolean menu), 2 .
26
Text(
instruction, 8 .
12, 9 .
6, A
.
29
placing on a graph, 8 .
12
Then
, 16 .
9, A
.
11
thick (
è
) graph style, 3 .
9
TI.82
link differences, 19 .
9
transmitting to/from, 19 .
4, 19 .
8, 19 .
9
TI82 STATS features, 17, 18 keyboard, 2, 3 key code diagram, 16
.
20
Link. See linking menu map, A
.
39
TI.GRAPH LINK
, 19
Time
axes format, 6
.
3
.
8, A
.
30
time value of money (
TVM
) calculating, 14
.
6
C/Y
variable (number of compounding periods per year), 14
.
14
formulas, A
.
54
FV
æ
variable (future value), 14
.
14
variable (annual interest rate), 14
.
14
. T (continued) .
time value of money (continued)
variable (number of payment
PMT
P/Y
periods), 14
.
14
variable (payment amount), 14
.
14
PV
variable (present value), 14
.
14
variable (number of payment periods per year), 14
.
14
tvm_FV
(future value), 14
tvm_I% tvm_
Ú
(interest rate), 14
.
.
7, A
.
31
7, A
(# payment periods), 14
.
31
.
7, A
.
31
tvm_Pmt
(payment amount), 14
.
6,
A
.
31
tvm_PV
(present value), 14
.
7, A
.
31
TVM Solver
, 14 variables, 14
.
14
.
4
TInterval
(onesample t confidence interval), 13 .
17, A
.
30
tpdf(
(studentt distribution probability
TRACE density function), 13 .
30, A
.
30
cursor, 3 .
18
entering numbers during, 3 .
19, 4
.
8,
5
.
6, 6
.
9
expression display, 3 .
14, 3
.
18
Trace
instruction in a program, 3 .
19,
A
.
30
transmitting error conditions, 19 .
6
from a TI.82 to a TI82 STATS, 19
.
9
items to another unit, 19 lists to a TI.82, 19 stopping, 19
.
6
.
6
.
4, 19
.
8
to an additional TI82 STATS, 19
T
(transpose matrix), 10 transpose matrix (
T
), 10
T.Test
.
7
.
12, A
.
34
.
12, A
.
34
trigonometric functions, 2
.
3
(onesample t test), 13
.
11, A
.
30
Index14
825915~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 2:25 PM Printed: 10/27/05 3:22
PM Page 14 of 16
. T (continued) .
turning on and off axes, 3
.
14
calculator, 1
.
2
coordinates, 3
.
14
expressions, 3
.
14
functions, 3
.
7
grid, 3
.
14
labels, 3
.
14
pixels, 8
.
16
points, 8
.
14
stat plots, 3
.
7, 12
.
35
tvm_FV
(future value), 14
tvm_I% tvm_
Ú
(interest rate), 14
.
.
7, A
.
31
7, A
(# payment periods), 14
.
.
tvm_Pmt
(payment amount), 14
31
7, A
.
.
6, A
31
.
31
tvm_PV
(present value), 14 .
7, A
.
31
twoproportion z confidence interval
(
2.PropZInt
), 13 .
21, A
.
20
twoproportion z test (
2.PropZTest
),
13
.
15, A
.
20
twosample ÛTest formula, A .
52
twosample t test formula, A .
53
twovariable statistics (
2.Var Stats
),
12
.
25, A .
31
. U .
u
sequence function, 6 .
3
user variables, A .
49
uv
/
uvAxes
(axes format), 6 .
8, A .
31
uw
/
uwAxes
(axes format), 6 .
8, A .
31
. V .
v
sequence function, 6 .
3
1.Var Stats
(onevariable statistics),
12
.
25, A
.
31
2.Var Stats
(twovariable statistics),
12
.
25, A
.
31
value
operation on a graph, 3
.
25
. V (continued) .
variables complex, 1
.
13
displaying and storing values, 1
.
14
equation solver, 2 graph databases, 1 graph pictures, 1
.
10
.
13
.
13
independent/dependent, 7
.
5
list, 1 real, 1
.
13, 11
.
3
matrix, 1
.
13
.
13, 10
.
3
recalling values, 1
.
15
solver editor, 2
.
9
statistical, 12 string, 15
.
29
.
4, 15
.
5
test and interval output, 13
.
28
types, 1 .
13
user and system, 1 .
13, A
.
49
VARS and Y.VARS
menus, 1 .
21
variance(
(variance of a list), 11 .
18, A .
31
variance of a list (
variance(
), 11 .
18, A .
31
VARS menu
GDB , 1 .
21
Picture , 1 .
21
Statistics , 1 .
21
String , 1 .
21
Table , 1 .
21
Window , 1 .
21
Zoom , 1 .
21
Vertical
(draw line), 8
.
6, A
.
31
viewing window, 3
.
11
vw
/
uvAxes
(axes format), 6
.
8
. W .
w
sequence function, 6
.
3
warranty information, B
.
14
Web
(axes format), 6
.
8, A
.
31
web plots, sequence graphing, 6
.
11
While
, 16
.
11, A
.
window variables
32
function graphing, 3
.
11
parametric graphing, 4
.
5
polar graphing, 5
.
4
sequence graphing, 6
.
7
Index15
825915~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 2:25 PM Printed: 10/27/05 3:22
PM Page 15 of 16
Index (continued)
. X .
XFact
zoom factor, 3 xintercept of a root, 3
xor
(Boolean) exclusive or operator, 2 x th
xyLine
A
root (
(
.
32
x
‡
), 2
Ó
.
6
.
24
.
26
) plot type, 12
.
31
@X
window variable,
3
.
12
.
26,
. Y .
YFact
zoom factor, 3
Y=
editor
.
24
function graphing, 3
.
5
parametric graphing, 4
.
4
polar graphing, 5
.
3
sequence graphing, 6
.
4
Y.VARS
menu
Function
, 1
.
21
Parametri c, 1
.
21
Polar , 1 .
21
On/Off , 1 .
21
@Y
window variable,
3
.
12
. Z .
ZBox
, 3 .
20, A .
32
ZDecimal
, 3 .
21, A .
32
zero
operation on a graph, 3 .
26
ZInteger
, 3 .
22, A .
32
ZInterval
(onesample z confidence interval), 13 .
16, A .
32
zoom, 3 .
20 – 3 .
24
cursor, 3 .
20
factors, 3 .
24
function graphing, 3 .
20
parametric graphing, 4 .
8
polar graphing, 5
.
6
sequence graphing, 6
.
10
ZoomFit
(zoom to fit function), 3
.
22,
A
.
33
Zoom In
(zoom in), 3
.
21, A
.
32
ZOOM
menu, 3
.
20
ZOOM MEMORY
menu, 3
Zoom Out
(zoom out), 3
.
23
.
21, A
.
32
ZoomRcl
(recall stored window), 3
.
23,
A
.
33
ZoomStat
(statistics zoom), 3
.
22, A
.
33
. Z (continued) .
ZoomSto
(store zoom window), 3
.
23,
A
.
33
ZPrevious
(use previous window), 3
.
23,
A
.
33
ZSquare
(set square pixels), 3
.
21, A
ZStandard
(use standard window), 3
.
33
.
22,
Z.Test
ZTrig
A
.
33
(onesample z test), 13
.
10, A
(trigonometric window), 3
.
34
.
22, A
.
34
Index16
825915~1.DOC TI83 international English Bob Fedorisko Revised: 10/26/05 2:25 PM Printed: 10/27/05 3:22
PM Page 16 of 16
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