Before Starting Calculations Operation Modes When using this calculator, it is necessary to select the proper mode to meet your requirements. This can be done by pressing [MODE] to scroll through sub-menus. Then select the appropriate mode by keying in the number. Press [MODE] once to read the first page of the main menu. COMP SD REG 1 2 3 AT-30i Press [MODE] again. Owner's Manual with advance statistical functions Disposing of the Calculator • Never dispose of the calculator by burning it. Doing so can cause certain components to suddenly burst, creating the danger of fire and personal injury. • The displays and illustrations (such as key markings) shown in this Owner's Manual are for illustrative purposes only, and may differ somewhat from the actual items they represent. • The contents of this manual are subject to change without notice. 0. If a character has been omitted from a formula, use the [3] and [4] key to move to the position where the character should have been input, and press [SHIFT] followed by [INS] key. Each press of [SHIFT] [INS] will create a space for input of one command. Press "MODE" once more to leave the menu. _ 0. Calculation Modes "COMP" mode : - general calculations, including function calculations can be executed. "SD" mode:- standard deviation calculation can be executed. "SD" symbol appears in display. "REG" mode:- regression calculations can be performed. "REG" symbol appears in display. Display Modes "FIX" mode:- specify number of decimal places. "Fix" symbol appears in display window. "SCI" mode:- specify number of significant digits. "Sci" symbol appears in display window. Batteries • After removing the batteries from the calculator, put them in a safe place where there is no danger of them getting into the hands of small children and accidently swallowed. • Keep batteries out of the reach of children. If accidentally swallowed, consult with a physician immediately. • Never charge batteries, try to take batteries apart, or allow batteries to become shorted. Never expose batteries to direct heat or dispose of them by incineration. • Misuse of batteries can cause them to leak acid that can cause damage to nearby items and creates the possibility of fire and personal injury. • Always make sure that a battery's positive (+) and negative (–) sides are facing correctly when you load it into the calculator. • Remove the batteries if you do not plan to use the calculator for a long time. • Use only the type of batteries specified for this calculator in this manual. • Do not mix old and new batteries. Do not mix alkaline, standard (carbon-zinc), or rechargeable (nickle cadmium) batteries. • Battery Contains Mercury. Do Not Put in Trash. Recycle or Manage as Hazardous Waste. 369x2 D Angular Measurement Modes "DEG" mode:- specify measurement in "degrees". "D" symbol appears in display window. "RAD" mode:- specify measurement in "radians". "R" symbol appears in display window. "GRA" mode:- specify measurement in "grads". "G" symbol appears in display window. Safety Precautions Be sure to read the following safety precautions before using this calculator. Keep this manual handy for later reference. Example: To correct an input of 369 2 to 369 2 :369[][]2 369xx2_ 0. [3][3][DEL] Press [MODE] further. Fix Sci Norm 1 2 3 Please read before using. If an unnecessary character has been included in a formula, use the [3] and [4] keys to move to the position of the error and press the "DEL" key. Each press of "DEL" will delete one command ( one step ). D Deg Rad Gra 1 2 3 2-lines display Scientific Calculator If after making corrections, input of the formula is complete, the answer can be obtained by pressing [ = ]. If, however, more is to be added to the formula, advance the cursor using the [4] key to the end of the formula for input. Example: To correct an input of 2.362 to sin 2.362 :2[•]36[x2] 2 . 3 6 2_ Note:• Mode indicators appear in the lower part of the display. • The "COMP", "SD", and "REG" modes can be used in combination with the angle unit modes. • Be sure to check the current calculation mode (COMP, SD, REG) and angle unit mode (DEG, RAD, GRA) before beginning a calculation. Calculation Priority Sequence Calculations are performed in the following order of precedence:1. Coordinate transformation: Pol(x, y),Rec(r, ) 2. Type A functions :These functions are those in which the value is entered and than the function key is pressed, such as x2, x–1, x!, º'''. 3. Powers and roots, xy, x√ 4. Fractions, ab/c 5. Abbreviated multiplication format in front of π, memory name or variable name, such as 2π, 5A, πA, etc. 6. Type B functions :These functions are those in which the function key is pressed and then the value is entered such as √, 3√, log, ln, ex, 10x, sin, cos, tan, sin–1, cos–1, tan–1, sinh, cosh, tanh, sinh–1, cosh–1, tanh–1, (–). 7. Abbreviated multiplication format in front of Type B functions, such as, 2√3, A log2, etc. 8. Permutation, combination, nPr, nCr 9. , 10. , • When functions with the same priority are used in series, execution is performed from right to left for :- exln√120 ➞ ex{ln(√120)}. Otherwise, execution is from left to right. • Operations enclosed in parentheses are performed first. Stacks This calculator uses memory areas, called "stacks", to temporarily store values (numeric stack) and commands (command stack) according to their precedence during calculations. The numeric stack has 10 levels and the command stack has 24 levels. A stack error (stk ERROR) occurs whenever you try to perform a calculation that is so complex that the capacity of a stack is exceeded. 0. D .362 0. D [sin] sin .362 The stored 10-digit [] Ans result (28.571421857) is (upper display) used when you continue the calculation by simply pressing [] or any other arithmetic function key. 14 [=] 400.000 (The final result is automatically rounded to the specified three decimal places.) Cancel specification by [MODE][MODE][MODE][3][1] 400. specifying "Norm" again. Rounding the Intermediate Result As the number of decimal places is specified, the intermediate result will be automatically rounded to the specified decimal places. However, the stored intermediate result is not rounded. In order to match the displayed value and the stored value, [SHIFT] [Rnd] can be input. Example 200714 = 400 rounded to 3 decimal places 200[]7 [] 14[=] [MODE][MODE][MODE][1][3] 200[]7 [=] The intermediate result is automatically rounded to the specified three decimal places. [SHIFT] [Rnd] round the stored intermediate result to the specified three decimal places Even after the [=] key has been pressed to calculate a result, it is possible to use this procedure for correction. Press the [3] key to move the cursor to the place where the correction is to be made. 14 [=] Cancel specification by [MODE][MODE][MODE][3][1] specifying "Norm" again. [] 28.571 Display (Lower) 23 + 4.5 –53 =–25.5 56(–12)(–2.5)=268.8 12369753274103= 6.9036806131012 (4.51075)(–2.3 10–79) = –1.03510–3 (2+3)102=500 23 [] 4.5 [] 53 [=] –25.5 56[][(–)]12[][(–)]2.5[=] 268.8 12369[] 7532 [] 74103[=] 6.90368061312 4.5[EXP]75 [] [(–)]2.3 [EXP] [(–)]79 [=] –1.035–03 [( ] 2 [] 3[ )][] 10[x2] [=] 500. (1105)7= 1[EXP]5 [] 7 [=] 14285.71429 14285.71429 (1105)714285= 1[EXP]5[]7 [] 0.7142857 14285 [=] 0.7142857 please note that internal calculation is calculated in 12 digits for a mantissa and the result is displayed and rounded off to 10 digits. 3 + 5 6 = 33 3 [] 5 [] 6 [=] 33. 7 8 4 5 = 36 7 [] 8 [] 4 [] 5 [=] 36. 1 2 3 4 5 6 1 [] 2 [] 3 [] 4 [] = 6.6 5 [] 6 [=] 6.6 100 (23) 4 = 80 100 [][( ] 2 [] 3[ )] [] 4 [=] 80. 2 3 ( 4 5 ) = 29 2 [] 3 [] [(] 4 [] 5 [=] 29. Closed parentheses occurring immediately before operation of the [=] key may be omitted. ( 7 2 ) ( 8 5 ) = 65 [( ] 7 [] 2 [ )][( ] 8 [] 5 [=] 65. A multiplication sign [] occurring immediately before an open parantheses can be omitted. 10 { 2 7 ( 3 6 )} 10 [][( ] 2 [] 7 [( ] 3 [] –55. = –55 6 [=] Handling Precautions • Be sure to press the "ON/AC" key before using the calculator for the first time. • Even if the calculator is operating normally, replace the battery at least once every three years. Dead battery can leak, causing damage to and malfunction of the calculator. Never leave the dead battery in the calculator. • The battery that comes with this unit discharges slightly during shipment and storage. Because ofthis, it may require replacement sooner than the normal expected battery life. • Low battery power can cause memory contents to become corrupted or lost completely. Always keep written records of all important data. • Avoid use and storage in areas subjected to temperature extremes. Very low temperatures can cause slow display response,total failure of the display, and shortening of battery life.Also avoid leaving the calculator in direct sunlight, neara window, near a heater or anywhere else it might become exposed to very high temperatures. Heat can cause discoloration or deformation of the calculator's case, anddamage to internal circuitry. • Avoid use and storage in areas subjected to large amounts of humidity and dust. Take care never to leave the calculator where it might besplashed by water or exposed to large amounts of humidity or dust. Such elements can damage internal circuitry. • Never drop the calculator or otherwise subject it to strong impact. • Never twist or bend the calculator. Avoid carrying the calculator in the pocket of your trousers or other tight-fitting clothing where it might be subjected to twisting or bending. • Never try to take the calculator apart. • Never press the keys of the calculator with a ball-point pen or other pointed object. • Use a soft, dry cloth to clean the exterior of the unit. If the calculator becomes very dirty, wipe it off with acloth moistened in a weak solution of water and a mildneutral household detergent. Wring out all excess moisture before wiping the calculator. Never use thinner, benzine or other volatile agents to clean the calculator. Doing so can remove printed markings and damage the case. Error Loacator Pressing [3] or [4] after an error occurs display the calculation with the cursor positioned at the location where the error occured. Percentage Calculations Use the "COMP" mode for percentage calculations. Overflow and Errors The calculator is locked up while an error message is on the display. Press [ON/AC] to clear the error, or press [3] or [4] to display the calculation and correct the problem. Percentage 26% of $15.00 Ratio 75 is what % of 250? "Ma ERROR" caused by:• Calculation result is outside the allowable calculation range. • Attempt to perform a function calculation using a value that exceeds the allowable input range. • Attempt to perform an illegal operation (division by zero, etc.). Action • Check your input values and make sure they are all within the allowable ranges. Pay special attention to values in any memory areas you are using. Specifying the Format of Calculation Results You can change the precision of calculation results by specifying the number of decimal places or the number of significant digits. You can also shift the decimal place of a displayed value three places to the left or right for one-touch conversions of metric weights and measures. Example Display (Lower) Operation Difference between [STO][M] and [M+], [SHIFT][M–] :Both [STO] [M] and [M+], [SHIFT] [M–] can be used to input results into memory, however when the [STO] [M] operation is used, previous memory contents are cleared. When either [M+] or [SHIFT] [M–] is used, value is added or subtracted to or from present sum in memory. Example: Input 456 into memory "M" using [STO] [M] procedure. Memory already contains value of 123. [ON/AC] [1] [2] [3] [STO] [M] M= 123. M D [ON/AC] [4] [5] [6] [STO] [M] [ON/AC] _ 15 []26 [SHIFT] [%] 3.9 75[]250 [SHIFT] [%] 30. Upon power up reset, the display format is defaulted at "Norm1". Each time when you press "[MODE] [MODE] [MODE] [3]" you can choose either "Norm 1" or "Norm 2" by keying in [1] or [2] respectively. Norm 1 :- all values less than 10–2 or greater than 109 are automatically expressed as exponents. Norm 2 :- all values less than 10–9 or greater than 109 are automatically expressed as exponents. Note: You cannot specify the display format (Fix, Sci) while the calculator is in Base-N mode. Specifying the Number of Decimal Places The calculator always performs calculations using a 10-digit mantissa and 2-digit exponent, and results are stored in memory as a 12-digit mantissa and 2-digit exponent no matter how many decimal places you specify. Intermediate results and final results are then automatically rounded off to the number of decimal places you have specified. It should be noted that displayed results are rounded to the specified number of decimal places, but stored results are normally not rounded. To specify the number of decimal places ( Fix ), press "[MODE] [MODE] [MODE] [1]" and then a value indicating the number of decimal places (0~9). To specify the number of significant digits (Sci.), select [SCI] in the sub-menu "FIX/SCI/NORM" and then you are asked to enter a value indicating the number of significant digits (0~9) as below. Sci 0~9? Display (Lower) Operation 1006 = 16.66666666 100[]6 [=] specify 5 significant [Mode][Mode][Mode][2][5] digits Cancel specification by [Mode][Mode][Mode][3][1] specifying "Norm" again. 123m456 = 56088m = 56.088km 78g0.96 = 74.88g = 0.07488kg M D D 0. 456. D D [ON/AC] [4] [5] [6] [M+] 456 M _ [RCL] [M] M= M M 456. D D 0. 579. D Special Functions Answer Function This unit has an answer function that stores the result of the most recent calculation. Once a numeric value or numeric expression is entered and [=] is pressed, the result is stored by this function. To recall the stored value, press the [Ans] [=] key. When [Ans] is pressed, "Ans" will appear on the display, and the value can be used in subsequent calculations. Example: 123456 = 579 789579 = 210 [ON/AC][1][2][3][][4][5][6][=] 123+456 [7][8][9][][Ans] 789–Ans_ 123[]456 [=] [ENG] 78[]0.96 [=] [SHIFT] [ENG] D 579. D [=] 16.66666667 Numeric values with 12 digits for a mantissa and 2 digits for an exponent can be stored in the "Ans" memory. The "Ans" memory is not erased even if the power of the unit is turned OFF. Each time [=] , [Shift] [%] , [M+] , [Shift] [M–] , and [STO] ( = A ~ F, M, X, Y ) is pressed, the value in the Ans memory is replaced with the new value produced by the calculation execution. When execution of a calculation results in an error, however, the "Ans" memory retains its current value. Note:- Contents of "Ans" memory are not altered when RCL ( = A~F, M, X, Y) is used to recall contents of variable memory. Also, contents of "Ans" memory are not altered when variables are input when the variable input prompt is displayed. 789–Ans 210. D Display (Lower) Operation 579. 16.66666667 1.666701 Shifting the Decimal Place You can use the key [ENG] to shift the decimal point of the displayed value three places to the left or right. Each 3-place shift to the left is the same as dividing the value by 1000, and each shift to the right is the same as multiplying by 1000. This means that this function is useful when converting metric weights and measures to other metric units. Example M 456. Example: Input 456 into memory "M" using M+. Memory already contains value of 123. [ON/AC] [1] [2] [3] [STO] [M] M= 123. M Note : "0" indicating 10 significant digits. Meanwhile, the "Sci" indicator will appear on the display. 56088. 56.08803 74.88 0.0748803 Omitting the multiplication sign () When inputting a formula as it is written, from left to right, it is possible to omit the multiplication sign () in the following cases :- – 13 – – 17 – Memory This calculator contains 9 standard memories. There are two basic types of memories, i.e., "variable" memories, which are accessed by using the [STO] and [RCL] keys in combination with the alphabets A, B, C, D, E, F, M, X and Y. The "independent" memory, which is accessed by using the [M+] , [Shift] [M–] and [RCL] and [M] keys. The independent memory uses the same memory area as variable M. Contents of both the variable and independent memories are protected even when the power is turned OFF. • Before the following functions :sin, cos, tan, sin–1, cos–1, tan–1, sinh, cosh, tanh, sinh–1, cosh–1, tanh–1, log, ln, 10x, ex, √, 3√, Pol(x,y), Rec(r, ) example: 2sin30, 10log1.2, 2√3, 2Pol(5, 12), etc. Variable memories Up to 9 values can be retained in memory at the same time, and can be recalled when desired. Example: Input 123 into memory "A" :[ON/AC] 123 123_ D [STO] [A] A= 0. [ON/AC] D A= 0. When formulas are input, the result of the formula's calculation is retained in memory. Example: Input the result of 123456 into memory "B" :[ON/AC] 123 [] 456 123X456_ 0. D B= Continuous Calculation Function Even if calculations are concluded with the [=] key, the result obtained can be used for further calculations. In this case, calculations are performed with 10 digits for the mantissa which is displayed. Example: To calculate 3.14 continuing after 34=12 [ON/AC] [3] [] [4] [=] 3x4 12. (continuing) [] [3] [•] [1] [4] A n s ÷3 . 1 4 _ [=] 12. A n s ÷3 . 1 4 3.821656051 D 123. D [STO] [B] • Before parentheses :example: 3(56), (A1)(B1), etc. D _ [RCL] [A] • Before fixed numbers, variales and memories :example: 2π, 2AB, 3Ans, etc. D 123. D Example: To calculate 133 = [AC] [1] [] [3] [] [3] [=] 1 ÷3 x 3 D [1] [] [3] [=] 1. 1 ÷3 0.333333333 D (continuing) [] [3] [=] Ansx3 D 56088. 1. D [ON/AC] _ D [RCL] [B] Fix 0~9? M= M – 16 – As with the number of decimal places, displayed results are rounded to the specified number of digits, but stored results are normally not rounded. Example M= Ans (upper display) 399.994 399.994 Specifying the Number of Significant Digits This specification is used to automatically round intermediate results and final results to the number of digits you have specified. Operation Addition/subtraction to or from sum in memory cannot be carried out with [M+], [SHIFT] [M–] keys in "SD" mode and "REG" mode. [ON/AC] Arithmetic Operations & Parenthesis Calculations • Arithmetic operations are performed by pressing the keys in the same order as noted in the formula. • For negative values, press [(-)] before entering the value • For mixed basic arithmetic operations, multiplication and division are given priority over addition and subtraction • Assuming that display mode "Norm 1" is selected. –9– Number of Input/output Digits and Calculation Digits The memory area used for calculation input can hold 79 "steps". One function comprises one step. Each press of numeric or , , and keys comprise one step. Though such operations as [SHIFT] [x!] (x–1 key) require two key operations, they actually comprise only one function, and, therefore, only one step. These steps can be confirmed using the cursor. With each press of the [3] or [4] key, the cursor is moved one step. 28.571 – 12 – –5– "Syn ERROR" caused by:• Attempt to perform an illegal mathematical operation. Action • Press to display the calculation with the cursor located at the location of the error. Make necessary corrections. 400. 400.000 –8– –1– "Stk ERROR" caused by:• Capacity of the numeric stack or operator stack is exceeded. Action • Simplify the calculation. The numeric stack has 10 levels and the operator stack has 24 levels. • Divide your calculation into two or more separate parts. Display (Lower) Operation When [SHIFT] [INS] are pressed, the space that is opened is displayed as " ". The function or value assigned to the next key you press will be inserted in the . To exit from the insertion mode, move the cursors, or press [SHIFT] [INS] , or press [=]. Example To clear memory contents, press [0] [STO] [M]. You can compare the final result obtained in the previous example with the final result of the following example. 0. D –4– "NORM" mode:- cancels "Fix" and "Sci" specifications. 0. 2.362 [SHIFT][INS] Display (Lower) Operation [RCL] [M] D [3][3][3][3][3] Example B= 0. 56088. D At this time, you should be able to see "Fix" on the display. The number of decimal places specified will remain in –6– – 10 – – 14 – – 18 – Whenever you input the 73rd step of any calculation, the cursor changes from "_" to "■" to let you know memory is running low. If you still need to input more, you should divide you calculation into two or more parts. effect until "Norm" (to select "Norm" press "[MODE] [MODE] [MODE] [3]") is specified or significant digits are specified using "[MODE] [MODE] [MODE] [2]". If a variable expression is entered, the expression is first calculated according to the values stored in the variable memories used in the expression. The result is then stored in the variable memory specified for the result. Example: Input the results of AB into memory "C" :[ON/AC] [ALPHA] [A] [] AXB_ 0. [ALPHA] [B] This function can be used with Type A functions ( x2, x–1, x!), , , xy, x√ and º' ". Example: Squaring the result of 786=13 [ON/AC] [7] [8] [] [6] [=] 7 8 ÷6 13. –2– Two-lines Display [ON/AC] [MODE] S A hyp M STO RCL SD REG D R G Fix Sci You can simultaneously check the calculation formula and its answer. The first line displays the calculation formula. The second line displays the answer. Keys Layout SHIFT REPLAY ALPHA OFF MODE When numeric values or calculation commands are input, they appear on the display from the left. Calculation results, however, are displayed from the right. The allowable input/output range (number of digits) of this unit is 10 digits for a mantissa and 2 digits for the exponent. Calculations, however, are performed internally with a range of 12 digits for a mantissa and 2 digits for an exponent. Example: 3 105 7 = 3[EXP]5[÷]7[=] x! x nPr Rec( nCr Pol( d/c A (–) º ,,, B C sin–1 hyp RCL B 7 y x ( ln D cos–1 E tan–1 F X ; 8 5 xn cos ) C yn 4 e log , INS 9 DEL tan Y xn–1 x 1 2 3 Rnd Ran# π 0 • EXP –3– + [1] _ M M– M+ DT CL D [3] 122 Mcl Scl ON/AC D [3] 123_ ÷ y – DRG % Ans = Example: To change an input of cos60 to sin60 :[cos] [6] [0] cos 60 [3] [3] [3] 0. D 0. D 0. sin 60 –7– 0. D cos 60 [sin] 0. [ON/AC] Fix Deg Rad Gra 1 2 3 Fix Sci Norm 1 2 3 [3] Operation 1006 = 16.66666666 100 [] 6 [=] specify 4 decimal places [MODE][MODE][MODE][1][4] cancel specification [MODE][MODE][MODE] [3] [1] 200714 = 400 200[]7 [] 14[=] rounded to 3 decimal [MODE][MODE][MODE][1][3] places 200 [] 7[ =] The intermediate result is automatically rounded to the specified three decimal places. – 11 – Deleting memories To delete all contents of variable memories, press [Shift] followed by [Mcl] [=]. Independent Memory Addition and subtraction (to and from sum) results can be stored directly in memory. Results can also be totalized in memory, making it easy to calculate sums. The icon "M" will be lighted as long as M is not empty. Example: Input 123 to independent memory. [ON/AC] [1] [2] [3] 123_ 0. [M+] [1] Example 6898824. D Norm 1~2? Display (Lower) 16.66666667 16.6667 16.66666667 400. 400.000 28.571 123 [=] Ans2 13. 169. Replay Function This function stores formulas that have been executed. After execution is complete, pressing either the [3] or [4] key will display the formula executed. Pressing [4] will display the formula from the beginning, with the cursor located under the first character. Pressing [3] will display the formula from the end, with the cursor located at the space following the last character. After this, using the [4] and [3] to move the cursor, the formula can be checked and numeric values or commands can be changed for subsequent execution. Example: [ON/AC] [1] [2] [3] [] [4] [5] [6] [=] 123x456 56088. D [4] 123x456 56088. [=] 123x456 56088. [3] 123x456_ 56088. D 123. D Recall memory data [ON/AC] A n s 2_ D 0. D 0.0000 COMP SD REG 1 2 3 [MODE] 6898824. D C= D (continuing) [x2] D _ [RCL] [C] D [MODE] C= D Fix 0~9? Reset to "Norm" [ON/AC] [MODE] Corrections To make corrections in a formula that is being input, use the [3] and [4] keys to move to the position of the error and press the correct keys. Example: To change an input of 122 to 123 :[1] [2] [2] 122_ 0. [STO] [C] Fix Sci Norm 1 2 3 3 E 5 ÷7–42857 0.1428571 D 6 [MODE] [4] (to specify 4 decimal places) yn–1 + A x sin r STO 10 x x2 a b/c ENG xy D Deg Rad Gra 1 2 3 3 E 5 ÷7 42857.14286 D x3 3 [MODE] D 3[EXP]5[÷]7[]42857[=] x –1 COMP SD REG 1 2 3 D _ D [RCL] [M] M= Add 25, subtract 12 25 [M+] 12 [SHIFT] [M–] 12 0. D 123. D Recall memory data [ON/AC] D 12. D 0. _ [RCL] [M] M= 136. D – 15 – – 19 – Example: 4.123.586.4 = 21.1496 4.123.587.1 = 7.6496 [ON/AC] [4] [•] [1] [2] [] [3] [•] [5] [8] [] [6] [•] [4] [=] [3] Example 4 .12x3.58+6. 21.1496 D 1 2x3.58+6.4 _ 21.1496 D [3] [3] [3] [3] 4 .12x3.58+6. 21.1496 D [] [7] [•] [1] 1 2x3.58–7.1 _ 21.1496 D [=] 4 .12x3.58–7. 7.6496 D The replay function is not cleared even when [ON/AC] is pressed or when power is turned OFF, so contents can be recalled even after [ON/AC] is pressed. Replay function is cleared when mode or operation is switched. Error Position Display Function When an ERROR message appears during operation execution, the error can be cleared by pressing the [ON/AC] key, and the values or formula can be re-entered from the beginning. However, by pressing the [3] or [4] key, the ERROR message is cancelled and the cursor moves to the point where the error was generated. Operation Using any four numbers from 1 to 7, how many four digit even numbers can be formed if none of the four digits consist of the same number? (3/7 of the total number of permutations will be even.) 7P437 = 360 If any four items are removed from a total of 10 items, how many different combinations of four items are possible? 10C4 = 210 If 5 class officers are being selected for a class of 15 boys and 10 girls, how many combinations are possible? At least one girl must be included in each group. 25C515C5 = 50127 [3] (or [4] ) 1 4 ÷0x2.3 D Correct the input by pressing [3] [SHIFT] [INS] [1] 1 4 ÷10x2.3 D [=] 0. 0. 10[nCr]4[=] 25[nCr]5[]15[nCr]5[=] 360. 210. 50127. Example 5 30 [DT] 50 [DT] 120 [SHIFT] [;] 31 [DT] To delete 120 [SHIFT] [;] 31 [DT], press [SHIFT] [CL]. Example 6 50 [DT] 120 [SHIFT] [;] 31 [DT] 40 [DT] 30 [DT] To delete 120 [SHIFT] [;] 31 [DT], press 120 [SHIFT] [;] 31 [SHIFT] [CL]. Example 7 [√] 10 [DT] [√] 20 [DT] [√] 30 [DT] To delete [√] 20 [DT], press [√] 20 [=] [Ans] [SHIFT] [CL]. Example 8 [√] 10 [DT] [√] 20 [DT] [√] 30 [DT] To delete [√] 20 [DT], press [√] 20 [SHIFT] [;] [(–)] 1 [DT]. Performing calculations The following procedures are used to perform the various standard deviation calculations. Key operation Result Population standard deviation, xσn Sample standard deviation, xσn–1 Mean, x Sum of square of data, ∑x2 Sum of data, ∑x Number of data, n [SHIFT][xσn] [SHIFT][xσn–1] [SHIFT][x] [RCL][A] [RCL][B] [RCL][C] Standard deviation and mean calculations are performed as shown below: Population standard deviation σn = √(∑(xix)2/n) where i = 1 to n Sample standard deviation σn–1 = √(∑(xix)2/(n-1)) where i = 1 to n Mean x = (∑x)/n Example Other Functions (√ , x2, x–1, x!, 3√, Ran#) Example Example: 1402.3 is input by mistake [ON/AC] [1] [4] [] [0] [] Ma ERROR [2] [.] [3] [=] 7[SHIFT][nPr]4[]3[] 7[=] Display (Lower) Operation √2√5 = 3.65028154 22324252 = 54 (3)2 = 9 1/(1/3–1/4) = 12 8! = 40320 3√(364249) = 42 Random number generation (number is in the range of 0.000 to 0.999) [√]2[][√]5[=] 2[x2][]3[x2][]4[x2] []5[x2][=] [(][(–)]3[)][x2][=] [(]3[x–1][]4[x–1][)][x–1][=] 8[SHIFT][x!][=] [3√][(]36[]42[]49[)][=] [SHIFT][Ran#][=] Operation Display (Lower) 3.65028154 54. 9. 12. 40320. 42. 0.792 (random) [MODE][2] (SD Mode) [SHIFT][Scl][=] (Memory cleared) 55[DT]54[DT]51[DT] 55[DT]53[DT][DT]54[DT] 52[DT] What is deviation of the [RCL][C](Number of data) unbiased variance, and [RCL][B](Sumof data) the mean of the above [RCL][A](Sum of square of data) data? [SHIFT][x][=](Mean) [SHIFT][xσn][=](Population SD) [SHIFT][xσn–1][=](Sample SD) [SHIFT][xσn–1] [x2][=](Sample variance) Display Data 55, 54, 51, 55, 53, 53, 54, 52 0. 0. 52. 8. 427. 22805. 53.375 1.316956719 1.407885953 Example Operation Temperature and length [MODE][3][1] of a steel bar ("REG" then select linear regression) Temp Length [SHIFT][Scl][=] (Memory cleared) 10ºC 1003mm 10[,]1003[DT] 15ºC 1005mm 15[,]1005[DT] 20ºC 1010mm 20[,]1010[DT] 25ºC 1011mm 25[,]1011[DT] 30ºC 1014mm 30[,]1014[DT] Using this table, the [SHIFT][A][=](Constant term A) regression formula and [SHIFT][B][=] correlation coefficient (Regression coefficient B) can be obtained. Based [SHIFT][r][=] (Correlation coefficient r) on the coefficient formula, the length of 18[SHIFT][y](Length at 18ºC) the steel bar at 18ºC 1000[SHIFT][x](Temp at 1000mm) and the temperature [SHIFT][r][x2][=] (Critical coefficient) at 1000mm can be estimated. Furthermore [(][RCL][F][–][RCL][C][] the critical coefficient [SHIFT][x][][SHIFT][y][)][] (r2) and covariance can [(][RCL][C][–]1[)][=](Covariance) also be calculated. Display 0. 0. 10. 15. 20. 25. 30. 997.4 0.56 0.982607368 1007.48 4.642857143 0.965517241 Deleting input data To delete input data, follow the procedures described for linear regression Performing calculations If 1/x is stored instead of x itself, the inverse regression formula y = A + ( B/x ) becomes the linear regression formula y = a + bx. Therefore, the formulas for constant term A, regression coefficient B and correlation coefficient r are identical the power and linear regression. A number of inverse regression calculation results differ from those produced by linear regression. Note the following: Linear regression Inverse regression ∑x ∑x2 ∑xy ∑(1/x) ∑(1/x)2 ∑(y/x) Example 35. Logarithmic regression Logarithmic regression calculations are carried out using the following formula: y = A + B•lnx Data input Press [MODE] [3] [2] to specify logarithmic regression under "REG" mode. Press [SHIFT] [Scl] [=] to clear the statistical memories. Input data in the following format: <x data>, <y data> [DT] • To make multiple entries of the same data, follow procedures described for linear regression. Deleting input data To delete input data, follow the procedures described for linear regression. Operation xi yi [MODE][3][4][2] 2 2 ("REG" then select Inv regression) 3 3 [SHIFT][Scl][=] (Memory cleared) 4 4 2[,]2[DT] 5 5 3[,]3[DT] 6 6 4[,]4[DT] Through inverse regression of the above 5[,]5[DT] data, the regression 6[,]6[DT] formula and correlation [SHIFT][A][=](Constant term A) coefficient are obtained. [SHIFT][B][=] Furthermore, the (Regression coefficient B) regression formula is [SHIFT][r][=] used to obtain the (Correlation coefficient r) respective estimated values of y and x, when 10[SHIFT][y](y when xi=10) xi = 10 and yi = 9. 9[SHIFT][x](x when yi=9) Display 0. 0. 2. 3. 4. 5. 6. 7.272727272 –11.28526646 –0.950169098 6.144200627 –6.533575316 1.982142857 1 4 ÷10x2.3 3.22 D – 20 – – 24 – Scientific Function Trigonometric functions and inverse trigonometric functions • Be sure to set the unit of angular measurement before performing trigonometric function and inverse trigonometric function calculations. • The unit of angular measurement (degrees, radians, grads) is selected in sub-menu. • Once a unit of angular measurement is set, it remains in effect until a new unit is set. Settings are not cleared when power is switched OFF. Example sin 63º52'41" = 0.897859012 cos (π/3 rad) = 0.5 tan (–35 grad) = –0.612800788 Operation [MODE][MODE][1]("DEG" selected) [sin] 63 [º ' "] 52 [º ' "] 41 [º ' "][=] [MODE][MODE][2]("RAD" selected) [cos][(] [SHIFT][π][]3 [)] [=] [MODE][MODE][3] Display (Lower) 0.897859012 0.5 ("GRA" selected) [tan] [(–)] 35 [=] –0.612800788 [MODE][MODE][1]("DEG") 2[sin] 45 [cos] 65 [=] 0.597672477 [SHIFT][sin–1] 0.5 [=] 30. [MODE][MODE][2]("RAD") [SHIFT][cos–1][(][√]2 []2 [)][=] 0.785398163 [][SHIFT][π][=] 0.25 tan–1 0.741 [MODE][MODE][1]("DEG") = 36.53844577º [SHIFT][tan–1]0.741[=] 36.53844576 = 36º32' 18.4" [SHIFT] [←º' "] 36º32º18.4º If the total number of digits for degrees/minutes/seconds exceed 11 digits, the higher order values are given display priority, and any lower-order values are not displayed. However, the entire value is stored within the unit as a decimal value. 2.5(sin–10.8cos–10.9) 2.5[] [(] [SHIFT] [sin–1]0.8 = 68º13'13.53" [] [SHIFT] [cos–1] 0.9 [)] [=] [SHIFT] [←º' "] 68º13º13.53º 2sin45ºcos65º = 0.597672477 sin–1 0.5 = 30 cos–1 (√2/2) = 0.785398163 rad = π/4 rad Example Operation √(1–sin240) = 0.766044443 1/2!1/4!1/6!1/8! = 0.543080357 [MODE][MODE][1]("DEG" selected) [√][(]1[][(][sin]40[)][x2] [)][=] [SHIFT][cos–1][Ans][=] 2[SHIFT][x!][x–1][] 4[SHIFT][x!][x–1][] 6[SHIFT][x!][x–1][] 8[SHIFT][x!][x–1][=] Example sinh3.6= 18.28545536 cosh1.23 = 1.856761057 tanh2.5= 0.986614298 cosh1.5sinh1.5 = 0.22313016 sinh–1 30 = 4.094622224 cosh–1 (20/15) = 0.795365461 x = (tanh–1 0.88) / 4 = 0.343941914 sinh–1 2cosh–11.5 = 1.389388923 sinh–1 (2/3)tanh–1(4/5) = 1.723757406 Operation [hyp][sin] 3.6 [=] [hyp][cos] 1.23 [=] [hyp][tan] 2.5 [=] [hyp][cos] 1.5 [][hyp] [sin] 1.5 [=] [hyp][SHIFT][sin–1] 30 [=] [hyp][SHIFT][cos–1][(] 20 [] 15 [)][=] [hyp][SHIFT][tan–1]0.88 []4[=] [hyp][SHIFT][sin–1]2[] [hyp][SHIFT][cos–1]1.5[=] [hyp][SHIFT][sin–1][(]2[] 3[)][][hyp][SHIFT][tan–1] [(]4[]5[)][=] Display (Lower) 18.28545536 1.856761057 0.986614298 0.22313016 4.094622224 0.795365461 0.343941914 1.389388923 log1.23 = 8.990511110–2 In90 = 4.49980967 log456In456 = 0.434294481 101.23 = 16.98243652 e4.5 = 90.0171313 104 • e–41.2 • 102.3 = 422.5878667 (–3)4 = 81 –34 = –81 5.62.3 = 52.58143837 7√123 = 1.988647795 (7823)–12 = 1.30511182910–21 233√644 = 10 23.4(5+6.7) = 3306232 Operation Display (Lower) [log] 1.23 [=] [In] 90 [=] [log]456[In]456 [=] 0.543080357 Example Operation 2/531/4 = 313/20 Display (Lower) 2[ab/c]5[]3[ab/c]1 [ab/c]4[=] 3⎦13⎦20. [ab/c](conversion to decimal) 3.65 Fractions can be converted to decimals, and then converted back to fractions. 456 11 3 /78 = 8 /13 3[ab/c]456[ab/c]78[=] 8⎦11⎦13. [SHIFT][d/c] 115⎦13. 1/25781/4572 b b 1[a /c]2578[]1[a /c] = 0.00060662 4572[=] 6.066202547–04 When the total number of characters, including integer, numerator, denominator and delimiter mark exceeds 10, the input fraction is automatically displayed in decimal format. 1/20.5 = 0.25 1[ab/c]2[].5[=] 0.25 1/3(–4/5)–5/6 = –11/10 1[ab/c]3[][(–)]4[ab/c]5 b []5[a /c]6[=] –1⎦1⎦10. 1/21/31/41/5 1[ab/c]2[]1[ab/c]3[] 13 b b = /60 1[a /c]4[]1[a /c]5[=] 13⎦60. (1/2)/3 = 1/6 [(]1[ab/c]2[)][ab/c]3[=] 1⎦6. 1/(1/31/4) = 15/7 b b 1[a /c][(]1[a /c]3[] b 1[a /c]4[)][=] 1⎦5⎦7. 0.089905111 4.49980967 0.434294481 – 36 – Regression Calculation In the REG mode, calculations including linear regression, logarithmic regression, exponential regression, power regression, inverse regression and quadratic regression can be performed. Performing calculations The logarithmic regression formula y = A + B•lnx. As x is input, In(x) will be stored instead of x itself. Hence, we can treat the logarithmic regression formula same as the linear regression formula. Therefore, the formulas for constant term A, regression coefficient B and correlation coefficient r are identical for logarithmic and linear regression. Quadratic Regression Quadratic regression calculations are carried out using the following formula: y = A + Bx + Cx2 Data input Press [MODE] [3] [4] [3] to specify quadratic regression under the "REG" mode. Press [SHIFT] [Scl] [=] to clear the statistical memories. Input data in this format: <x data>,<y data> [DT] • To make multiple entries of the same data, follow procedures described for linear regression. Deleting input data To delete input data, follow the procedures described for linear regression. Press [MODE] [3] to enter the "REG" mode: COMP SD REG 1 2 3 and then select one of the following regression types:Lin Log Exp 1 2 3 Lin: linear regression Log: logarithmic regression Exp: exponential regression press [4] for the other three regression types:Pwr Inv Quad 1 2 3 Pwr: power regression Inv: inverse regression Quad: quadratic regression Linear regression Linear regression calculations are carried out using the following formula: y = A + Bx. Data input Press [MODE] [3] [1] to specify linear regression under the "REG" mode. Press [Shift] [Scl] [=] to clear the statistical memories. Input data in the following format: <x data> [,] <y data> [DT] • When multiples of the same data are input, two different entry methods are possible: Example 1 Data: 10/20, 20/30, 20/30, 40/50 Key operation: 10 [,] 20 [DT] 20 [,] 30 [DT] [DT] 40 [,] 50 [DT] The previously entered data is entered again each time the [DT] key is pressed (in this case 20/30 is re-entered). Example Operation Display xi yi [MODE][3][2] 0. 29 1.6 ("REG" then select LOG regression) 50 23.5 [SHIFT][Scl][=] (Memory cleared) 0. 74 38 29[,]1.6[DT] 29. 103 46.4 50[,]23.5[DT] 50. 118 48.9 74[,]38[DT] 74. The logarithmic 103. regression of the above 103[,]46.4[DT] data, the regression 118[,]48.9[DT] 118. formula and correlation [SHIFT][A][=](Constant term A) –111.1283975 coefficient are obtained. [SHIFT][B][=](Regression coefficient B) 34.02014748 Furthermore, respective [SHIFT][r][=](Correlation coefficient r) 0.994013946 estimated values y and 80[SHIFT][y](y when xi=80) 37.94879482 x can be obtained for 224.1541314 xi = 80 and yi = 73 using 73[SHIFT][x](x when yi=73) the regression formula. A number of logarithmic regression calculation results differ from those produced by linear regression. Note the following: Linear regression Logarithmic regression ∑x ∑x2 ∑xy ∑Inx ∑(Inx)2 ∑y•Inx Example Exponential regression Exponential regression calculations are carried out using the following formula: y = A•eB•x (ln y = ln A +Bx) Data input Press [MODE] [3] [3] to specify exponential regression under the "REG" mode. Press [SHIFT] [Scl] [=] to clear the statistical memories. Input data in the following format: <x data>,<y data> [DT] • To make multiple entries of the same data, follow procedures described for linear regression. Deleting input data To delete input data, follow the procedures described for linear regression. Example 2 Data: 10/20, 20/30, 20/30, 20/30, 20/30, 20/30, 40/50 Key operation: 10 [,] 20 [DT] 20 [,] 30 [SHIFT] [;] 5 [DT] 40 [,] 50 [DT] By pressing [SHIFT] and then entering a semicolon followed by a value that represents the number of times the data is repeated (5, in this case) and the [DT] key, the multiple data entries (for 20/30, in this case) are made automatically. Performing calculations If we assume that lny = y and lnA = a', the exponential regression formula y = A•eB•x (ln y = ln A +Bx) becomes the linear regression formula y =a' + bx if we store In(y) instead of y itself. Therefore, the formulas for constant term A, regression coefficient B and correlation coefficient r are identical for exponential and linear regression. Replacing the Battery Dim figures on the display of the calculator indicate that battery power is low. Continued use of the calculator when the battery is low can result in improper operation. Replace the battery as soon as possible when display figures become dim. D 1 R 2 Example Define degree first Change 20 radian to degree To perform the following calculation :10 radians+25.5 gradients The answer is expressed in degree. G 3 Operation [MODE][MODE][1]("DEG" selected) 20[SHIFT][DRG>][2][=] 10[SHIFT][DRG>][2] []25.5[SHIFT][DRG>][3] [=] Display 20r 1145.91559 10r25.5g 595.9077951 Degrees, Minutes, Seconds Calculations You can perform sexagesimal calculations using degrees (hours), minutes and seconds. And convert between sexagesimal and decimal values. Example Operation To express 2.258 degrees 2.258[º' "][=] in deg/min/sec. To perform the calculation: 12[º' "]34[º' "]56[º' "][] 12º34'56"3.45 3.45[=] Display 2º15º28.8 43º24º31.2 Deleting input data There are various ways to delete value data, depending on how and where it was entered. Example 1 10 [,] 40 [DT] 20 [,] 20 [DT] 30 [,] 30 [DT] 40 [,] 50 To delete 40 [,] 50, press [ON/AC] Example 2 10 [,] 40 [DT] 20 [,] 20 [DT] 30 [,] 30 [DT] 40 [,] 50 [DT] To delete 40 [,] 50 [DT], press [SHIFT][CL] Example 3 To delete 20 [,] 20 [DT], press 20 [,] 20 [SHIFT][CL] Example 4 [√] 10 [,] 40 [DT] [√] 40 [,] 50 [DT] To delete[√]10[,]40[DT], press [√]10[=][Ans][,]40[SHIFT][CL] A number of exponential regression calculation results differ from those produced by linear regression. Note the following: Linear regression Exponential regression ∑y ∑y2 ∑xy ∑Iny ∑(Iny)2 ∑x•Iny Example Operation xi yi [MODE][3][3] 6.9 21.4 ("REG" then select Exp regression) 12.9 15.7 [SHIFT][Scl][=] (Memory cleared) 19.8 12.1 6.9[,]21.4[DT] 26.7 8.5 12.9[,]15.7[DT] 35.1 5.2 19.8[,]12.1[DT] Through exponential regression of the above 26.7[,]8.5[DT] data, the regression 35.1[,]5.2[DT] formula and correlation [SHIFT][A][=](Constant term A) coefficient are obtained. [SHIFT][B][=] Furthermore, the (Regression coefficient B) regression formula is [SHIFT][r][=] used to obtain the (Correlation coefficient r) respective estimated values of y and x, when 16[SHIFT][y](y when xi=16) xi = 16 and yi = 20. 20[SHIFT][x](x when yi=20) Display 0. 0. 6.9 12.9 19.8 26.7 35.1 30.49758742 –0.049203708 Statistical Calculations This unit can be used to make statistical calculations including standard deviation in the "SD" mode, and regression calculation in the "REG" mode. Key Operations to recall regression calculation results Performing calculations If we assume that lny = y, lnA =a' and ln x = x, the power regression formula y = A•xB (lny = lnA + Blnx) becomes the linear regression formula y = a' + bx if we store In(x) and In(y) instead of x and y themselves. Therefore, the formulas for constant term A, regression coefficient B and correlation coefficient r are identical the power and linear regression. A number of power regression calculation results differ from those produced by linear regression. Note the following: x=7.5 and y=–10, what are r and rad? r=25 and = 56º, what are x and y? r=4.5 and =2π/3 rad, what are x and y? 12.5(r) –0.927295218() 13.97982259(x) 20.72593931(y) –2.25(x) 3.897114317(y) Example Operation Taking any four out of 10[SHIFT][nPr]4[=] ten items and arranging them in a row, how many different arrangements are possible? 10P4 = 5040 – 23 – Standard Deviation In the "SD" mode, calculations including 2 types of standard deviation formulas, mean, number of data, sum of data, and sum of square can be performed. Data input 1. Press [MODE] [2] to specify SD mode. 2. Press [SHIFT] [Scl] [=] to clear the statistical memories. 3. Input data, pressing [DT] key (= [M+]) each time a new piece of data is entered. Example Data: 10, 20, 30 Key operation: 10 [DT] 20 [DT] 30 [DT] • When multiples of the same data are input, two different entry methods are possible. Example 1 Data: 10, 20, 20, 30 Key operation: 10 [DT] 20 [DT] [DT] 30 [DT] The previously entered data is entered again each time the DT is pressed without entering data (in this case 20 is re-entered). Example 2 Data: 10, 20, 20, 20, 20, 20, 20, 30 Key operation: 10 [DT] 20 [SHIFT] [;] 6 [DT] 30 [DT] By pressing [SHIFT] and then entering a semicolon followed by value that represents the number of items the data is repeated (6, in this case) and the [DT] key, the multiple data entries (for 20, in this case) are made automatically. Permutation and Combination Total number of permutations nPr = n!/(nr)! Total number of combinations nCr = n!/(r!(nr)!) Display (Lower) 5040. Specifications Power supply: AG13 x 2 batteries Operating temperature: 0º ~ 40ºC (32ºF ~ 104ºF) Power regression Power regression calculations are carried out using the following formula: y = A•xB (lny = lnA + Blnx) Data input Press [MODE] [3] [4] [1] to specify "power regression". Press [SHIFT] [Scl] [=] to clear the statistical memories. Input data in the following format: <x data>,<y data> [DT] • To make multiple entries of the same data, follow procedures described for linear regression. Deleting input data To delete input data, follow the procedures described for linear regression Coordinate Transformation • This scientific calculator lets you convert between rectangular coordinates and polar coordinates, i.e., P(x, y) ↔ P(r, ) • Calculation results are stored in variable memory E and variable memory F. Contents of variable memory E are displayed initially. To display contents of memory F, press [RCL] [F]. • With polar coordinates, can be calculated within a range of –180º< ≤180º. (Calculated range is the same with radians or grads.) 24.98979792(r) 55.92839019() 55º55º42.2() Auto Power Off Calculator power automatically turns off if you do not perform any operation for about six minutes. When this happens, press [ON/AC] to turn power back on. 13.87915739 8.574868045 – 34 – [MODE][MODE][1]("DEG" selected) [Pol(]14 [,]20.7[)][=] [RCL][F] [SHIFT][←º' "] [MODE][MODE][2]("RAD" selected) [Pol(]7.5[,][(–)]10[)][=] [RCL][F] [MODE][MODE][1]("DEG" selected) [SHIFT][Rec(]25 [,]56[)][=] [RCL][F] [MODE][MODE][2]("RAD" selected) [SHIFT][Rec(]4.5[,][(]2[] 3[][SHIFT][π][)][)][=] [RCL][F] To replace the battery:• Remove the screws that hold the back cover in place and then remove the back cover, • Remove the old battery, • Wipe off the side of the new battery with a dry, soft cloth. Load it into the unit with the positive(+) side facing up. • Replace the battery cover and secure it in place with the screws. • Press [ON/AC] to turn power on. –0.997247351 – 30 – x=14 and y=20.7, what are r and º? Display Degree, Radian, Gradient Interconversion Degree, radian and gradient can be converted to each other with the use of [SHIFT][DRG>]. Once [SHIFT] [DRG>] have been keyed in, the "DRG" selection menu will be shown as follows. – 26 – Operation Operation xi yi [MODE][3][4][3] 29 1.6 ("REG" then select Quad regression) 50 23.5 [SHIFT][Scl][=] 0. 74 38 29[,]1.6[DT] 29. 103 46.4 50[,]23.5[DT] 50. 118 48 74[,]38[DT] 74. Through power 103. regression of the above 103[,]46.4[DT] data, the regression 118[,]48[DT] 118. formula and correlation [SHIFT][A][=](Constant term A) –35.59856935 coefficient are obtained. [SHIFT][B][=] 1.495939414 Furthermore, the (Regression coefficient B) regression formula is [SHIFT][C][=] –6.716296671–03 used to obtain the (Regression coefficient C) respective estimated –13.38291067 values of y and x, when 16[SHIFT][y](y when xi=16) xi = 16 and yi = 20. 20[SHIFT][x](x1 when yi=20) 47.14556728 [SHIFT][x](x2 when yi=20) 175.5872105 – 37 – – 22 – Example To read the value of ∑x3, ∑x4 or ∑x2y, you can recall memory [RCL] M, Y and X respectively. – 33 – 10. 3306232.001 Display (Lower) Performing calculations The following procedures are used to perform the various linear regression calculations. The regression formula is y = A + Bx + Cx2 where A, B, C are regression coefficients. C = [(n∑x2(∑x)2) (n∑x2y∑x2∑y )(n∑x3∑x2∑x) (n∑xy ∑x∑y)][(n∑x2(∑x)2) (n∑x4(∑x2)2)(n∑x3∑x2∑x)2] B = [n∑xy∑x∑yC (n∑x3∑x2∑x)](n∑x2(∑x)2) A = (∑yB∑xC∑x2) / n – 29 – [SHIFT][10x] 1.23 [=] 16.98243652 [SHIFT][ex]4.5[=] 90.0171313 [SHIFT][10x]4[][SHIFT][ex] [(–)]4[]1.2[][SHIFT][10x] 2.3[=] 422.5878667 [(][(–)] 3 [)] [xy] 4 [=] 81. [(–)] 3 [xy] 4 [=] –81. 5.6 [xy] 2.3 [=] 52.58143837 7 [SHIFT][x√] 123 [=] 1.988647795 [(]78[]23[)][xy][(–)]12[=] 1.305111829–21 2[]3[]3[SHIFT][x√]64 []4[=] 2[]3.4[xy][(]5[]6.7[)][=] – 32 – – 25 – 1.723757406 Logarithmic and Exponential Functions Example 0.766044443 40. Fractions Fractions are input and displayed in the order of integer, numerator and denominator. Values are automatically displayed in decimal format whenever the total number of digits of a fractional value (interger + numerator + denominator + separator marks) exceeds 10. – 21 – Performing Hyperbolic and Inverse Hyperbolic Functions Display (Lower) – 28 – Deleting input data There are various ways to delete value data, depending on how and where it was entered. Key operation Result [SHIFT][A][=] [SHIFT][B][=] [SHIFT][C][=] [SHIFT][r][=] [SHIFT][x][=] [SHIFT][y][=] [SHIFT][yσn] [SHIFT][yσn–1] [SHIFT][y] [SHIFT][xσn] [SHIFT][xσn–1] [SHIFT][x] [RCL][A] [RCL][B] [RCL][C] [RCL][D] [RCL][E] [RCL][F] Constant term of regression A Regression coefficient B Regression coefficient C Correlation coefficient r Estimated value of x Estimated value of y Population standard deviation, yσn Sample standard deviation, yσn–1 Mean, y Population standard deviation, xσn Sample standard deviation, xσn–1 Mean, x Sum of square of data, ∑x2 Sum of data, ∑x Number of data, n Sum of square of data, ∑y2 Sum of data, ∑y Sum of data, ∑xy Performing calculations The following procedures are used to perform the various linear regression calculations. The regression formula is y = A + Bx. The constant term of regression A, regression coefficient B, correlation r, estimated value of x, and estimated value of y are calculated as shown below: A = ( ∑y∑x )/n B = ( n∑xy∑x∑y ) / ( n∑x2(∑x )2) r = ( n∑xy∑x∑y ) / √ (( n∑x2(∑x )2)( n∑y2(∑y )2)) y = A + Bx x = ( yA) / B Example 1 40 [DT] 20 [DT] 30 [DT] 50 [DT] To delete 50, press [SHIFT] [CL]. Example 2 40 [DT] 20 [DT] 30 [DT] 50 [DT] To delete 20, press 20 [SHIFT] [CL]. Example 3 30 [DT] 50 [DT] 120 [SHIFT] [;] To delete 120 [SHIFT] [;] , press [ON/AC]. Example 4 30 [DT] 50 [DT] 120 [SHIFT] [;] 31 To delete 120 [SHIFT] [;] 31, press [AC]. – 27 – Linear regression Power regression ∑x ∑x2 ∑y ∑y2 ∑xy ∑Inx ∑(Inx)2 ∑Iny ∑(Iny)2 ∑Inx•Iny Example Operation xi yi [MODE][3][4][1] 28 2410 ("REG" then select Pwr regression) 30 3033 [SHIFT][Scl][=] (Memory cleared) 33 3895 28[,]2410[DT] 35 4491 30[,]3033[DT] 38 5717 33[,]3895[DT] Through power regression of the above 35[,]4491[DT] data, the regression 38[,]5717[DT] formula and correlation [SHIFT][A][=](Constant term A) coefficient are obtained. [SHIFT][B][=] Furthermore, the (Regression coefficient B) regression formula is [SHIFT][r][=] used to obtain the (Correlation coefficient r) respective estimated values of y and x, when 40[SHIFT][y](y when xi=40) xi = 40 and yi = 1000. 1000[SHIFT][x](x when yi=1000) – 38 – Display 0. 0. 28. 30. 33. 35. 38. 0.238801069 2.771866156 0.998906255 6587.674587 20.26225681 Inverse regression Power regression calculations are carried out using the following formula: y = A + ( B/x ) Data input Press [MODE] [3] [4] [2] to specify "inverse regression". Press [SHIFT] [Scl] [=] to clear the statistical memories. Input data in the following format: <x data>,<y data> [DT] • To make multiple entries of the same data, follow procedures described for linear regression. – 31 – – 35 –

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