Ativa DS-700 Product Manual - Page 2
Performing Hyperbolic and Inverse Hyperbolic Functions - 36 scientific calculator
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Example: 4.123.586.4 = 21.1496 4.123.587.1 = 7.6496 [ON/AC] [4] [•] [1] [2] [] [3] [•] [5] [8] [] [6] [•] [4] [=] 4.12x3.58+6. 21.1496 D [3] 12x3.58+6.4_ 21.1496 D [3] [3] [3] [3] 4.12x3.58+6. 21.1496 D [] [7] [•] [1] 12x3.58-7.1_ 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. Example: 1402.3 is input by mistake [ON/AC] [1] [4] [] [0] [] [2] [.] [3] [=] Ma ERROR [3] (or [4] ) Correct the input by pressing [3] [SHIFT] [INS] [1] [=] - 20 - 14÷0x2.3 0. D 14÷10x2.3 0. D 14÷10x2.3 3.22 D Example Operation Using any four numbers 7[SHIFT][nPr]4[]3[] from 1 to 7, how many 7[=] 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 10[nCr]4[=] removed from a total of 10 items, how many different combinations of four items are possible? 10C4 = 210 If 5 class officers are 25[nCr]5[]15[nCr]5[=] 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 Display (Lower) 360. 210. 50127. Other Functions (√ , x2, x-1, x!, 3√, Ran#) Example Operation √2√5 = 3.65028154 [√]2[][√]5[=] 22324252 = 54 2[x2][]3[x2][]4[x2] []5[x2][=] (3)2 = 9 [(][(-)]3[)][x2][=] 1/(1/3-1/4) = 12 [(]3[x-1][]4[x-1][)][x-1][=] 8! = 40320 8[SHIFT][x!][=] 3√(364249) = 42 [3√][(]36[]42[]49[)][=] Random number [SHIFT][Ran#][=] generation (number is in the range of 0.000 to 0.999) Display (Lower) 3.65028154 54. 9. 12. 40320. 42. 0.792 (random) - 24 - 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 [SHIFT][xσn] [SHIFT][xσn-1] [SHIFT][x] [RCL][A] [RCL][B] [RCL][C] 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 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 Operation Data 55, 54, 51, 55, 53, [MODE][2] (SD Mode) 53, 54, 52 [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 0. 0. 52. 8. 427. 22805. 53.375 1.316956719 1.407885953 1.982142857 - 28 - Example Operation Temperature and length [MODE][3][1] of a steel bar ("REG" then select linear regression) Temp 10ºC 15ºC 20ºC 25ºC 30ºC Length 1003mm 1005mm 1010mm 1011mm 1014mm [SHIFT][Scl][=] (Memory cleared) 10[,]1003[DT ] 15[,]1005[DT ] 20[,]1010[DT ] 25[,]1011[DT ] 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][=] on the coefficient (Correlation coefficient r) formula, the length of 18[SHIFT][y](Length at 18ºC) the steel bar at 18ºC and the temperature at 1000mm can be 1000[SHIFT][x](Temp at 1000mm) [SHIFT][r][x2][=] (Critical coefficient) 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 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: , [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. - 32 - 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 ∑x ∑x2 ∑xy Inverse regression ∑(1/x) ∑(1/x)2 ∑(y/x) Example 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 6 5 6 3[,]3[DT ] Through inverse 4[,]4[DT ] 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 used to obtain the respective estimated [SHIFT][r][=] (Correlation coefficient r) 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 - 36 - 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. Display Example Operation (Lower) sin 63º52'41" [MODE][MODE][1]("DEG" selected) = 0.897859012 [sin] 63 [º ' "] 52 [º ' "] 41 [º ' "][=] 0.897859012 cos (π/3 rad) = 0.5 [MODE][MODE][2]("RAD" selected) [cos][(] [SHIFT][π][]3 [)] [=] 0.5 tan (-35 grad) [MODE][MODE][3] = -0.612800788 ("GRA" selected) [tan] [(-)] 35 [=] -0.612800788 2sin45ºcos65º [MODE][MODE][1]("DEG") = 0.597672477 2[sin] 45 [cos] 65 [=] 0.597672477 sin-1 0.5 = 30 [SHIFT][sin-1] 0.5 [=] 30. cos-1 (√2/2) [MODE][MODE][2]("RAD") = 0.785398163 rad [SHIFT][cos-1][(][√]2 []2 = π/4 rad [)][=] 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 - 21 - Example √(1-sin240) = 0.766044443 1/2!1/4!1/6!1/8! = 0.543080357 Operation [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][=] Display (Lower) 0.766044443 40. 0.543080357 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. Display Example Operation (Lower) 2/531/4 = 313/20 2[ab/c]5[]3[ab/c]1 [ab/c]4[=] [ab/c](conversion to decimal) 3⎦13⎦20. 3.65 Fractions can be converted to decimals, and then 3456/78 = 811/13 1/25781/4572 = 0.00060662 converted back to fractions. 3[ab/c]456[ab/c]78[=] 8⎦11⎦13. [SHIFT][d/c] 115⎦13. 1[ab/c]2578[]1[ab/c] 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[=] 1/3(-4/5)-5/6 = -11/10 1[ab/c]3[][(-)]4[ab/c]5 []5[ab/c]6[=] 1/21/31/41/5 1[ab/c]2[]1[ab/c]3[] = 13/60 1[ab/c]4[]1[ab/c]5[=] (1/2)/3 = 1/6 [(]1[ab/c]2[)][ab/c]3[=] 1/(1/31/4) = 15/7 1[ab/c][(]1[ab/c]3[] 1[ab/c]4[)][=] 0.25 -1⎦1⎦10. 13⎦60. 1⎦6. 1⎦5⎦7. - 25 - Regression Calculation In the REG mode, calculations including linear regression, logarithmic regression, exponential regression, power regression, inverse regression and quadratic regression can be performed. 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: [,] [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). - 29 - 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. Example Operation Display xi yi [MODE][3][2] 29 1.6 ("REG" then select LOG regression) 50 23.5 [SHIFT][Scl][=] (Memory cleared) 74 38 29[,]1.6[DT ] 103 46.4 118 48.9 50[,]23.5[DT ] The logarithmic 74[,]38[DT ] regression of the above 103[,]46.4[DT] data, the regression 118[,]48.9[DT] formula and correlation [SHIFT][A][=](Constant term A) coefficient are obtained. [SHIFT][B][=](Regression coefficient B) Furthermore, respective estimated values y and [SHIFT][r][=](Correlation coefficient r) x can be obtained for 80[SHIFT][y](y when xi=80) xi = 80 and yi = 73 using 73[SHIFT][x](x when yi=73) the regression formula. 0. 0. 29. 50. 74. 103. 118. -111.1283975 34.02014748 0.994013946 37.94879482 224.1541314 A number of logarithmic regression calculation results differ from those produced by linear regression. Note the following: Linear regression ∑x ∑x2 ∑xy Logarithmic regression ∑Inx ∑(Inx)2 ∑y•Inx 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: , [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. - 33 - 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: , [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. 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 To read the value of ∑x3, ∑x4 or ∑x2y, you can recall memory [RCL] M, Y and X respectively. Example Operation Display xi yi [MODE][3][4][3] 29 1.6 ("REG" then select Quad regression) 50 23.5 [SHIFT][Scl][=] 0. 74 38 103 46.4 118 48 29[,]1.6[DT ] 50[,]23.5[DT ] 29. 50. Through power 74[,]38[DT ] 74. regression of the above 103[,]46.4[DT] 103. data, the regression 118[,]48[DT] 118. formula and correlation [SHIFT][A][=](Constant term A) coefficient are obtained. [SHIFT][B][=] Furthermore, the (Regression coefficient B) -35.59856935 1.495939414 regression formula is used to obtain the respective estimated values of y and x, when [SHIFT][C][=] (Regression coefficient C) 16[SHIFT][y](y when xi=16) -6.716296671-03 -13.38291067 xi = 16 and yi = 20. 20[SHIFT][x](x1 when yi=20) 47.14556728 [SHIFT][x](x2 when yi=20) 175.5872105 - 37 - Performing Hyperbolic and Inverse Hyperbolic Functions Example Operation sinh3.6= 18.28545536 [hyp][sin] 3.6 [=] cosh1.23 = 1.856761057 [hyp][cos] 1.23 [=] tanh2.5= 0.986614298 [hyp][tan] 2.5 [=] cosh1.5sinh1.5 [hyp][cos] 1.5 [][hyp] = 0.22313016 [sin] 1.5 [=] sinh-1 30 = 4.094622224 [hyp][SHIFT][sin-1] 30 [=] cosh-1 (20/15) [hyp][SHIFT][cos-1][(] 20 = 0.795365461 x = (tanh-1 0.88) / 4 [] 15 [)][=] [hyp][SHIFT][tan-1]0.88 = 0.343941914 []4[=] sinh-1 2cosh-11.5 [hyp][SHIFT][sin-1]2[] = 1.389388923 [hyp][SHIFT][cos-1]1.5[=] sinh-1 (2/3)tanh-1(4/5) [hyp][SHIFT][sin-1][(]2[] = 1.723757406 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 1.723757406 Logarithmic and Exponential Functions Example 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 [log] 1.23 [=] [In] 90 [=] [log]456[In]456 [=] Display (Lower) 0.089905111 4.49980967 0.434294481 [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[)][=] 10. 3306232.001 - 22 - 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. D R G 1 2 3 Example Operation Define degree first [MODE][MODE][1]("DEG" selected) Change 20 radian to 20[SHIFT][DRG>][2][=] degree To perform the following 10[SHIFT][DRG>][2] calculation :- []25.5[SHIFT][DRG>][3] 10 radians+25.5 gradients [=] The answer is expressed in degree. 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 - 26 - 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. 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] - 30 - 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. A number of exponential regression calculation results differ from those produced by linear regression. Note the following: Linear regression ∑y ∑y2 ∑xy Exponential regression ∑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 35.1 5.2 12.9[,]15.7[DT ] Through exponential 19.8[,]12.1[DT] 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 used to obtain the respective estimated [SHIFT][r][=] (Correlation coefficient r) 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 -0.997247351 13.87915739 8.574868045 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: , [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 - 34 - 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. 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. 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. Specifications Power supply: AG13 x 2 batteries Operating temperature: 0º ~ 40ºC (32ºF ~ 104ºF) - 38 - 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.) Example x=14 and y=20.7, what are r and º? 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? Operation Display (Lower) [MODE][MODE][1]("DEG" selected) [Pol(]14 [,]20.7[)][=] 24.98979792(r) [RCL][F] [SHIFT][←º' "] 55.92839019() 55º55º42.2() [MODE][MODE][2]("RAD" selected) [Pol(]7.5[,][(-)]10[)][=] 12.5(r) [RCL][F] -0.927295218() [MODE][MODE][1]("DEG" selected) [SHIFT][Rec(]25 [,]56[)][=] 13.97982259(x) [RCL][F] 20.72593931(y) [MODE][MODE][2]("RAD" selected) [SHIFT][Rec(]4.5[,][(]2[] 3[][SHIFT -2.25(x) [RCL][F] 3.897114317(y) Permutation and Combination Total number of permutations nPr = n!/(nr)! Total number of combinations nCr = n!/(r!(nr)!) 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 Display (Lower) 5040. - 23 - 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. 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. Deleting input data There are various ways to delete value data, depending on how and where it was entered. 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 - Key Operations to recall regression calculation results Key operation [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] Result 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 - 31 - 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: Linear regression ∑x ∑x2 ∑y ∑y2 ∑xy Power regression ∑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 38 5717 30[,]3033[DT ] Through power 33[,]3895[DT ] 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 used to obtain the respective estimated [SHIFT][r][=] (Correlation coefficient r) 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) 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: , [DT] • To make multiple entries of the same data, follow procedures described for linear regression. - 35 -