Casio Fx82tl Manual
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26 Mastering the Calculator using the Casio fx-82TL Example Use your calculator to find the mean, standard deviation and variance for data set B: –18, 1, 3, 9, 20. (the variance is the square of the standard deviation) __________________________________________________________________________ After you are in the statistics mode and cleared the statistics memories, the keystrokes required are: and the display will read 5 and the display will read 3 and the display will read 13.87443693 and the display will read 192.5 The mean is 3, the standard deviation is 13.87 and the variance is 192.5. The button accesses a number of extra statistical functions. (M, Y and X you will rarely use in basic statistics.) = Σx2 = Σy2 = Σx3 = Σx = Σy = Σx2y = n = Σxy = Σx4 In the example below, the progressive calculations are shown simply to give you some understanding of the underlying processes – you should do one or two examples in detail and then check them by calculator.
Mastering the Calculator using the Casio fx-82TL 27 10.2 Mean and standard deviation of frequency distribution Given below is the frequency table for the weights (kg) of a random sample of 30 first year university female students. Find the standard deviation, the variance and the mean. The calculations needed to obtain the standard deviation without statistical keys for these data are: Σx2 = 602 × 2 + 612 × 14 + 622 × 8 + 632 + 642 × 5 = 114 495 Σx = 60 × 2 + 61 × 14 + 62 × 8 + 63 + 64 × 5 = 1 853 s= = Thus:s= 1.2 kg and s2 = 1.4 kg2 = Note: In calculations like the above you should carry as many decimals as possible until the final result. The number of decimals to be retained at the end depends on the accuracy of the data values – one rule of thumb is to have one more decimal than in the original data. Notice how the frequencies were used in the above calculation. The calculator usage now has a small modification because we have been given the frequencies for the variable values. (There is no need to input each single observation.) Graduate’s weight (kg)FrequencyCumulative frequency 6022 611416 62824 63125 64530 Σxi 2Σxi()2n⁄ – n1 – --------------------------------------- 114 495 1 853()230 ⁄ – 29 --------------------------------------------------------114 495 114 453.6333– 29 ---------------------------------------------------------- 1 . 4 2 64== xΣx n------1853 30 ------------ 61.8 kg==
28 Mastering the Calculator using the Casio fx-82TL The keystrokes required are: and the display should read 30 and the display should read 61.766667 and the display should read 1.1943353 and the display should read 1.4264369 Thus, as expected s = 1.2 kg, s2 = 1.4 kg2 and = 61.8 kg Exercise 6 Find the mean, standard deviation and variance of (a) The annual rainfall data for the years 1971 – 1990 Ye a r1971197219731974197519761977197819791980 Rain (mm)1 3409901 1201 736 2601 1001 3791 1251 4301 446 Ye a r1981198219831984198519861987198819891990 Rain (mm)1 4591 6781 3459781 0021 1101 5461 6721 4671 123 x
Mastering the Calculator using the Casio fx-82TL 29 (b) The sample of snail foot lengths Answers: (a) Rainfall statistics mean: µ = 1 265.3 mm standard deviation: = 336.4 mm variance: σ2 = 113141.7 mm2 (b) Snail statistics mean: = 3.4 cm standard deviation: s = 0.70 cm variance: s2 = 0.49 cm2 Snail foot length (cm) 2.24.13.54.53.23.73.02.6 3.41.63.13.33.83.14.73.7 2.54.33.43.62.93.33.93.1 3.33.13.74.43.24.11.93.4 4.73.83.22.63.93.04.23.5 σn-1 x
30 Mastering the Calculator using the Casio fx-82TL 11. Linear regression Example Suppose we had a sample of 10 of the same type of banana. Their lengths and skin thicknesses were measured. Below is a summary of the results. STEPS 1. To put the calculator into regression mode press 2. Think of the sample of bananas as having two variables –let x be the variable length of banana –let y be the variable thickness of banana For each banana you have to put in both numbers. Banana12345678910 Length (mm)16.215.816.514.916.916.815.615.615.715.4 Thickness (mm)1.11.21.11.00.91.21.11.20.90.8 Put into linear regression mode and a small REG appears accesses the keys with ⎡ ⎤ in blue The key is used to access other statistical data will display the number of observations. Other functions of the button should be marked on the calculator cover for entering the second set of data For entering the first set of data
Mastering the Calculator using the Casio fx-82TL 31 To put in the first set of numbers, press the following keys: is used for the 1st variable is used for the 2nd variable Continue in this manner After you have input all the numbers, check to see you have 10 samples. Press . The display should read 10 To find the linear regression equation in the form y = a + bx you need to find the value of a and b. These keys are formed as A and B under the and keys. The button is used for all buttons with a blue ⎡ ⎤ symbol under it. Press a is 0.3651 Press b is 0.0430 ∴the equation is y = 0.3651 + 0.0430x To find the correlation coefficient press r = 0.1928 There is not a high correlation between the thickness of bananas and the length of bananas tested.
32 Mastering the Calculator using the Casio fx-82TL The calculator will also give you other statistics about this sample. Use to get the mean thickness (1.055mm) or use to get the standard deviation (0.64mm) or use to get ∑ x (sum of all lengths = 159.4mm). You can also use the to predict the length, given the thickness. Example If 0.6 is the thickness Press The display will read 5.46625 Similarly you can use to predict the thickness, given the length. Example If 12mm is the length Press The display will read 0.8807
Mastering the Calculator using the Casio fx-82TL 33 12. Trigonometric functions The keys involved are: Important: Make sure that your calculator is in the correct mode. For example, if your calculator has R or G on the display and you wish to work in degrees, press mode twice and then select 1 for degrees. Your screen should now display D. Example 1 In the right-angled triangle below, the length of the side opposite the 20° angle needs to be calculated. To find the length of the side labelled x cm, use 5 cm 20˚ x cm
34 Mastering the Calculator using the Casio fx-82TL The keystrokes on the calculator are: or The display should read 1.819851171, so the length of x is about 1.8 cm. Example 2 In the right-angled triangle below, the length of the hypotenuse needs to be calculated. To find the length of the side labelled x cm, use: The keystrokes on the calculator are: The display should read 20.466631, so the length of the hypotenuse is about 20.5 cm. Example 3 Given the lengths of two of the sides in the right-angled triangle below, find the value of the angle θ in degrees: θ tan 20 5 5tan20 x x°= ⇒=° x cm 20˚ 7 cm 7sin 20 7 sin 20 x x°= ⇒= ° 2 cm 1cm θ
Mastering the Calculator using the Casio fx-82TL 35 In the diagram, so To find the value of θ, you need to use the cos–1 key. The calculator keystrokes are: Note: You must first get the value of the division by using the brackets. Your display should read 60°. If it does not, check that you are in degree mode. 13. Exponential and logarithmic functions There are two log keys on your calculator, with their associated exponential keys. The latter are accessed by first using the shift key: The ‘log’ key uses base 10 and the ‘ln’ key uses base e (natural logarithm). 1cos2θ=11cos ( )2θ−=