Casio fx-82TL

Statistical calculations

Learning Skills

Introduction:
This sheet will teach you how to use the Casio fx82TL calculator to perform statistical operations. See also our handout for mathematical functions. Any further queries please contact Student Central
This sheet will teach you to:
Put your calculator into statistical mode Enter observations Display the descriptive statistics Enter group data Perform linear regression

1. Statistical Mode

To put your calculator into statistics mode press MODE 2
A small SD will appear on the display
To clear the statistical memory press, this should be done before entering any new data. SHIFT AC.on = AC/on
2. Entering single variable observations
To enter observations press M+ after entering the observation

Number of scores

The number of scores (n) is 4 this is displayed while entering
Example 2.1 Enter 10, 12, 13, 16 Calculator steps: 10 M+ 12 M+ 13 M+

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3. Display the Descriptive Statistics
Calculator symbol mean Sample standard deviation Population standard deviation Sample variance Scores added up

Common symbol

Calculator steps

answer

SHIFT SHIFT

12.75 2.5

3 = o,,,

6.25 51

Scores squared then added up
The RCL key is on the same row as the M+ key and the o,,, key and (-) key are both in the row above.
4. Entering observations from a frequency table
To enter observations from a frequency table type in; Observation Example 4.1: Enter the following table into your calculator score Calculator steps: SHIFT CLR 1 , , , , = M+ M+ M+ M+ frequency SHIFT , frequency M+
1. Remember when entering new data you must clear the memory first 2. By using the shift key you are accessing the semi colon which is used to separate the score from its frequency. 3. The total number of observations is 33

SHIFT SHIFT SHIFT SHIFT

Once the observations are entered the mean and standard deviation are found as above.

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If the scores are a sample
If the scores are a population

x 12.394 s 2.263

12.394

409 5233

x x5233

5. Entering Grouped data

To enter grouped data you first have to find the midpoint of each group. This is done by adding together the lowest and highest value from each group and then dividing it by two. We then use these as our observations. Example 5.1: group > 0 up to and including 10 >10 up to and including 20 >20 up to and including 30 >30 up to and including 40 frequency 21 30
To find the midpoint of each group: (0+10)/2=5 (10+20)/2=15 (20+30)/2=25 (30+40)/2=35 Calculator steps: SHIFT AC/on (n = 109) If the scores are a sample Approximate: Approximate: Approximate: If the scores are a population Approximate: Approximate: Approximate:
= , , , , AC/on M+ M+ M+ M+ The mean and standard deviation are only approximate because we are using each class centre to approximate the individual observations

20.138

11.220

s 11.272

127.064

125.898

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6. Linear Regression Mode
To put your calculator into statistics mode press MODE 3 1
A small REG will appear on the display

Again it is necessary to clear previous data before entering any new information. SHIFT AC/on = AC/on
7. Entering x and y data sets
To enter x and y observations press x value , y value M+
Example 7.1 x score (independent variable) 10 y score (dependent variable) 27
Calculator steps: SHIFT 10 , , , , , AC/on 27 M+ M+ M+ M+ M+ = AC/on
The comma is used to separate an x score from a y score, whereas the semi colon is used to separate a score from its frequency.

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8. Regression output
SHIFT 7 = this will give A the y-intercept of the regression line

A = 16.189

SHIFT 8 = this will give B the slope of the regression line

B = 0.946

SHIFT ( = this will give r the correlation coefficient

r = 0.417

The means are found by using the SHIFT key and the keys as shown on the calculator. The sums are found by using the RCL key and the 6 keys in the row above the RCL key. When you have finished your regression question it is important to get out of that mode before doing any other calculations.

9. For more information

Visit our Learning Skills website at http://www.csu.edu.au/division/studserv/learning

Copyright

Learning Skills, Charles Sturt University, December, 2008

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Mastering the Calculator using the Casio fx-82TL

10. Statistics

10.1 Mean and standard deviation single data
x The formula for the mean is x = ----n The formulas for the sample standard deviation are s = ( xi x ) ----------------------n1

(Theoretical formula)

x i2 ( x i ) n -------------------------------------n1

(Working formula)

Your calculator will calculate the mean and standard deviation for you (the population standard deviation n or the sample standard deviation n-1 in data calculations you will usually use the sample standard deviation.) The differentiation between and s varies with different calculators. On the Casio fx-82TL, is denoted by n and s is denoted by n-1. The positions of these keys is shown on the diagram below.
input data key A, B, C, D, E, F M, X and Y used with
(key for population standard deviation)
(key for sample standard deviation) (key for mean)
To find the mean and standard deviation, firstly you must access the statistics mode of the calculator by using the keys by SD will appear in the centre of the screen. followed
Note that once you are in the statistics mode, the keys shown within the blue lines and pink letters are active. There are 14 blue keys and 9 pink keys on the Casio fx-82TL. Make sure you can locate them. Before starting any computations always clear the statistics memories using Mcl. Press
I will use the data set A (5, 2, 3, 4, 11) to demonstrate the use of the calculator. Note that I have shown the use of the key where necessary.
Step 1: Input the observations. Use the key to input data (no need to press ).
Step 2: Check that the correct number of observations have been inputted. [Note this is shown on the inside cover of your calculator under statistical data.] Press The display should read 5. Step 3: Display the mean and the display should read 3 Step 4: Display the standard deviation (assume the data set is a sample) and the display should read 5.7008771 __________________________________________________________________________
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.)
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.
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.

Graduates weight (kg) 64

Frequency 5

Cumulative frequency 30

The calculations needed to obtain the standard deviation without statistical keys for these data are: x2 = + + + 632 + = x = + + + 63 + = s = x2 ( x i ) n i -------------------------------------n495 ( ) 30 ------------------------------------------------------- = 29 s = 1.2 kg and s2 = 1.4 kg2

= Thus:

114 453.6333 --------------------------------------------------------- = 29

1.4264

x 1853 x = ----- = ----------- = 61.8 kg n 30 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.)
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 x = 61.8 kg Exercise 6 Find the mean, standard deviation and variance of (a) The annual rainfall data for the years 1971 1990
Year Rain (mm) Year Rain (mm)

1972 990

1975 260
(b) The sample of snail foot lengths
Snail foot length (cm) 2.2 3.4 2.5 3.3 4.7 4.1 1.6 4.3 3.1 3.8 3.5 3.1 3.4 3.7 3.2 4.5 3.3 3.6 4.4 2.6 3.2 3.8 2.9 3.2 3.9 3.7 3.1 3.3 4.1 3.0 3.0 4.7 3.9 1.9 4.2 2.6 3.7 3.1 3.4 3.5
Answers: (a) Rainfall statistics mean: = 1 265.3 mm standard deviation: n-1 = 336.4 mm variance: 2 = 113141.7 mm2 (b) Snail statistics mean: x = 3.4 cm standard deviation: s = 0.70 cm variance: s2 = 0.49 cm2