Casio Fx82tl Manual

							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. 
						

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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 
						

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(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  
						

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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 
						

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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−=