28 Mastering the Calculator using the Casio fx-82MS
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:
Σx
2
= 60
2
× 2 + 61
2
× 14 + 62
2
× 8 + 63
2
+ 64
2
× 5 = 114 495
Σx = 60 × 2 + 61 × 14 + 62 × 8 + 63 + 64 × 5 = 1 853
s =
=
Thus: s = 1.2 kg and s
2
= 1.4 kg
2
=
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)
Frequency
Cumulative
frequency
60 2 2
61 14 16
62 8 24
63 1 25
64 5 30
Σx
i
2
Σx
i
()
2
114 495 1 853()
2
30⁄–
29
--------------------------------------------------------
114 495 114 453.6333–
29
---------------------------------------------------------- 1.426
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