Page 149 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Quantitative Techniques – I

Notes 7.8.1 Calculation of Standard Deviation

There are two methods of calculating standard deviation: (i) Direct Method (ii) Short-cut Method

Direct Method

1. Individual Series: If there are n observations X , X , ...... X , various steps in the calculation
1 2 n
of standard deviation are:
X i
(a) Find X .
n
(b) Obtain deviations X i X for each i = 1, 2, ...... n.

n 2
(c) Square these deviations and add to obtain X i X .
i 1
2
n
X i X
(d) Compute variance, i.e., 2 i 1 .
n
(e) Obtain s as the positive square root of 2 .
The above method is appropriate when X is a whole number. If X is not a whole number, the
standard deviation is conveniently computed by using the transformed form of the above
formula, given below.

1 2 1
2
= X i X = X X X X

n n i i
1 2 2 1 2
i =
(The 2nd term is sum of deviations from X , which is equal to zero.)
2
1 2 2 1 2 X i
X i X X i or
n n n
= Mean of squares – Square of mean.

Example: Calculate variance and standard deviation of the weights of ten persons.
Weights (in kgs) : 45, 49, 55, 50, 41, 44, 60, 58, 53, 55
Solution:
Calculation of standard deviation
Let u X X

45 49 55 50 41 44 60 58 53 55 510
–6 –2 4 –1 –10 –7 9 7 2 4 0
36 4 16 1 100 49 81 49 4 16 356

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