Page 234 - DSOC404_METHODOLOGY_OF_SOCIAL_RESEARCH_ENGLISH

Methodology of Social Research

notes d = the difference (x – M) of the central value (x) of class–interval and M where M is
arithmetic mean
N = total sum of frequencies

(i) By Short–cut Method

S f d 2  S f d  2
σ = i −  
N  N 
The formula can be further simplified as below

σ = i NS f d −S ) 2
2
( f d
N
in the above formula
σ = Standard Deviation
t = interval range
f = frequency of elements
d = the difference (x–M) of the central value (x) of class–interval where x is arithmetic
mean
N = total sum of frequencies
in order to make it more clear the use of above formulae for computation of standard deviation, we
shall consider example of each type of series.

(a) Simple Series

Example 4 find out the standard deviation of the following values:

10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32

solution: We will use Direct Method to solve it in the following way
S d 2
Formula σ =
N

obtained Marks Variation (d) from mean (M) square of Variation
(X) here Mean = 21 (d )
2
10 –11 121
12 –9 81
14 –7 49

16 –5 25
18 –3 9
20 –1 1

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