Page 232 - DSOC404_METHODOLOGY_OF_SOCIAL_RESEARCH_ENGLISH

Methodology of Social Research

notes 28.8 standard Deviation
It is represented as S.D or σ (small sigma) in symbolic way. One major problem in computation
of mean deviation is that we do not consider the positive (+) or negative (–) sign and consider it
as additive. We overcome this problem in standard deviation. We square the value of variation in
order to eliminate the effect of positive and negative sign in variation. then we calculate the value
of standard variation.

Task What is meant by standard deviation? Give a brief explanation.

Computation of Standard Deviation

We do the following computation to calculate the value of standard deviation.
1. We find out the square (d ) of variation from the arithmetic mean.
2
2. We find the sum of squares of variations (Sd ).
2
3. We divide this sum by the number (N) of elements S d 2 .
N
S d 2
4. Then we find out the square root of the obtained value .
N
in this way, the formula for standard Deviation is
S d 2
S.D. or σ =
N
to make it more clear, we can expand d as d = x – M as
S (x M− ) 2
σ =
N
Where
σ = Standard Deviation
x = Variable value or values of different elements in a series or sequence
M = Arithmetic mean of elements
N = total number of elements
d = (x – M)
S d 2
The technique which uses the formula σ = N to calculate standard deviation is known as the direct
method of calculating standard deviation. if the arithmetic mean of the elements is not an integer,
then d comes out to be a decimal number making the calculation cumbersome. in order to avoid this
we use a concise technique.

Formula for Short–cut Method—

S (x − A ) 2 S  (x − A ) 2
S.D. or σ = N −   N  

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