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Unit–28: Measures of Dispersion: Standard Deviation

b. If it is required to find the mean of a simple series, then– notes

S f d S fd
d = =δ or
n S f
Where the different symbols used in the above equation are defined as
d = Mean deviation
f = frequency of elements
d = Variation of each element from the mean (can be
arithmetic mean/median/mode)
fd = Product of frequency of elements and their
variation
∑ fd = sum of product of frequency of elements and their
variation
∑ f or n = sum of frequency
Now let us solve some practical questions based on the above methods.

28.6 Simple Series

To find out the mean deviation of a simple series:
a. firstly calculate mean (depending upon question whether it is arithmetic mean, median or
mode)
b. find out the value of variation of each element from the mean (arithmetic mean or median
or mode)
c. Find out the sum of all variations i.e. ∑d.
d. find out the total number of elements (as represented by n).
e. Lastly use ∑d/n formula to calculate the mean deviation.

Did You Know? To calculate mean deviation from arithmetic mean, one has to first calculate
arithmetic mean.

the above rules to solve questions will become clearer from the below examples.

Example 2 the weekly wages of labourers in a workshop is given as follows. find
out the mean deviation of the wages while considering arithmetic mean
as well as mode separately.
Wages are (in `) 120, 135, 142, 135, 140, 155, 135, 125, 146, 160, and 150.

solution: (i) Considering arithmetic mean as basis in order to find the mean deviation in the given
question from the arithmetic mean, we need to first find the arithmetic mean, which is found out
as:

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