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Unit–28: Measures of Dispersion: Standard Deviation

notes

Notes in the computation of Mean Deviation, whether we use Arithmetic Mean, Median
or Mode, it is not necessary that the final result should be the same in all the cases.
it can be same as well as different also.

28.7 Discrete series

to compute mean deviation in a discrete series:
a. We have to calculate the mean (depending on question whether it is arithmetic mean, median
or mode) first.
b. Then we have to compute the difference between each value of element and the mean (arithmetic
mean, median or mode) which is represented as ‘d’ in equation.
c. Then we have to compute the product (fd) of the frequency (represented as ‘f’ in equation) and the
variation.
d. Then we have to add all such products to obtain the sum of products Sfd.
e. Then we have to compute the sum Sf of frequencies (f) or n.
S f d S fd
f. finally we have to use or to compute mean deviation.
S f n
the above rules to solve questions can be easily understood using the following examples.

Example 3 the following are the marks obtained by students in statistics. Using
arithmetic mean, median and mode as basis, find out the mean deviation
for all the three cases.
obtained 12 25 27 30 35 15 40 45 50 35
Marks
No. of 4 3 2 2 5 8 9 6 7 4
students

Solution: (i) Considering Arithmetic Mean as Basis—in order to calculate the mean deviation
using arithmetic mean, we first need to compute the arithmetic mean, which is computed as shown
below:

table 28.1
obtained Marks (x) no. of students (f) f.x (product)
12 4 (12 × 4) = 48
25 3 (25 × 3) = 75
27 2 (27 × 2) = 54

30 2 (30 × 2) = 60

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