Page 144 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Unit 7: Measures of Dispersion

7.7 Mean Deviation or Average Deviation Notes

Mean deviation is a measure of dispersion based on all the observations. It is defined as the
arithmetic mean of the absolute deviations of observations from a central value like mean,
median or mode. Here the dispersion in each observation is measured by its deviation from a
central value. This deviation will be positive for an observation greater than the central value
and negative for less than it.

7.7.1 Calculation of Mean Deviation

The following are the formulae for the computation of mean deviation (M.D.) of an individual
series of observations X , X , ..... X :
1 2 n
1 n
1. M.D. from X X i X
n i 1

1 n
M d X i M d
2. M.D. from n i 1

1 n
M o X i M o
3. M.D. from n i 1

In case of an ungrouped frequency distribution, the observations X , X , ..... X occur with respective
1 2 n
n
1
X
frequencies f , f , ..... f such that f X i X
i f = N. The corresponding formulae for M.D. can be written as:
1 2 n i
N i 1
1 n
1. M.D. from X f X i X
i
N i 1
1 n
2. M.D. from M d f X i M d
i
N i 1
1 n
3. M.D. from M o f X i M o
i
N i 1
The above formulae are also applicable to a grouped frequency distribution where the symbols
X , X , ..... X will denote the mid-values of the first, second ..... nth classes respectively.
1 2 n
Remarks: We state without proof that the mean deviation is minimum when deviations are
taken from median.

Coefficient of Mean Deviation

The above formulae for mean deviation give an absolute measure of dispersion. The formulae
for relative measure, termed as the coefficient of mean deviation, are given below:

.
.
M D from X
4. Coefficient of M.D. from X
X

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