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Unit 7: Measures of Dispersion

Demerits Notes

1. As compared to the quartile deviation and range, etc., it is difficult to understand and
difficult to calculate.
2. It gives more importance to extreme observations.

3. Since it depends upon the units of measurement of the observations, it cannot be used to
compare the dispersions of the distributions expressed in different units.

Uses of Standard Deviation

1. Standard deviation can be used to compare the dispersions of two or more distributions
when their units of measurements and arithmetic means are same.
2. It is used to test the reliability of mean. It may be pointed out here that the mean of a
distribution with lower standard deviation is said to be more reliable.

7.8.5 Skewness

Skewness of a distribution refers to its asymmetry. The symmetry of a distribution implies that
for a given deviation from a central value, there are equal number of observations on either side
of it. If the distribution is asymmetrical or skewed, its frequency curve would have a prolonged
tail either towards its left or towards its right hand side. Thus, the skewness of a distribution is
defined as the departure from symmetry. We may note here that there may be a situation where
two or more frequency distributions are same with regard to mean and variance but not so with
regard to skewness.

Figure 7.1: Positively verses Negatively Skewed Distribution
Positively Skewed Distribution

Negatively Skewed Distribution

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