“ The coefficient of variation is a relative measure of disperison’. We may calculate coefficient of variation using any of the measure of dispersion such as range, quartile deviation, mean deviation and standard deviation.

Illustrate the use of coefficient of variation in these cases.

There are two types of dispersion absolute measure and relative measures of dispersion. Absolute measures of dispersion are measured in the same units as those of variables considered. This feature of measures of dispersion may create difficulty if we want to compare dispersion in two sets of values which have (i) different central values and (ii) different units of measurement.

In order to overcome this difficulty it is desirable to eliminate the units. This can be done if we use a relative measure of dispersion which is a pure number and do not depend on units of measurement. The relative measure of dispersion is called the cofficient of variation. It may be expressed as ratio or express it in percentage.

The most commonly used coefficient of variation is ratio of standard deviation we may also express in percentage as

Where σ is the standard deviation and m is arithmetic mean.

We may also compute the coefficient of variation as

if we are using the range as measure of. dispersion.

if we are using quartile deviation as measure of dispersion.

Similarly using mean deviation,