Measures of Dispersion: Coefficient of Variation

What is the Coefficient of Variation?

The coefficient of variation measures variability in relation to the mean (or average) and is used to compare the relative dispersion in one type of data with the relative dispersion in another type of data. The data to be compared may be in the same units, in different units, with the same mean, or with different means.

When is the Coefficient of Variation Useful?

Suppose you want to evaluate the relative dispersion of grades for two classes of students: Class A and Class B. The coefficient of variation can be used to compare these two groups and determine how the grade dispersion in Class A compares to the grade dispersion in Class B. This is one example of how the coefficient of variation can be applied.

How is the Coefficient of Variation Calculated?

The coefficient of variation is a calculation built on other calculations -- the standard deviation and the mean -- as follows:

This reads as 'the coefficient of variation is equal to the standard deviation divided by the mean, multiplied by 100 (to produce a percentage).

The steps required for calculating the coefficient of variation are:

1. Calculate the mean for the data set.
2. Calculate the standard deviation.
3. Divide the standard deviation by the mean.
4. Multiply the result of step 3 by 100.

An Exercise in Calculating the Coefficient of Variation

Since we already calculated the standard deviation and mean for the previous lesson, let's use those numbers to determine the coefficient of variation. Here are the steps with the numbers from the previous lesson:

1. The mean is 50 (from the previous lesson).
2. The standard deviation is 18.4.
3. 18.4 / 50 = .368
4. .368 * 100 = 36.8%

The last step converts the value we have calculated into a percentage. We can now say that the coefficient of variation for the data we evaluated is 36.8%.