Coefficient of Variation

The coefficient of variation is the ratio of the standard deviation to the mean:

The coefficient of variation provides a way to compare the dispersion of values of samples/populations around their means.  The graphic below shows two normally distributed populations, both with a mean of 1000, the one on the left has a standard deviation of 100 and the one on the right has a standard deviation of 20, giving coefficients of variation of 0.10 and 0.02 respectively.

In this case, where the means are the same, the coefficient of variation provides no more information than the standard deviations themselves.  The coefficient of variation is more use when populations have different means and standard deviations.  The graphic below is loosely based on the annual precipitation at two points in areas with signifianctly different climates.

Whilst there are marked differences in the mean and standard deviation of the precipitation at the two places, the coefficients of variation are of similar magnitude. It would take a larger dataset to infer a relationshop between climate type and coefficient of variation.