What does a coefficient of variation tell you?

Answer 1

It tells you about the size of variation relative to the size of the observation, and it has the advantage that the coefficient of variation is independent of the units of observation. Here is a example to help you see it.

If you have a data set with weights, the value of the standard deviation of a set of weights will be different depending on whether they are measured in grams or lbs or micrograms etc. For example if you look at the weights of kids from birth to 18 years, some countries measure in lbs other in kg and some even use stones. The coefficient of variation, however, will be the same in both cases as it does not depend on the unit of measurement. So you can obtain information about the children's weight variation around the world by using the coefficient of variation to look at all the ratios of standard deviations to mean in each country.

To compute it we look the ratio of the standard deviation to the mean .