### Use the coefficient of variation to compare dispersion expressed in different units of measurement

Previous posts on statistics have covered variance and standard of deviation (See my post of Feb. 18, 2011: variance; and Feb. 21, 2011: standard deviation.). Statistical analysts can take the calculations of dispersion one step farther. When they divide the standard deviation of a set of data by the average of the set, they produce what is called the coefficient of variation. It expresses the standard deviation as a percentage of the sample mean.

The coefficient of variation (CV) has one primary purpose. It is useful when you care about the size of variation relative to the size of the observation set, but that is not all. It also has the significant advantage that it is independent of the units of observation. For example, the value of the standard deviation of a set of invoice amounts will be different depending on whether they are measured in dollars or pound sterling. The coefficient of variation, however, can be compared for both as it does not depend on the currency. Alternatively, if a general counsel wanted to understand better the distribution of cases by elapsed months and by total fees – two different measurement units – the CV would tell which one ranges more widely.