Using the Range to Calculate the Coefficient of Variation

Abstract

In this research a coefficient of variation (CV_high-low) is calculated from the highest and lowest values in a set of data. Use of CV_high-low when the population is normal, leptokurtic, and skewed is discussed. The statistic is the most effective when sampling from the normal distribution. With the leptokurtic distributions, CV_high-low works well for comparing the relative variability between two or more distributions but does not provide a very “good” point estimate of the population coefficient of variation. With skewed distributions CV_high-low works well in identifying which data set has the more relative variation but does not specify how much difference there is in the variation. It also does not provide a “good” point estimate.