Coefficient of Variation

Abstract

If the absolute dispersion is defined as the standard deviation, and the average is the mean, the relative dispersion is called the coefficient of variation (CV) or coefficient of dispersion. The relationship between mean and dispersion is very important in the geosciences and is expressed by the coefficient of variation according to: (13.1) $$CV\% = 100\sigma /mean$$ where a = standard deviation. The coefficient of variation is attractive as a statistical tool because it apparently permits the comparison of variates free from scale effects; i.e., it is dimensionless. However, it has appropriate meaning only if the data achieve ratio scale. The coefficient of variation can be plotted as a graph to compare data. A CV exceeding say about 30 percent is often indicative of problems in the data or that the experiment is out of control. Variates with a mean less than unity also provide spurious results and the coefficient of variation will be very large and often meaningless.