Percent Coefficient of Variation (%CV) Formula for Log-transformed Data from Lognormal Distributions

Abstract

The coefficient of variation (CV) serves as a dimensionless metric commonly employed to assess the variability within a population in relation to its standard deviation. It is conventionally expressed as a percentage (1). When considering the percent coefficient of variation (%CV) for data subjected to logarithmic transformation, it becomes crucial to apply the appropriate %CV formulation designed for lognormally distributed data. A thorough examination of various journals reveals a recurring issue where the %CV formula for log-transformed data is inaccurately applied, particularly in cases involving naturally exponential distributions that undergo transformation to linearity (i.e., lognormal distributions). This chapter establishes a framework for the accurate application of the mathematical formula for %CV in the context of data derived from a lognormal probability distribution.