The coefficient of variation for a population measurement with nonzero mean is given by σ/μ, where μ is the population mean and σ is the population standard deviation. what is the method of moments estimate of the coefficient of variation? prove that the coefficient of variation is invariant under rescalings of the distribution, i. e., under transformations of the form t(x) = cx for constant c > 0. it is this invariance that leads to the coefficient of variation being an appropriate measure of sampling variability in certain problems, as it is independent of the units we use for the measurement.