Coefficient of Variation

Abstract

The coefficient of variation measures the variability of a series of numbers independently of the unit of measurement used for these numbers. In order to do so, the coefficient od variation eliminates the unit of measurement of the standard deviation of a series of numbers by dividing it by the mean of these numbers. The coeffi-cient of variation can be used to compare distributions obtained with different units, such as, for example, the variability of the weights of newborns (measured in grams) with the size of adults (measured in centimeters). The coefficient of variation is meaningful only for mea-surements with a real zero (i.e., " ratio scales ") because the mean is meaningful (i.e., unique) only for these scales. So, for example, it will be meaningless to compute the coefficient of variation of the temperature measured in degrees Fahrenheit, because changing the measurement to degrees Celsius will not change the temperature but will change the value of the coefficient of variation (because the value of zero for Celsius is thirty-two for Fahrenheit and therefore the mean