Performance of three averaging methods for various distributions

Abstract

The performance of three averaging methods, namely the sample median, the sample arithmetic mean, and the sample geometric mean, are analyzed in tenns of their bias, variance, and mean square error. The bias and variance are numerically evaluated for various parent distributions and plotted versus the number, N, of data points employed in the sample statistics. Also, the limiting behaviors, as N increases without limit, are derived. It is found that the best averaging method is very dependent upon the distribution of the data, with the sample median being favored for data with occasional large out-liers.