The Midrange of a Sample as an Estimator of the Population Midrange

A study is made of the distribution of the midranges of samples from five different symmetric populations of limited range, and of the relative efficiency of midrange and mean in estimating the population midrange, or mean, or median. (For a symmetric distribution these three averages are of course identical.) It is found that the midrange is more efficient than the mean for all of the populations considered, and that this efficiency increases with decreasing α4(= μ4/[sgrave]4), the standardized fourth moment. The values of α4 for the five populations studied are 2.19, 2.14, 1.8, 1.19, and 1.