On Bounding Moments from Grouped Data.

This article derives bounds on a wide class of moments of the underlying distribution from data grouped in intervals when the mean of each group is given. The extremal distributions are constructed yielding the upper and lower bounds to moments of the form Integral of h(x)dF(x), where h(x) is convex and F(x) is concave. To illustrate the results, bounds on the variance and Gini index are presented for two theoretical distributions. [ABSTRACT FROM AUTHOR]