A Short Note on the Generalized Measures of Central Tendency in the Median Family

Abstract

This short paper is a note on the location measures such as the median. Usually, the median is defined in terms of the variate values, but here we obtain the median as a function of the arithmetic mean of the index values. This approach immediately enables us to define other measures on the power mean of index values (of which harmonic, geometric and arithmetic analogs in the median family) which are readily obtainable. A computer program is appended.

Keywords: median, power mean Holder mean, index set

JEL Classification: C00, C02