The use of mean values vs. medians in inequality analysis

Abstract

The mean value and the median are analyzed as alternative measures for both income average and poverty lines. Inequality and poverty being related, yet separate, issues requires separate arguments in both cases. Relative poverty lines that are proportional to either the mean or the median income are compared by statistical properties and in the light of poverty axioms. In particular, the mean turns out to be favourable when relative poverty lines are extended by considering each income as the smallest of all larger incomes. Such truncations which lend to the concept of self-similarity are formally introduced. They induce the same class of income distributions for mean and median-based poverty notions with the median exhibiting drastically more inequality than the mean.