Bipolar mean for ordinal variables

This paper proposes, for ordinal variables, a new type of mean called bipolar mean, that is a frequency distribution with the total size n concentrated on one category or on two consecutive categories. The bipolar mean is coherent with the usual statistics dominance that is based on the retro-cumulative frequencies. The paper shows that the number of bipolar means that it is possible to get for the frequency distributions with k categories and total size n is nk ¿n+1. Note that the traditional means utilised for ordinal variables (the median and the mode) take only k categories. Two applications are presented to show how the BM works.