Bipolar mean and mean deviation about the bipolar mean for discrete quantitative variables

Recently, Maffenini and Zenga (2005) have introduced, for the ordinal variables, the bipolar mean that can be seen as a frequencies distribution. In this paper, the bipolar mean has been extended to the discrete variables. Moreover for these variables it has been introduced a new variability measure: the mean deviation about the bipolar mean. It has been shown that, for the discrete variables, the mean deviation about the bipolar mean is less or equal to the mean deviation about the arithmetic mean. A new interpretation of the mean deviations in terms of ¿unitary steps¿ has been given too. Finally, the mean deviation about the bipolar mean can be considered as a Gini¿s dissimilarity index