The bipolar mean in sensory analysis

The bipolar mean has been recently proposed with the aim of summarizing the ordinal variables (Walter Maffenini and Michele Zenga, 2005) [1]. It is a synthetic distribution where the total size n is concentrated on one of the k categories of the variable or, at most, on two consecutive categories. This measure is derived according to the usual statistical dominance criterion that is based on the retro-cumulative frequencies. Further improvements of the bipolar mean include extensions to discrete quantitative variables and a new variability measure, i.e. the mean deviation about the bipolar mean. The bipolar mean can be applied also to ordinal variables whose categories are expressed as scores on a numerical scale. Hence, the new way to summarize these variables can be useful in sensory analysis, where it is often necessary to compare frequency distributions representing the evaluations on some characteristics about different products made by judges or tasters. The assessment is usually based on simple synthetic measures such as the arithmetic mean or the median, but these indexes can provide contradictory answers. In this work we propose the normalization of the mean deviation of the bipolar mean. Moreover, some empirical evidences in sensory analysis are given with the purpose of showing how the bipolar mean and the relative mean deviation can sometimes overcome the comparison problems.