Compositional data

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In statistics, compositional data is data in which each data point is an n-tuple of nonnegative numbers whose sum is 1. Typically each of the n components p_i of each data point (p₁, ..., p_n) says what proportion (or "percentage") of a statistical unit falls into the ith category in a list of n categories.

For example,

Each data point may correspond to a rock composed of three different minerals; a rock of which 10% is the first mineral, 30% is the second, and the remaining 60% is the third would correspond to the triple (0.1, 0.3, 0.6); a data set would contain one such triple for each rock in a sample of rocks.

Each data point may correspond to a town; a town in which 35% of the people are Christians, 55% are Muslims, 6% are Jews, and the remaining 4% are others would correspond to the quadruple (0.35, 0.55, 0.06, 0.04); a data set would correspond to a list of towns.

Very often ternary plots are used in analysis of compositional data.