Examples
- 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 ; 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 ; a data set would correspond to a list of towns.
- In chemistry, compositions can be expressed as molar concentrations of each component. As the sum of all concentrations is not determined, the whole composition of D parts is needed and thus expressed as a vector of D molar concentrations. These compositions can be translated into weight per cent multiplying each component by the appropriated constant.
- In a survey, the proportions of people positively answering some different items can be expressed as percentages. As the total amount is identified as 100, the compositional vector of D components can be defined using only D − 1 components, assuming that the remaining component is the percentage needed for the whole vector to add to 100.
- In probability and statistics, a partition of the sampling space into disjoint events is described by the probabilities assigned to such events. The vector of D probabilities can be considered as a composition of D parts. As they add to one, one probability can be suppressed and the composition is completely determined.
Read more about this topic: Compositional Data
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—Bernard Mandeville (1670–1733)