Mutually exclusive: a unit cannot fit into more than one category

Collectively exhaustive: the categories account for everything inside the population

An ‘classification schema’, meaning a way to describe and classify a population of units (and also a means of organising information), would ideally be mutually exclusive and collectively exhaustive.

For example, the outcomes possible from flipping a coin are heads or tails. An outcome cannot be both head and tail (therefore mutually exclusive) and all outcomes are captured by the classes head and tail (collectively exhaustive).

Another example is the legal forms of a business: sole trader, partnership, corporation, trust. A business cannot take more than one of these (mutually exclusive) and all businesses fall under one of these categories (collectively exhaustive).

However, there may often be populations where classification schemes are unable to hold both properties of ‘mutually exclusive’ and ‘collectively exhaustive’. For example, gender – male and female – would fail to describe people that identify in both or neither classes.