Definition:Ranking
This page is about ranking. For other uses, see rank.
Definition
Let $S$ be a set of discrete data which has been linearly ordered by a total ordering $\QQ$.
The ranking of $x \in S$ is the index of $x$ in the sequence induced on $S$ by $\QQ$.
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Also known as
A ranking is often known as a rank, but $\mathsf{Pr} \infty \mathsf{fWiki}$ prefers ranking as the name suggests emphasis on the process of creating the ordering upon which the ranking is assigned.
Hence on $\mathsf{Pr} \infty \mathsf{fWiki}$ the term rank in this context refers specifically to the index of a given $x \in S$ under the ranking imposed upon $S$.
Ranked data can be referred to as ordinal data, for which it is useful to compare the term ordinal variable.
Examples
Numbers
A set of numbers can always be ranked, either in ascending or descending order, according to what is appropriate.
Personal Parameters
Let $S$ be a sample from a population of people.
$S$ can be ranked according to a personal characteristic like height or age.
Subjective Ranking
A ranking can be based on a subjective judgment, for example:
- the ranking of participants by judges of a talent contest
- the ranking of preferences in a tasting test.
Also see
- Results about rankings can be found here.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): rank: 2.
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): rank: 2.
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): rank (in statistics)