Editing Percentile (section)

{{Short description|Statistic which divides a data set into 100 parts and analyzes it as a percentage}}

In [[statistics]], a '''''k''-th''' '''percentile''', also known as '''percentile score''' or '''centile''', is a [[Raw score|score]] (e.g., a data point) {{em|below which}} a given [[percentage]] ''k'' of all scores in its [[frequency distribution]] exists ("'''exclusive'''" definition) or a score {{em|at or below which}} a given percentage of the all scores exists ("'''inclusive'''" definition); i.e. a score in the ''k''-th percentile would be above approximately ''k''% of all scores in its set. For example, the 97th percentile of data is a data point below which 97% of all data points exist (by the exclusive definition). Percentiles depends on how scores are arranged.

Percentiles are a type of [[quantile]]s, obtained adopting a subdivision into 100 groups. The 25th percentile is also known as the first ''[[quartile]]'' (''Q''<sub>1</sub>), the 50th percentile as the ''[[median]]'' or second quartile (''Q''<sub>2</sub>), and the 75th percentile as the third quartile (''Q''<sub>3</sub>). For example, the 50th percentile (median) is the score {{em|below}} (or {{em|at or below}}, depending on the definition) which 50% of the scores in the distribution are found.

Percentiles are expressed in the same [[unit of measurement]] as the input scores, {{em|not}} in [[percent]]; for example, if the scores refer to [[human weight]], the corresponding percentiles will be expressed in kilograms or pounds.
In the [[Limit (mathematics)|limit]] of an infinite [[sample size]], the percentile approximates the ''[[percentile function]]'', the inverse of the [[cumulative distribution function]].

A related quantity is the ''[[percentile rank]]'' of a score, expressed in [[percent]], which represents the fraction of scores in its distribution that are less than it, an exclusive definition.
Percentile scores and percentile ranks are often used in the reporting of [[test score]]s from [[norm-referenced test]]s, but, as just noted, they are not the same. For percentile ranks, a score is given and a percentage is computed. Percentile ranks are exclusive: if the percentile rank for a specified score is 90%, then 90% of the scores were lower.  In contrast, for percentiles a percentage is given and a corresponding score is determined, which can be either exclusive or inclusive. The score for a specified percentage (e.g., 90th) indicates a score below which (exclusive definition) or at or below which (inclusive definition) other scores in the distribution fall.