percentyle

Percentyle is a statistical term referring to a value in a data distribution below which a given percentage of observations fall. In practice, it describes the position of a data point within an ordered dataset and is commonly used to summarize distributions. While percentile is the standard term in English, percentyle appears in some languages or older texts as a variant spelling or transcription.

Calculation typically starts with a set of observations x(1) ≤ x(2) ≤ … ≤ x(n). For a desired percentile p (0 < p < 100), a common rule is to compute the position h = p/100 × (n + 1). If h is an integer, the pth percentile is x(h). If h is not an integer, interpolation is used between the neighboring order statistics: percentile = x(⌊h⌋) + (h − ⌊h⌋) × [x(⌈h⌉) − x(⌊h⌋)]. Different software packages may use alternative conventions, such as h = p/100 × (n − 1) or the nearest-rank method, which can yield different results, particularly in small samples.

Percentiles are widely used to describe and compare distributions. They appear in standardized test scores, growth or reference charts in medicine, income or wealth distributions, and quality control. They allow statements like “the 90th percentile is 120,” meaning 90% of observations fall at or below 120.

Limitations include sensitivity to sample size, outliers, and the chosen calculation method. Because different rules can produce different percentiles, it is important to specify the method used when reporting them. See also percentile, centile, quantile, and quartile.