Percentiels

Percentiels, or percentiles in English, are values that partition a dataset into one hundred equal parts. The p-th percentile is the value below which p percent of the observations fall. For example, the 50th percentile is the median, dividing the data into two halves of equal size.

In a finite data set, the p-th percentile can be defined in several equivalent but slightly different ways. A common convention sorts the data and uses a position h = p/100 × (N + 1), where N is the number of observations. If h is an integer, the percentile is the value at that rank; if not, it is obtained by linear interpolation between the surrounding data points. Other conventions use p × (N − 1)/100 + 1 or rely on integer ranks only. Because of these differences, percentile values can vary slightly depending on the method chosen.

Percentiles are distinct from percentile ranks, which express how a value compares within a distribution (the percentage of observations at or below a given score). They are related to other measures such as quartiles (25th, 50th, 75th percentiles) and reveal the distribution’s shape, dispersion, and skew.

Applications include growth charts in pediatrics, educational testing, income distributions, and quality control. They are useful for describing relative standing and for identifying thresholds or outliers without assuming a specific distribution.

Computation and tools: common implementations include R’s quantile function, Python’s numpy.percentile or scipy, and spreadsheet functions such as Excel’s PERCENTILE or PERCENTILE.INC. Caveats include sensitivity to sample size, ties, and the chosen interpolation method, which can affect the exact percentile values.