percentiilit

Percentiilit are a statistical concept used to describe the distribution of a dataset. A percentile indicates the value below which a given percentage of observations fall. For a dataset of size N sorted in nondecreasing order, the p-th percentile (where 0 < p < 100) is a value such that at least p percent of the observations are at or below it, and at least (100 − p) percent are at or above it. In probability terms, the p-th percentile is the p/100 quantile of the distribution; for continuous distributions it corresponds to the inverse of the cumulative distribution function at p/100.

Common interpretations include that the 50th percentile is the median, while the 25th and 75th percentiles define the first and third quartiles, which are often used to summarize the spread of a distribution. Percentiliitin are widely used in statistics, education, medicine, psychology, and growth monitoring to compare individuals or groups to a reference population.

Calculation methods vary, especially in small samples. Some common conventions include the nearest-rank method, which selects a data point as the percentile based on a fixed ranking rule, and interpolation methods that estimate percentiles by linearly interpolating between order statistics. Different software packages and standards may adopt different conventions, leading to small differences in reported values.

Limitations include sensitivity to sample size, the handling of ties, and the fact that percentiles describe relative standing rather than absolute intervals between values. They are often complemented by other measures such as quartiles, the median, and the empirical percentile function (ECDF) for a fuller view of a distribution.