Percentil

Percentile is a statistical measure that indicates the value below which a given percentage of observations in a group fall. The p-th percentile, where p is between 0 and 100, represents a cutoff so that at least p percent of data lie at or below that value and at least (100 − p) percent lie at or above it. The term percentile is common in English, while many languages use a corresponding term such as percentil.

Calculation approaches vary, especially for small samples or grouped data. Two widely used methods are:

- Nearest-rank method: if a dataset has n observations sorted in ascending order, the p-th percentile is the value at position k = ceil(p/100 × n). For example, with five values, the 40th percentile uses the second value in the ordered list.

- Linear interpolation method: compute pos = p/100 × (n + 1). If pos is an integer, take the value at that position; if not, interpolate between the surrounding data points. This yields a smoother percentile, particularly for larger datasets.

Common reference points include the 25th, 50th, and 75th percentiles, which correspond to the first quartile, median, and third quartile, respectively. Percentiles are used to summarize distributions, compare groups, and interpret standardized test scores or growth charts. They provide a way to understand relative standing without assuming a normal distribution. Limitations include sensitivity to data quality and the fact that different percentile definitions can yield different results, especially in small samples. Related concepts include deciles and quartiles, which are specific percentile divisions. In practice, the choice of method should be stated when reporting percentile values.