mediën

The medián, or median, is a measure of central tendency in statistics. In a finite data set, after sorting the values, if the number of observations n is odd, the medián is the middle value x( (n+1)/2 ). If n is even, it is the average of the two central values x(n/2) and x(n/2+1). For a random variable, the medián is any value m such that P(X ≤ m) ≥ 0.5 and P(X ≥ m) ≥ 0.5. In continuous distributions, the medián is unique if the cumulative distribution function is strictly increasing.

The medián is robust to outliers and skewed data, unlike the arithmetic mean. It coincides with the mean only in symmetric distributions. As a 50th percentile, it is a specific case of a quantile and can be defined for data that are ordinal, provided the order is meaningful. For grouped data, the medián can be estimated from a frequency table using class midpoints and linear interpolation within the containing class.

Computation for large data sets often uses selection algorithms, such as quickselect, which can determine the medián in linear time without fully sorting the data. The medián is widely used to summarize skewed distributions, such as income, property values, or other economically relevant variables, where extreme values would unduly influence the mean. It also serves as a robust alternative in various statistical procedures and as a fundamental component of quantile-based analyses. See also: quantile, 50th percentile.