The median of a statistical distribution with distribution function D(x) is the value x such D(x) = 1/2. For a symmetric distribution, it is therefore equal to the mean. Given order statistics Y_1 = min_j X_j, Y_2, ..., Y_(N - 1), Y_N = max_j X_j, the statistical median of the random sample is defined by x^~ congruent {Y_((N + 1)/2) | if N is odd 1/2(Y_(N/2) + Y_(1 + N/2)) | if N is even auto right match (Hogg and Craig 1995, p. 152) and commonly denoted μ_(1/2) or x^~. The median of a list of data is implemented as Median[list].

mean | midrange | mode | order statistic | Pearson mode skewness