In statistics the median is the value that separates a dataset. It is the middle value.

What is the median used for?

For practical purposes, the median of a sample can be used to estimate the population mean, while the sample mean may be more efficient than the sample median when data is contaminated by the heavy-tailed or mixed distributions. If the distribution of X is such that the expectation exists, then m is a sample median if it minimizes mean absolute error.

History of the statical use of the median

The median may have first appeared in Edward Wright's 1599 book Certaine Errors in Navigation, but it is hard to verify that Wright described the modern notion. The term median was first used in 1843 by Antoine Augustin Cournot and Gustav Theodor Fechner, but was later popularized in sociology and psychology by F. Y. Edgeworth and Francis Galton. Later statistical statisticians encouraged the use of medians for its intuitive clarity and ease of computation, but eventually the arithmetic mean replaced it as the notion of generic average.