The median of a set of numbers is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as the “middle" value. The basic feature of the median in describing data compared to the mean (often simply described as the "average") is that it is not skewed by a small proportion of extremely large or small values, and therefore provides a better representation of the center. Median income, for example, may be a better way to describe the center of the income distribution because increases in the largest incomes alone have no effect on the median. For this reason, the median is of central importance in robust statistics.

Median is a 2-quantile; it is the value that partitions a set into two equal parts.

The median of a finite list of numbers is the "middle" number, when those numbers are listed in order from smallest to greatest.

If the data set has an odd number of observations, the middle one is selected (after arranging in ascending order). For example, the following list of seven numbers,

has the median of 6, which is the fourth value.

If the data set has an even number of observations, there is no distinct middle value and the median is usually defined to be the arithmetic mean of the two middle values. For example, this data set of 8 numbers

has a median value of 4.5, that is ${\displaystyle (4+5)/2}$. (In more technical terms, this interprets the median as the fully trimmed mid-range).

In general, with this convention, the median can be defined as follows: For a data set ${\displaystyle x}$ of ${\displaystyle n}$ elements, ordered from smallest to greatest,