In probability theory and statistics, a median is described as the number separating the higher half of a sample, a population, or a probability distribution, from the lower half. The median of a finite list of numbers can be found by arranging all the observations from lowest value to highest value and picking the middle one. If there is an even number of observations, the median is not unique, so one often takes the mean of the two middle values.

At most half the population have values less than the median and at most half have values greater than the median. If both groups contain less than half the population, then some of the population is exactly equal to the median.

There may be more than one median: for example if there are an even number of cases, and the two middle values are different, then there is no unique middle value. Notice, however, that at least half the numbers in the list are less than or equal to either of the two middle values, and at least half are greater than or equal to either of the two values, and the same is true of any number between the two middle values. Thus either of the two middle values and all numbers between them are medians in that case.