In statistics, what does the median represent in a data set?

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The central idea here is how we identify a typical or central value in a data set. The median is the middle value when all the data are lined up from smallest to largest, splitting the data into two halves. In an odd-sized set, there’s a single middle value that sits exactly in the center. In an even-sized set, there isn’t one exact middle, so we take the average of the two central values to find the median.

This makes the median a good summary of the center for skewed data or data with outliers, because it isn’t pulled toward extreme values the way the average can be. For comparison, the average (mean) sums all values and divides by the count, which can be influenced by exceptionally large or small numbers, and the mode is simply the most frequent value, not necessarily near the center of the data. For example, with 1, 2, 3, 100, the median is the average of 2 and 3, which is 2.5, while the mean would be pulled toward 100.