Median

The middle value of a dataset when sorted in order -- half the values fall below it, half above.

Descriptive StatisticsBeginnerFree

In Plain English

Line up every value from smallest to largest; the median is the one sitting right in the middle, or the average of the two middle values for an even-sized dataset. Unlike the mean, a few extreme outliers barely move it -- exactly why home prices and incomes are usually reported as medians, not means.

Definition

For a sample sorted in ascending order, the median is the middle value if $n$ is odd, $X_{(\frac{n + 1}{2})}$ , or the average of the two middle values if $n$ is even, $\frac{X _{(n /2)} + X _{(n /2 + 1)}}{2}$ . It is the 50th percentile of the data.

Formula

Median = ⎩ ⎨ ⎧ X_{(\frac{n + 1}{2})} \frac{X _{(n /2)} + X _{(n /2 + 1)}}{2} n odd n even

Notation

X_{(k)}

—The k-th smallest value (order statistic) in the sorted data

Properties

The median is robust to outliers in a way the mean isn't -- a dataset's most extreme value can change substantially without moving the median at all, as long as it doesn't cross the middle.
For symmetric distributions, the median equals the mean; for skewed distributions, the median sits closer to where most of the data is concentrated, while the mean gets pulled toward the tail.
The median minimizes the sum of absolute deviations from every point in the dataset -- the L1 analogue of the mean's least-squares (L2) optimality property.

At a Glance

Also calledthe 50th percentile

Robust tooutliers -- barely moves even with extreme values

vs. the meanless affected by skew

Common useincome, home prices, other right-skewed data

Related Terms

Mean Percentile Central Tendency

Last updated August 8, 2026← Back to the Dictionary