Definition:Median (Statistics)

Definition
Let $S$ be a set of quantitative data.

Let $S$ be arranged in order of size.

The median is the element of $S$ that is in the middle of that ordered set.

Suppose there are an odd number of elements of $S$ such that $S$ has cardinality $2 n - 1$.

The median of $S$ in that case is the $n$th element of $S$.

Suppose there are an even number of elements of $S$ such that $S$ has cardinality $2 n$.

Then the middle of $S$ is not well-defined, and so the median of $S$ in that case is the arithmetic mean of the $n$th and $n + 1$th elements of $S$.

Also see

 * Definition:Measure of Central Tendency


 * Definition:Arithmetic Mean
 * Definition:Mode