# Category:Medians

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This category contains results about **Medians**.

Definitions specific to this category can be found in Definitions/Medians.

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 $S$.