[[Probability theory MOC]]
# Median

Let $X$ be a [[real random variable]].
A value $m$ is a **median** of $X$ iff $\mathbb{P}(X\leq m) \geq \frac{1}{2}$ and $\mathbb{P}(X \geq m) \geq \frac{1}{2}$. #m/def/prob 

## Properties

- A median $m$ minimizes the mean absolute error $\Ex[\abs{X-x}]$


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