## Definition The ==Median== of a random variable $X$ is the value $m$ such that $P(X \leq m) \geq 0.5$ and $P(X \geq m) \geq 0.5$. For a continuous distribution, it satisfies $F(m) = 0.5$. The median is a robust measure of central tendency that is less sensitive to outliers than the mean. > [!example]- If $X$ has PDF $f(x) = 2x$ for $0 \leq x \leq 1$, what is the median? > Find $m$ such that $F(m) = 0.5$: > $ F(m) = \int_0^m 2x\, dx = m^2 = 0.5 $ > $ m = \sqrt{0.5} = \frac{\sqrt{2}}{2} \approx 0.707 $