Median

• Definition: Let $X$ be a continuous random variable with PDF $f_X$. The median of $X$ is a point $c\in\mathbb{R}$ such that

$$\int\limits_{-\infty}^{\infty} f_X(x) \; dx = \int\limits_{c}^{\infty} f_X(x) \; dx$$

• Theorem: The median of a random variable $X$ is the point $c$ such that $F_X(c) = 0.5$.