information:classification, quality:correction, structural:scholar_edition, information:highlighting
Probability distributions

For any real -valued probability distribution with cumulative distribution function F, a median is defined as any real number m that satisfies the inequalities lim x → m − F (x) ≤ 1 2 ≤ F (m) {\displaystyle \lim _{x\to m-}F(x)\leq {\frac {1}{2}}\leq F(m)} (cf. the drawing in the definition of expected value for arbitrary real-valued random variables). An equivalent phrasing uses a random variable X distributed according to F: P (X ≤ m) ≥ 1 2 and P (X ≥ m) ≥ 1 2. {\displaystyle \operatorname {P} (X\leq m)\geq {\frac {1}{2}}{\text{ and }}\operatorname {P} (X\geq m)\geq {\frac {1}{2}}\,.}