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  "body": "\n## Definition\n\nLet $X$ be a real random variable on a probability space $(\\Omega, \\mathcal{F}, P)$.\nA median of $X$ is a real number $m$ with\n$$P(X \\le m) \\ge \\frac{1}{2} \\quad \\text{and} \\quad P(X \\ge m) \\ge \\frac{1}{2}.$$\n\n## Remarks\n\nEach real random variable has a median, and the medians form a closed bounded interval. For example, $Q(1/2)$ is a median, where $Q$ is the [[quantile function|0B3Q3XDM5X]].\nThe median can be different from the mean. For the exponential distribution with rate $\\lambda$, the median is $\\ln 2 / \\lambda$ and the mean is $1/\\lambda$.\nFor a fair coin coded as $0$ and $1$, each $m \\in [0, 1]$ is a median.\nFor a sorted data set $x_1 \\le \\dots \\le x_n$ with $n$ odd, the median is $x_{(n+1)/2}$. For $n$ even, one usually takes the mean of the two middle values.\n\n## Explanations\n\n### L1 human\n\nThe median is the middle value: half of the chance lies on each side of it.\nThe median of the incomes in a country is often more useful than the mean.\nA few very large incomes do not move the median much.\n",
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