**Medians of Probability Distributions**

For any probability distribution on the real line **R** with cumulative distribution function *F*, regardless of whether it is any kind of continuous probability distribution, in particular an absolutely continuous distribution (and therefore has a probability density function), or a discrete probability distribution, a median is by definition any real number *m* that satisfies the inequalities

or, equivalently, the inequalities

in which a Lebesgue–Stieltjes integral is used. For an absolutely continuous probability distribution with probability density function *ƒ*, the median satisfies

Any probability distribution on **R** has at least one median, but there may be more than one median. Where exactly one median exists, statisticians speak of "the median" correctly; even when the median is not unique, some statisticians speak of "the median" informally.

Read more about this topic: Median

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