Formally, a median of a population is any value such that at least half of the population is less than or equal to the proposed median and at least half is greater than or equal to the proposed median. As seen … See more

The median can be used as a measure of location when one attaches reduced importance to extreme values, typically because a distribution is See more

Optimality property
The mean absolute error of a real variable c with respect to the random variable X is
$${\displaystyle E(\left|X-c\right|)\,}$$
Provided that the probability distribution of X is such that the above expectation exists, then m is a … See more

Efficient computation of the sample median
Even though comparison-sorting n items requires See more

For any real-valued probability distribution with cumulative distribution function F, a median is defined as any real number m that satisfies the inequalities
An equivalent phrasing uses a random variable X distributed according to F:
Note that this … See more

Jensen's inequality states that for any random variable X with a finite expectation E[X] and for any convex function f
$${\displaystyle f[E(x)]\leq E[f(x)]}$$
This inequality … See more

Previously, this article discussed the univariate median, when the sample or population had one-dimension. When the dimension is two or … See more