The median of a finite list of numbers is the "middle" number, when those numbers are listed in order from smallest to greatest.
If the data set has an odd number of observations, the … See more

Optimality property
The mean absolute error of a real variable c with respect to the random variable X is
Provided that the probability distribution of X is such that the … See more

The sample median
Efficient computation of the sample median
Even though comparison-sorting n items requires Ω(n log n) operations, selection algorithms can compute the kth-smallest of n items with … See more

Interpolated median
When dealing with a discrete variable, it is sometimes useful to regard the observed values as being midpoints of underlying continuous intervals. An example of this is a Likert scale, on which opinions or preferences are … 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 … See more

Jensen's inequality states that for any random variable X with a finite expectation E[X] and for any convex function f
This inequality generalizes to the median as well. We say a function f: R → R is a C function if, for any t,
is a See more

Previously, this article discussed the univariate median, when the sample or population had one-dimension. When the dimension is two or higher, there are multiple concepts that extend the definition of the univariate median; each such multivariate median … See more