In statistics and probability theory, **median** is described as the numerical value separating the higher half of a sample, a population, or a probability distribution, from the lower half. The *median* of a finite list of numbers can be found by arranging all the observations from lowest value to highest value and picking the middle one. If there is an even number of observations, then there is no single middle value; the median is then usually defined to be the mean of the two middle values.

A median is only defined on one-dimensional data, and is independent of any distance metric. A geometric median, on the other hand, is defined in any number of dimensions.

In a sample of data, or a finite population, there may be no member of the sample whose value is identical to the median (in the case of an even sample size); if there is such a member, there may be more than one so that the median may not uniquely identify a sample member. Nonetheless, the value of the median is uniquely determined with the usual definition. A related concept, in which the outcome is forced to correspond to a member of the sample, is the medoid. At most, half the population have values strictly less than the *median*, and, at most, half have values strictly greater than the median. If each group contains less than half the population, then some of the population is exactly equal to the median. For example, if *a* < *b* < *c*, then the median of the list {*a*, *b*, *c*} is *b*. If *a* <> *b* <> *c* as well, then only *a* is strictly less than the median, and only *c* is strictly greater than the median. Since each group is less than half (one-third, in fact), the leftover *b* is strictly equal to the median (a truism).

Likewise, if *a* < *b* < *c* < *d*, then the median of the list {*a*, *b*, *c*, *d*} is the mean of *b* and *c*; i.e., it is (*b* + *c*)/2.

The median can be used as a measure of location when a distribution is skewed, when end-values are not known, or when one requires reduced importance to be attached to outliers, e.g., because they may be measurement errors.

In terms of notation, some authors represent the median of a variable *x* either as or as There is no simple, widely accepted standard notation for the median, so the use of these or other symbols for the median needs to be explicitly defined when they are introduced.

Read more about Median: Measures of Location and Dispersion, Medians of Probability Distributions, Medians in Descriptive Statistics, Jensen's Inequality For Medians, Multivariate Median, Median-unbiased Estimators, History

### Other articles related to "median":

**Median**- History

... The idea of the

**median**originated in Edward Wright's book on navigation (Certaine Errors in Navigation) in 1599 in a section concerning the determination of ... a regression method based on the L1 norm and therefore implicitly on the

**median**... The distribution of both the sample mean and the sample

**median**were determined by Laplace in the early 1800s ...

...

**Median**household income in 2000 was $72,568 ...

**Median**home cost in ZIP 91364 is (2007) $944,500 and cost of living in ZIP 91364 is (2007) 76.26% higher than the U.S ... Woodland Hills neighborhood statistics population 59,661

**median**household income $89,946 ...

... The

**median**age was 37 years ... The

**median**household income was $39,895, and the

**median**family income was $45,088 ... Males had a

**median**income of $31,973 versus $22,252 for females ...

... The

**median**age was 36 years ... The

**median**household income was $27,335 and the

**median**family income was $31,843 ... Males had a

**median**income of $26,436 versus $18,665 for females ...

**Median**

... be summarized as follows In general, there is no single formula to find the

**median**for a binomial distribution, and it may even be non-unique ... results have been established If np is an integer, then the mean,

**median**, and mode coincide and equal np ... Any

**median**m must lie within the interval ⌊np⌋ ≤ m ≤ ⌈np⌉ ...