related topics
{math, number, function}
{rate, high, increase}
{household, population, female}

In probability theory and statistics, a median is described as the numeric 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.[1][2]

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), and, 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 less than the median, and, at most, half have values greater than the median. If both groups contain 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 {abc} is b, and, if a < b < c < d, then the median of the list {abcd} 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. A disadvantage of the median is the difficulty of handling it theoretically.[citation needed]


Full article ▸

related documents
Best, worst and average case
Kolmogorov-Smirnov test
Log-normal distribution
Cauchy distribution
Whittaker–Shannon interpolation formula
Search engine (computing)
Range encoding
Partial fractions in integration
Real line
Regular space
T1 space
Euler's criterion
Stirling number
Dyadic rational
Heaviside step function
Intersection (set theory)
Cayley's theorem
Magma computer algebra system
Polynomial time
Borel-Cantelli lemma
Category (mathematics)
Magma (algebra)
Nowhere dense set
Separated sets
Syntactic sugar
Double negative elimination
Twin prime conjecture