mean

This is the number most commonly used as the average. It may be called the arithmetic mean to distinguish it from other means such as those described below. When each number ai is to have weight wi  >  0, the weighted mean is equal to

The geometric mean of the positive numbers a1, a2,…, an is

It is a theorem of elementary algebra that, for any positive numbers a1, a2,…, an, the arithmetic mean is greater than or equal to the geometric mean; that is,

The harmonic mean of positive numbers a1, a2,…, an is the number h such that 1/h is the arithmetic mean of 1/a1, 1/a2,…, 1/an. Thus

For any set of positive numbers, a1, a2,…, an the harmonic mean is less than or equal to the geometric mean, and therefore also the arithmetic mean, and equality takes place for all three measures if and only if all the terms in the set are equal.

In statistics, the mean of a sample of observations x1, x2,…, xn is called the sample mean and is denoted by so that

The mean of a random variable X is equal to the expected value E(X). This may be called the population mean and denoted by µ. A sample mean may be used to estimate µ.

See also arithmetic-geometric mean iteration.

• sector
• segment
• selection
• selection bias
• self-adjoint
• self-inverse
• self-reference
• self-selected samples
• self-similarity
• semi-
• semicircle
• semi-decidable
• semi-direct product
• semigroup
• semi-interquartile range
• semi-metric
• semi-norm
• semiprime
• semi-regular polyhedron
• semi-regular tessellation
• semi-vertical angle
• sense
• sensitivity analysis
• separable
• separable