Mean

A mean is Homogeneous and has the property that a mean $\mu$ of a set of numbers $x_i$ satisfies

$$\min(x_1,\ldots,x_n)\leq\mu\leq\max(x_1,\ldots,x_n).$$

There are several statistical quantities called means, e.g., Arithmetic-Geometric Mean, Geometric Mean, Harmonic Mean, Quadratic Mean, Root-Mean-Square. However, the quantity referred to as ``the'' mean is the Arithmetic Mean, also called the Average.

See also Arithmetic-Geometric Mean, Average, Generalized Mean, Geometric Mean, Harmonic Mean, Quadratic Mean, Root-Mean-Square