# Mean

The mean of a set of real numbers usually refers to the arithmetic mean of the set (also known as the average). For example, the arithmetic mean of the members of the set {3, 5, 10} is

$\frac{3 + 5 + 10}{3} = \frac{18}{3} = 6.$

However, there are numerous other kinds of various means used in mathematics and statistics.

## Types of Means

The arithmetic mean, geometric mean, harmonic mean, and root mean square are all special cases of the power mean.

## Inequalities and Optimization

There are numerous inequalities that relate different types of means. The most common are part of the RMS-AM-GM-HM inequality chain. This inequality chain is a set of special cases of the Power mean inequality.