# 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

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

## Types of Means

- Arithmetic mean
- Geometric mean
- Harmonic mean
- Power mean
- quadratic mean (also known as the root mean square)

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.