Mean

The mean of a set of real numbers usually refers to the arithmetic mean of the set (also known as the average). 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
• Root mean square (a.k.a. the quadratic mean

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.