Mean
From AoPSWiki
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
- 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.
