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.