Loosely speaking, a mean is a way to describe a collection of numbers such that the mean in some sense describe the “average” entry of these numbers. The most familiar mean is the arithmetic mean, and unless otherwise noted, by mean, we always mean the arithmetic mean.

Example

Mathematically, we define a mean as follows:

Definition

• is a homogeneous function of degree 1. That is, if is a multiset, then
  
• For any set of real numbers,
  

Pythagoras identified three types of means: the arithmetic mean, the geometric mean, and the harmonic mean. However, in the sense of the above definition, there is a wealth of ther means too. For instance, the minimum function and maximum functions can be seen as “trivial” means. Other well-known means include:

• median,
• mode,
• arithmetic-geometric mean,
• arithmetic-harmonic mean,
• harmonic-geometric mean,
• root-mean-square (sometimes called the quadratic mean),
• identric mean,
• contraharmonic mean,
• Heronian mean,
• Cesàro mean,
• maximum function, minimum function