Means

Definition: Means

Let $a_1,\dots ,a_n$ be a list of real numbers.

The harmonic mean of $a_1,\dots ,a_n$ is

$$\frac{n}{\frac{1}{a_1}+\cdots +\frac{1}{a_n}}=\frac{n}{{\sum }_{k=1}^n\frac{1}{a_k}}$$

The geometric mean of $a_1,\dots ,a_n$ is

$$\sqrt[n]{a_1\times \cdots \times a_n}$$

The arithmetic mean of $a_1,\dots ,a_n$ is

$$\frac{a_1+\cdots +a_n}{n}=\frac{1}{n}\sum _{k=1}^n{a}_k$$

The root-mean square or quadratic mean of $a_1,\dots ,a_n$ is

$$\sqrt{\frac{a_1^2+\cdots +a_n^2}{n}}$$