Means

Definition: Means

Let \(a_1, \dotsc, a_n\) be a list of [[The Real Numbers|real numbers]].

The harmonic mean of \(a_1, \dotsc, a_n\) 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 \(a_1, \dotsc, a_n\) is

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

The arithmetic mean of \(a_1, \dotsc, a_n\) 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 \(a_1, \dotsc, a_n\) is

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