Definition:Harmonic Mean

Definition
Let $x_1, x_2, \ldots, x_n \in \R$ be real numbers which are all strictly positive.

The harmonic mean $H_n$ of $x_1, x_2, \ldots, x_n$ is defined as:


 * $\ds \dfrac 1 {H_n} := \frac 1 n \paren {\sum_{k \mathop = 1}^n \frac 1 {x_k} }$

That is, to find the harmonic mean of a set of $n$ numbers, take the reciprocal of the arithmetic mean of their reciprocals.

Also see

 * Definition:Mean


 * Definition:Arithmetic Mean
 * Definition:Geometric Mean
 * Definition:Hölder Mean


 * AM-HM Inequality
 * GM-HM Inequality