Definition:Harmonic Mean

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

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


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

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


 * Arithmetic Mean is Never Less than Harmonic Mean