Definition:Harmonic Mean

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This page is about the harmonic mean. For other uses, see Definition: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

  • Results about harmonic mean can be found here.


Sources