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:

$\displaystyle \frac 1 {H_n} := \frac 1 n \left({\sum_{k=1}^n \frac 1 {x_k}}\right)$

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

See Also

• Mean
• Arithmetic Mean Never Less than Harmonic Mean

Sources

• K.G. Binmore: Mathematical Analysis: A Straightforward Approach (1977)... (previous)... (next): $\S 1.12 \ (5)$