Weighted harmonic mean - Definition

In statistics, given a set of data,

X = { x₁, x₂, ..., x_n}

and corresponding weights,

W = { w₁, w₂, ..., w_n}

the weighted harmonic mean is calculated as

<math> \bar{x} = \sum_{i=1}^n w_i \bigg/ \sum_{i=1}^n \frac{w_i}{x_i} <math>

Note that if all the weights are equal, the weighted geometric mean is the same as the harmonic mean.

Weighted versions of other means can also be calculated. Probably the best known weighted mean is the weighted arithmetic mean, usually simply called the weighted mean. Another example of a weighted mean is the weighted geometric mean.

See also

average, summary statistics, central tendency

References

• http://mathworld.wolfram.com/ChisiniMean.html