Weighted harmonic mean

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In statistics, given a set of data,

X = { x1, x2, ..., xn}

and corresponding weights,

W = { w1, w2, ..., wn}

the weighted harmonic mean is calculated as

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

Note that if all the weights are equal, the weighted harmonic 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.

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