Weighted mean - Definition and Overview

In statistics, given a set of data,

X = { x₁, x₂, ..., x_n}

and corresponding weights,

W = { w₁, w₂, ..., w_n}

the weighted mean is calculated as

<math>

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

Note that if all the weights are equal, the weighted mean is the same as the arithmetic mean. While weighted means generally behave in a similar fashion to arithmetic means, they do have a few counter-intuitive properties, as captured for instance in Simpson's paradox.

Weighted versions of other means can also be calculated. Examples of such weighted means include the weighted geometric mean and the weighted harmonic mean.

See also

average, summary statistics, central tendency