Weighted arithmetic mean

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

${\bar {x}}={\frac {\sum _{i=1}^{n}w_{i}\cdot x_{i}}{\sum _{i=1}^{n}w_{i}}}.$

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, but are not commonly used.

See also

average, summary statistics, central tendency