## ::Weighted arithmetic mean

### ::concepts

Weighted::sigma Right::weights Variance::mathbf Sample::weighted Mathrm::class Sigma::begin

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The **weighted arithmetic mean** is similar to an ordinary arithmetic mean (the most common type of average), except that instead of each of the data points contributing equally to the final average, some data points contribute more than others. The notion of weighted mean plays a role in descriptive statistics and also occurs in a more general form in several other areas of mathematics.

If all the weights are equal, then 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 counterintuitive properties, as captured for instance in Simpson's paradox.

**Weighted arithmetic mean sections**

Intro Examples Mathematical definition Statistical properties Dealing with variance Weighted sample variance Weighted sample covariance Vector-valued estimates Accounting for correlations Decreasing strength of interactions Exponentially decreasing weights Weighted averages of functions See also Notes Further reading External links

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