::Weighted arithmetic mean

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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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