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Calculating a weighted average
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 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. 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. In the special case, often encountered in practice, where the weights are normalized (i.e. are nonnegative and sum up to 1), the denominator of the fraction simplifies to 1. |
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