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Weighted Mean

Statistical Glossary

Weighted Mean:

The weighted mean is a measure of central tendency . The weighted mean Math image of a set of Math image values Math image is computed according to the following formula:


  • Math image are non-negative coefficients, called “weights”, that are ascribed to the corresponding values Math image .

Only the relative values of the weights Math image matter in determining the value of the weighted mean. In other words, if you multiply each weight Math image by a positive value Math image and recalculate the weighted mean with new weights Math image , then the value Math image remains the same.

The greater the weight Math image in respect to other weights, the greater the contribution of the corresponding datum Math image into the resultant value Math image of the weighted mean.

The weighted mean is used, for example, to aggregate a set of scores (e.g. examination scores on different subjects) to a single resultant score. In this case, the magnitude of the weights Math image reflects the importance of their respective subjects. (For this reason, the weighted mean is sometimes named the aggregate mean ).

Besides its use as a descriptive statistic , the weighted mean is also used to construct filters .

See also Mean values (comparison) and the online short course Basic Concepts in Probability and Statistics

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