Weighted Mean

The weighted mean of a discrete set of numbers {x_1,x_2,...,x_n} with weights {w_1,w_2,...,w_n} is given by


where each weight w_i is a nonnegative real number and


For a continuous set of numbers x(t) parameterized by the variable t defined over the set T and a weight distribution w(t) also defined over T with w(t) nonnegative for all t in T and


the weighted mean of x is given by


Weighted means have many applications in physics, including finding the center of mass and moments of inertia of an object with a known density distribution and computing and electric and magnetic multipole moments of charge and current distributions, respectively.

Weighted means are also commonly used in statistics, for instance, in population studies.

See also

Arithmetic Mean, Mean

This entry contributed by David Terr

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Cite this as:

Terr, David. "Weighted Mean." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

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