The weighted mean of a discrete set of numbers with weights is given by
(1)
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where each weight is a nonnegative real number and
(2)
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For a continuous set of numbers parameterized by the variable defined over the set and a weight distribution also defined over with nonnegative for all and
(3)
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the weighted mean of is given by
(4)
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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.