Weighted Mean

The weighted mean of a discrete set of numbers with weights is given by

(1)

where each weight is a nonnegative real number and

(2)

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)

the weighted mean of is given by

(4)

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.