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.