The weighted mean, also called the weighted arithmetic 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 function 
on a set 
and a nonnegative function 
on 
satisfying
 |
(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 electric and magnetic multipole moments of charge and current distributions, respectively.
Weighted means are also commonly used in statistics, for instance, in population studies.
