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.
