Weighted Mean
The weighted mean of a discrete set of numbers ![<span style=]()
{x_1,x_2,...,x_n}" src="http://mathworld.wolfram.com/images/equations/WeightedMean/Inline1.gif" style="height:14px; width:87px" /> with weights ![<span style=]()
{w_1,w_2,...,w_n}" src="http://mathworld.wolfram.com/images/equations/WeightedMean/Inline2.gif" style="height:14px; width:93px" /> 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.
