1. Weighted Mean

2. Weighted Mean
The weighted arithmetic mean is similar to an ordinary arithmetic mean (the most common type of average), except that instead of each of the data points contributing equally to the final average, some data points contribute more than others.
The notion of weighted mean plays a role in descriptive statistics and also occurs in a more general form in several other areas of mathematics.
If all the weights are equal, then the weighted mean is the same as the arithmetic mean.

3. The Statistical Properties
Therefore data elements with a high weight contribute more to the weighted mean than do elements with a low weight. The weights cannot be negative. Some may be zero, but not all of them (since division by zero is not allowed).

4. In Excel
To find a weighted average, follow these steps:In a new worksheet, type the following data: A1: Cost B1: Cases A2: $.20 B2: 10 A3: $.30 B3: 40
Type the formula below in any blank cell (it is not necessary to type this formula as an array):=SUMPRODUCT(A2:A3,B2:B3)/SUM(B2:B3) or  =((A2*B2)+(A3*B3))/SUM(B2:B3)
All four sets are identical when examined using simple summary statistics, but vary considerably when graphed

5. In R weighted.mean(x, w, ...) ## GPA from Siegel 1994
wt <- c(5, 5, 4, 1)/15
x <- c(3.7,3.3,3.5,2.8)
xm <- weighted.mean(x, wt) x
an object containing the values whose weighted mean is to be computed. w
a numerical vector of weights the same length as x giving the weights to use for elements of x.