Weighted average

Weighted averages are a way to combine the averages of two data sets of different sizes. This is similar to calculating sum totals on a histogram.

For example, two classes are described. Class A has 10 students who had an average test score of 75. Class B has 15 students with an average test score of 90. A question might then ask what the combined average of the two classes is.

The most basic way is to simply calculate the total scores of both groups: number of students  • average score, and then add those two totals together and divide by the total number of students.

(75 •10) + (90•15) = 750 + 1350 = 2100 

210025=84

The other way to do this is to take the ratio of the two numbers of students, and then weight each of the averages according to that ratio.

# Students in Group A# Students in Group B=1015=23 There are 2 students in group A for every 3 students in group B. Multiply both averages by their weights in the ratio, and then divide by the total number of students within that ratio.

(75•2) + (90•3) = 150 + 270 = 420 

4205=84

The math is the same as above, but scaled down by a factor of 5, which makes the numbers a bit easier to work with.

Finally, one can also take the ratio numbers, and use them to calculate which portion of each average should be used for the weight average.

Group A weight = 

25 Group A Weight * Group A Average 

25∙75=30

Group B weight = 

35 Group B Weight * Group B Average 

35∙90=54

54 + 30 = 84

Any of these methods yields the same number, so students should choose whichever seems most easy or intuitive to them.