Weighted average method problems and solutions

Also called Weighted Average

A mean where some values contribute more than others.

Mean

When we do a simple mean (or average), we give equal weight to each number.

Here is the mean of 1, 2, 3 and 4:

Add up the numbers, divide by how many numbers:

Mean =  1 + 2 + 3 + 44  =  104  = 2.5

Weights

We could think that each of those numbers has a "weight" of ¼ (because there are 4 numbers):

Mean = ¼ × 1 + ¼ × 2 + ¼ × 3 + ¼ × 4
= 0.25 + 0.5 + 0.75 + 1 = 2.5

Same answer.

 

Now let's change the weight of 3 to 0.7, and the weights of the other numbers to 0.1 so the total of the weights is still 1:

Mean = 0.1 × 1 + 0.1 × 2 + 0.7 × 3 + 0.1 × 4
= 0.1 + 0.2 + 2.1 + 0.4 = 2.8

This weighted mean is now a little higher ("pulled" there by the weight of 3).

 

Decisions

Weighted means can help with decisions where some things are more important than others: