What is a weighted average?

Answer 1

A weighted average multiplies each data point by an arbitrary 'weight' and divides by the sum of the weights. Your everyday garden variety average, or arithmetic mean, is actually a special case of a weighted average, except all the weights are equal to 1.

Selection of weights are largely arbitrary but generally based on sound reasoning (e.g. relative population sizes). As another example, let's say you have 5 reviewers of a product giving their overall satisfaction rating. The scores are 9, 7, 6, 7, 3. However you have a very high regard for Reviewer 1 so you assign her a weight of 15 (and the others remain at weight=1).

The average score is (9+7+6+7+3)/5=6.4

The weighted average score is (15*9+7+6+7+3)/(15+4)=8.3

The weighted average is much closer to Review 1's opinion due to your weighting decision.

The weight is often NOT arbitrary as in the above example. If a bank wants to know the average interest rate for its portfolio, the weight is the principal balance of each loan. If there are only two loans, one for $999,990 at 6% and one for $10 at 12%, the AVERAGE RATE is 9% [(6 + 12)/2]. However, the weighted average rate is only 6.00006% [(((.06*999990)+(.12*10))/1000000)].