How to calculate a weighted average
A weighted average is used when not every value in a set carries the same importance. Instead of adding everything up and dividing by the count (like a simple average), each value is multiplied by its weight before the sum, and the result is divided by the sum of the weights, not by the number of values.
Formula
weighted average = (value1 × weight1 + value2 × weight2 + ... + valueN × weightN) ÷ (weight1 + weight2 + ... + weightN). A grade of 8 with weight 2 and a grade of 6 with weight 3 give (8 × 2 + 6 × 3) ÷ (2 + 3) = 6.8.
Where weighted averages show up
It's the basis of grading on school report cards (an exam counts more than an assignment), of GPA calculations at universities (courses with different credit hours count differently), of financial indices (an investment portfolio weights each asset by the amount invested), and of surveys (responses from larger groups can carry more weight than smaller ones).
Example with school grades
In a term with an exam (weight 5), an assignment (weight 3), and participation (weight 2), grades of 7, 9, and 10 respectively give a weighted average of (7 × 5 + 9 × 3 + 10 × 2) ÷ 10 = 8, even though the simple average of those three values would be 8.67. The difference shows the effect of giving the exam more weight.
Relative weight
The relative weight table shows what share of the total weight each item represents. That makes it easier to see which values are really pulling the final result up or down, something that isn't obvious from the raw numbers alone.