A weighted average gives some values more influence than others. It is appropriate when the observations represent different quantities, credits, exposure, or importance.
The formula
Multiply each value by its weight, add the products, and divide by the sum of the weights. If weights already sum to one, the final division is built into the inputs.
A grade example
A test worth 60% scored at 80 and a project worth 40% scored at 90 produce 0.60 x 80 + 0.40 x 90 = 84. The result is not the same as treating both scores as equally important.
Check the weights
Negative weights and a zero total weight usually signal an input problem. The result should normally sit between the smallest and largest values when all weights are positive.
A worked example
Worked example: a 60% test score of 80 and a 40% project score of 90 produce 84, not 85. The larger assessment contributes more to the final average.
Check that weights represent the real allocation and that no observation is accidentally counted twice. The result should stay within the input range when all weights are positive.
Weights should represent exposure or importance, not be chosen only to make an answer look favorable. Keep the original values and weights in the record so the average can be reproduced.
Weighted averages are transparent when the weights represent a real allocation and are stated clearly.
COMMON QUESTIONS
Frequently asked questions
Do weights have to be percentages?
No. Any proportional weights work, as long as the total is not zero.
Can a weighted average be outside the input range?
Not when all weights are positive. A result outside the range suggests negative or inconsistent weights.