How this calculation works
A larger weight gives a value more influence. The two lists must have the same length, and at least one weight must be positive. Zero-weight values do not affect the result.
Weighted mean = sum(value × weight) ÷ sum(weights)A worked example
Values 80, 90 and 100 weighted 1, 2 and 1 produce a weighted average of 90.
Good to know
Assumes the idealized model described above. Use consistent units and independently verify figures before a consequential decision.
A small high-weight group can dominate the result
Scores of 60 and 100 have an ordinary mean of 80. Weight the first score three times as much as the second and the weighted mean becomes 70. The numerical values are unchanged, but their contributions to the summary differ.
Multiplying all weights by the same positive factor does not change the result. Weights 3 and 1, 30 and 10, or 75 and 25 express the same relative influence.
Align each weight with its corresponding value
The first weight belongs to the first value, the second to the second value, and so on. A shifted list can produce a plausible-looking number that answers the wrong question. Both lists must have equal lengths.
Negative weights are outside this tool’s averaging model. Zero weights are permitted, but at least one weight must be positive. Do not average subgroup averages without their appropriate weights if subgroup sizes differ.
A few questions, answered
Do the weights have to sum to 100?
No. The tool normalizes them by their total. Relative proportions are what matter.
Can a value have weight zero?
Yes. It contributes nothing to the weighted mean.