Weighted Mean Calculator
Compute a weighted average from a list of values and their weights — where some numbers count more than others — with the sum of weights.
How it works
Weighted mean = Σ(value × weight) ÷ Σ(weight)
A weighted mean lets some values count more than others by multiplying each by a weight before averaging. You sum every value times its weight, then divide by the total of the weights — so a value with double the weight influences the result twice as much. When all weights are equal it collapses back to the ordinary arithmetic mean; the weights only matter when they differ.
Worked example
For values 90, 80, 70 with weights 3, 2, 1, the weighted total is 90·3 + 80·2 + 70·1 = 270 + 160 + 70 = 500, and the weights sum to 6. The weighted mean is 500 ÷ 6 ≈ 83.33 — higher than the plain average of 80 because the largest value carries the most weight.
Sources: Weighted arithmetic mean — Wikipedia
Frequently asked questions
How is a weighted mean different from a normal average?
A normal average treats every value equally; a weighted mean lets each value carry a different importance through its weight. Course grades where exams count more than quizzes, or a portfolio return where bigger holdings matter more, are classic cases where weighting is needed.
Do the weights have to add up to 1?
No. The formula divides by the sum of the weights, so any positive scale works — weights of 3, 2, 1 give the same answer as 0.5, 0.333, 0.167. Weights are often normalized to sum to 1 only for convenience.
Can a weight be zero?
Yes. A weight of zero simply drops that value from the average entirely, as if it were not there. What you cannot have is every weight zero, because dividing by a total of zero is undefined.
Related calculators
For education — check assumptions (sample size, distribution) before using statistics in real decisions.