Weighted Average Calculator

How to use?

Put the values in one column and the weight that matches each one in the other, always one per line and in the same order. Picture 4 tests with grades 8.5, 7.0, 9.5, 6.0 and weights 3, 2, 4, 1. The weighted mean works out as (8.5×3 + 7.0×2 + 9.5×4 + 6.0×1) ÷ (3+2+4+1).

Weighted mean: formula and example

The weighted mean is defined as MP = Σ(xᵢ·pᵢ) / Σpᵢ, where each value xᵢ contributes proportionally to its weight pᵢ. Unlike the arithmetic mean, which treats every observation equally, the weighted mean reflects that some values matter more. Example (grades): test 1 score 7 with weight 2, test 2 score 9 with weight 3 → MP = (7·2 + 9·3)/(2+3) = 41/5 = 8.2. If all weights are equal, the weighted mean reduces to the arithmetic mean. Weights must be non-negative and their sum must be positive.

Applications

Academic grading: GPA (grade point average) and Brazilian CR (coeficiente de rendimento) weight courses by credit hours. ENEM uses item response theory, which is implicitly a weighted scheme by item difficulty. Economics: the IPCA (Brazilian CPI) weights each item by its share of household spending. Finance: a portfolio's return is the weighted mean of asset returns by capital allocated. Statistics: meta-analysis combines studies weighted by inverse variance.

FAQ

Do weights need to sum to 1? No. The formula divides by Σpᵢ, so any positive scale works. Normalizing to 1 (percentages) is convenient but not required.

Can a weight be zero? Yes — a zero-weight value is simply excluded. Negative weights are not standard and break the interpretation.

Weighted mean vs arithmetic mean? If all weights are equal, both give the same result. When weights differ, the weighted mean shifts toward values with higher weight.