What Is a Weighted Average?

A weighted average assigns each value a weight that reflects its relative importance, then computes Σ(wᵢ·xᵢ) ÷ Σwᵢ. It appears everywhere: final grades (exams worth more than quizzes), stock portfolios (large holdings move returns more), and economics (price indices weight goods by how much people buy).

How to Calculate a Weighted Average

Weighted Average = Σ(wᵢ × xᵢ) ÷ Σwᵢ — multiply each value by its weight, add the products, then divide by the total weight. If weights are percentages summing to 100, the division is simply by 100. The weights do not need to sum to 100; they just need to be positive.

Weighted vs Simple Average

The simple average treats every observation equally. The weighted average is the same formula with all weights set equal. When your data is naturally unequal — larger accounts, heavier assignments, bigger market segments — the weighted average is the honest summary, because a 10% gain in a position that is half your portfolio matters far more than the same gain in a tiny holding.