Weighted Mean Calculator - Calculate Weighted Average

The weighted mean — also called the weighted average — is a generalization of the arithmetic mean that accounts for the fact that not all values contribute equally to the average. Each value is multiplied by a weight that reflects its importance, frequency, or proportion, and the products are summed and then divided by the total weight. When all weights are equal, the weighted mean reduces to the simple arithmetic mean, which is why the arithmetic mean is a special case of the weighted mean. The formula is x̄w = (w₁x₁ + w₂x₂ + … + wₙxₙ) / (w₁ + w₂ + … + wₙ). The weights can be any positive numbers — they do not need to sum to 1 or to 100. Proportional weights (summing to 1) and percentage weights (summing to 100) give the same result, and so do integer frequency weights. The calculator normalises automatically, so you can enter class sizes, portfolio dollar amounts, or survey response counts directly as weights without converting them to fractions. Grade calculation is one of the most common uses. A course might assign 20% weight to homework, 30% to the midterm, and 50% to the final. If a student scores 88 on homework, 72 on the midterm, and 84 on the final, the weighted mean is (0.20×88 + 0.30×72 + 0.50×84) / 1.0 = (17.6 + 21.6 + 42.0) = 81.2. A simple average of 88, 72, and 84 would give 81.33 — close but different, and the difference grows when weights are very unequal. In finance, the weighted mean is used to compute the average return on a portfolio where each asset has a different dollar value invested. An investor with $10,000 in Asset A (returning 5%), $25,000 in Asset B (returning 8%), and $15,000 in Asset C (returning −2%) has a portfolio return of (10000×0.05 + 25000×0.08 + 15000×(−0.02)) / 50000 = (500 + 2000 − 300) / 50000 = 4.4%. The simple average return of 3.67% would be misleading because Asset B represents half the portfolio. In statistics, the weighted mean arises whenever samples are drawn with unequal probabilities or when sub-group means must be combined: a national average income that properly weights each region by its population, a meta-analysis that weights studies by their sample sizes, or a survey that post-stratifies responses by demographic group. In physics and engineering, the centre of mass is the weighted mean position where the weights are the masses of individual components. The weighted mean is also fundamental to expectation in probability theory: E[X] = Σ xᵢ P(X=xᵢ), which is precisely the weighted mean with probabilities as weights.