Enter your values and their corresponding weights into the Weighted Mean Calculator to compute a weighted average where each value contributes proportionally to its importance. Add as many value-weight pairs as you need — the calculator returns the weighted mean, sum of weights, and a full breakdown of how each pair contributes to the final result.
Weighted Mean
--
Sum of Weights
--
Sum of (Value × Weight)
--
Valid Value-Weight Pairs
--
Use the weighted mean when different values contribute unequally to the overall result — for example, grades with different credit hours, or items with different quantities. The regular (arithmetic) mean treats all values equally. If every value is equally important, both methods give the same answer.
The weighted mean is calculated as μw = (w₁x₁ + w₂x₂ + … + wₙxₙ) ÷ (w₁ + w₂ + … + wₙ). You multiply each value by its weight, sum all those products, then divide by the total sum of the weights.
Weights should reflect the relative importance or frequency of each value. For course grades, the credit hours are a natural weight. For financial portfolios, the proportion of capital invested in each asset works well. Weights don't need to sum to any specific number — the formula handles normalization automatically.
Yes, weights can be any positive real number including decimals and fractions. For example, weights of 0.25, 0.50, and 0.25 work perfectly. Just ensure no weight is negative, as negative weights don't have a standard statistical interpretation in most contexts.
Yes, the values (x) you are averaging can be negative numbers. Only the weights themselves should be non-negative. The formula works correctly with any real-number values, so negative temperatures, returns, or scores are all valid inputs.
Yes, exactly. When every weight is the same — whether all 1s, all 2s, or any equal value — the weighted mean simplifies to the arithmetic mean. The equal weights cancel out during division, leaving you with a simple sum divided by count.
The sum of weights is the denominator in the weighted mean formula — it represents the total relative importance across all your data points. A larger sum of weights isn't better or worse; it simply normalizes the weighted sum so the result sits within the range of your original values.
Yes. Enter each possible outcome as a value and its probability as the corresponding weight. Make sure all probabilities (weights) sum to exactly 1. The weighted mean then equals the expected value (E[X]) of that discrete random variable.