Weighted Mean Calculator
Enter value and weight pairs to get the weighted average — with the simple mean shown for comparison.
From 3 pairs · Σwx = 500, Σw = 6
Compare the two: the weighted mean pulls toward the values carrying the largest weights, while the simple mean treats every value equally.
The weighted mean multiplies each value by its weight, adds those products, and divides by the total weight: Σwx ÷ Σw. For values 90, 80, 70 with weights 3, 2, 1 that is (270 + 160 + 70) ÷ 6 = 500 ÷ 6 = 83.33, higher than the simple mean of 80 because the 90 carries the most weight.
What a weighted mean is
A weighted mean is an average in which some values count for more than others. Instead of treating every number equally, you assign each a weight — how much it should influence the result — then combine them in proportion to those weights. It answers questions the simple mean cannot: what is my course grade when the final exam is worth more than a quiz, or what is the average price when some items sold in far larger quantities?
When every weight is equal, the weighted mean collapses back to the ordinary arithmetic mean. The two differ only when the weights differ, and the gap between them tells you how much the heavier-weighted values are shifting the average.
sum of each value times its weight, divided by the sum of the weights
Worked example
Three exam scores 90, 80, 70 weighted 3, 2, 1.
- 1 Multiply each value by its weight. 90 × 3 = 270, 80 × 2 = 160, 70 × 1 = 70.
- 2 Add the products to get Σwx. 270 + 160 + 70 = 500.
- 3 Add the weights to get Σw. 3 + 2 + 1 = 6.
- 4 Divide Σwx by Σw. 500 ÷ 6 = 83.33 — the weighted mean. The simple mean of 90, 80, 70 is 240 ÷ 3 = 80, so weighting the 90 more heavily raises the average.
Contribution of each pair
Each value’s share of the numerator is its weight times its value (wᵢxᵢ).
| Value (xᵢ) | Weight (wᵢ) | Contribution (wᵢxᵢ) |
|---|---|---|
| 90 | 3 | 270 |
| 80 | 2 | 160 |
| 70 | 1 | 70 |
| Σ | 6 | 500 |
Where weighted means show up
Course grades. A syllabus rarely weights everything equally — a final worth 40% and homework worth 10% call for a weighted mean, with the percentage weights standing in for wᵢ.
Grade point averages. A GPA is a weighted mean of grade points weighted by course credit hours, so a 4-credit course moves your GPA twice as much as a 2-credit one.
Price indices and averages. Consumer price indices and average prices weight each item by how much is bought, so staples influence the figure more than rarely purchased goods. Any time some data points genuinely matter more than others, the weighted mean is the honest average.