Weighted Mean Calculator
A weighted mean is an average in which each value contributes not equally, but in proportion to its own weight (its importance). Midterm-and-final course grades (midterm 40%, final 60%), credit-weighted course averages, and index calculations are all cases where a plain arithmetic mean gives the wrong answer; the correct method is to multiply every value by its weight and divide by the sum of the weights.
All you need to do is enter the values and their matching weights into the two boxes in the same order: the weighted mean, the sum of weights, and — for comparison — the simple mean are computed instantly, together with a table showing each value's contribution and a chart of the weight distribution. It is built for students working out a passing course grade and for anyone producing a credit-weighted average.
Formula
Weighted Mean = (w₁·x₁ + w₂·x₂ + … + wₙ·xₙ) / (w₁ + w₂ + … + wₙ) Example (midterm 40%, final 60%): Grade = (Midterm × 0.40) + (Final × 0.60)
The common mistake is to multiply by the weights and add them up, but forget to divide by the sum of the weights. If the weights are percentages that add up to 100, skipping the division changes nothing; but with weights that do not add up to 100 — course credits, for instance — omitting it makes the result completely wrong.
How to Calculate
- Enter your values (grades, prices, scores) into the first box, in order.
- Enter the weight of each value into the second box, in the same order — the two lists must contain the same number of items.
- Weights can be percentages (40, 60) or credits (3, 4, 2); they do not have to add up to 100.
- Read the weighted mean, the contribution table, and the weight distribution chart in the results section.
Worked Examples
Midterm and final course grade (40% - 60%)
For a student who scores 70 on the midterm and 85 on the final, the course grade is (70×40 + 85×60) / 100 = (2,800 + 5,100) / 100 = 79. The simple mean would be 77.5; because the final carries more weight, the result comes out higher.
Weighted mean: 79.00 · Sum of weights (Σw): 100 · Weighted total (Σw·x): 7,900
Credit-weighted course average
A student who scores 80 in a 4-credit course, 65 in a 3-credit course, and 90 in a 2-credit course has a weighted mean of (320 + 195 + 180) / 9 = 695 / 9 ≈ 77.22. The simple mean would be 78.33.
Weighted mean: 77.22 · Sum of weights (Σw): 9.00 · Weighted total (Σw·x): 695
Weights that do not add up to 100
With the value 100 carrying a weight of 1 and the value 50 carrying a weight of 3, the result is (100×1 + 50×3) / 4 = 250 / 4 = 62.5. The heavier value, 50, pulls the mean toward itself.
Weighted mean: 62.50 · Sum of weights (Σw): 4.00 · Weighted total (Σw·x): 250