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How to use
A weighted average lets each value contribute according to its weight instead of treating every observation equally. Enter matching lists of values and weights to get the weighted mean, weighted sum, total weight and simple mean, plus an optional next value needed to reach a target average. For values 80 and 90 with weights 2 and 3, the weighted mean is (80×2+90×3)/(2+3)=86. If a new item has weight 5 and the target mean is 90, the required value is [90×(5+5)−430]/5=94. Check that 94 is allowed by the real grading scale and that the new weight uses the same scale as the existing weights.
- Enter the values, then enter the same number of weights in matching order.
- Weights may be percentages such as 20,30,50 or proportional coefficients such as 2,3,5; they must be non-negative with a positive total.
- Optionally enter a target average and the next item’s weight to solve the required next value.
How it is calculated
Example
For values 85, 92 and 78 with weights 20, 30 and 50, the weighted sum is 8360 and total weight is 100, so the weighted average is 83.6. The simple average is 85, showing the effect of the weights.
Important notes
Weights are normalized automatically, so 20/30/50 gives the same result as 2/3/5. The calculator does not assume a grading scale or pass threshold. If a required next value lies outside your real allowed range, the target is not achievable with that one item under that range.
Worked examples and interpreting results
Scores 80 and 90 with weights 40 and 60 give a weighted average of 86. The second score has more influence because its weight is larger; an ordinary mean gives both scores equal influence.
| Case | Calculation | Result |
|---|---|---|
| Average with weights 40 and 60 | (80×40 + 90×60) ÷ (40 + 60) | 86 |
| Average with weights 2 and 3 | (80×2 + 90×3) ÷ (2 + 3) | 86 |
| Mean of 80 and 90 with weights 2 and 3 | (80 × 2 + 90 × 3) ÷ (2 + 3) | 86 |
| New value with weight 5 to reach mean 90 | [90 × (5 + 5) − 430] ÷ 5 | 94 |
How to check the result
Relative weights need not total 100; multiplying every weight by the same factor leaves the average unchanged. Match each value to its corresponding weight, and do not use a weight list totaling zero.
Weighted average formula for scores and grades
Multiply each value by its matching weight, sum the products, then divide by the sum of weights. Weighted averages help combine grades with unequal credit hours and measurements with different importance, unlike simple means.
- 80 with weight 2 and 90 with weight 3: (80×2 + 90×3) ÷ (2+3) = 86
- 70 with weight 1 and 90 with weight 4: (70×1 + 90×4) ÷ (1+4) = 86
- 4 with weight 2 and 5 with weight 1: (4×2 + 5×1) ÷ (2+1) = ≈ 4.33
Calculation caution
A zero total weight makes this average undefined. Using an unweighted mean when course credit hours differ can distort the resulting grade.
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Frequently asked questions
Do weights have to add to 100?
No. The formula divides by the actual total weight, so any proportional non-negative weights work.
Can a weight be zero?
Yes. A zero-weight value contributes nothing, but the total weight across all entries must be positive.
How is the next value for a target calculated?
The calculator solves target = (current weighted sum + next value×next weight) ÷ (current total weight + next weight).
Do weights 2 and 3 give the same mean as 20 and 30?
Yes, for the current mean, because every weight is scaled equally. If adding a new item, scale its weight by the same factor as well.
How can I check a weighted mean?
With nonnegative weights and positive total weight, the mean must lie between the smallest and largest positive-weight values. A result outside that range indicates an input or calculation problem.