Mean, median and mode
Find mean, median, all repeated modes, range, sum and a sorted list. See how an outlier changes the average compared with the middle value.
Weighted average calculator with contribution steps
Give observations different influence with explicit nonnegative weights. Enter one value and one weight per row. The weights do not have to sum to one or one hundred: the calculation divides by their actual total.
Free to use, with no sign-in. Inputs and results stay in this page and are not sent with the form. Download a result before leaving; this tool does not save your work.
Worked result
The weighted average is 78.
- Multiply each value by its own weight.
- Add the three products to obtain 7800.
- Divide by the total weight, 100.
Combine three assessments weighted 20, 30 and 50
The illustrative scores are 80, 90 and 70. Their weights sum to 100, so the weighting can also be read as percentages.
Weighted total = 80×20 + 90×30 + 70×50
= 1600 + 2700 + 3500 = 7800
Total weight = 20 + 30 + 50 = 100
Weighted average = 7800/100 = 78The ordinary mean is 80, but the lowest score receives the largest weight. A result of 78 is therefore plausible. Changing all weights from 20, 30, 50 to 2, 3, 5 leaves the weighted mean unchanged.
Normalize by the weights you actually have
A weighted mean is a sum of weighted values divided by the sum of the weights. Zero-weight rows contribute nothing. At least one weight must be positive to determine a result.
Weights can represent frequencies, time spent, credits or a chosen allocation. Those interpretations are not interchangeable. For example, averaging rates across groups usually needs the relevant exposure or denominator, rather than an unweighted mean of group percentages.
weighted average = Σ(value × weight)/Σ(weight)
normalized weight = weight/Σ(weight)
contribution = value × normalized weightInput limits and common mistakes
Each row must contain exactly two finite numbers: value followed by weight. Negative weights are rejected. Up to 1,000 rows are accepted; values and weights are bounded to absolute magnitude 1e100.
The calculation is a weighted arithmetic mean, not a geometric mean, an investment-return model or a policy decision about missing assessments. Missing rows are not inferred, and omitted assessments are not automatically treated as zero.
Questions about weighted average
Must weights sum to 100?
No. Weights 20, 30, 50 and 2, 3, 5 produce the same answer because both sets normalize to the same shares.
How do I combine averages from different group sizes?
Use each group’s average as its value and its actual group size as its weight, when the groups measure the same quantity and do not overlap.
Why reject a zero total weight?
There is no normalized allocation when all weights are zero. Dividing by a zero total weight is undefined.
Sources and verification
These references explain the formulas or formats. The worked examples above were created for this tool and checked against independent calculations or format round trips. AI-assisted development does not imply a named human expert review.
- OpenStax: means and frequency-weighted calculations — Means calculated from frequencies and the interpretation of center.
Published 2026-10-23. Examples are illustrations, not measurements of a service or claims about search rankings.
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Further reading
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