Example from start to finish
Scores 82, 91, and 76 with weights 20, 50, and 30 produce a weighted sum of 8,470. Divide by total weight 100 to obtain 84.7. This Weighted Mean example can be compared with spread around a mean.
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Weighted Mean Calculator
Average values after assigning each observation its own influence. Its weighted mean sits beside the working formula for a quick arithmetic check.
Weighted Mean inputs
Set up the calculation
Where this calculation appears
Course grades, portfolio components, survey groups, product ratings, and blended costs rarely contribute equally. Weighting preserves those different contributions instead of treating every listed value as one identical observation.
What the formula is measuring
A weighted mean multiplies every observation by a weight, adds those products, and divides by the total weight. Equal weights reproduce the ordinary arithmetic mean. For a connected concept in Weighted Mean, see compound growth.
The roles assigned to values and matching weights explain the operation that produces weighted mean.
Manual method
Pair each value with its weight, calculate every product, total the products, total the weights, and divide. If weights are percentages summing to 100, the denominator is 100.
Where the shortcut stops
A common mistake is dividing by the number of values instead of the sum of weights. Also confirm that each weight lines up with the intended value; shifting one list by a position changes the result silently. If the Weighted Mean assumptions do not fit, consider weighted grades.
Keep any applicable units beside the source values; the browser cannot detect a silent mismatch during weighted mean.
Interpreting changes in the inputs
Treat each labeled field as part of the definition, not merely an empty box. The field assignment determines what the displayed weighted mean describes. Convert measured values to compatible units first and retain their original precision until the final rounding choice.
Scaling every weight by the same nonzero factor leaves the answer unchanged. Increasing one weight pulls the mean toward its paired value rather than necessarily making the mean larger. Predict that movement before recalculating the weighted mean; disagreement points to an input-role or sign issue.
A weighted mean is not a weighted sum. Division by total weight normalizes the result back to the scale of the original values. Here the requested quantity is specifically weighted mean.
Report the weighted mean at a precision justified by the inputs. A long browser decimal is computational detail, not evidence that the source values were measured that accurately. When an exact symbolic form is conventional, keep it beside the rounded value so later work is not forced to reuse an early approximation.
Keep the supplied inputs with the result, including any units and the final rounding place. The displayed formula then preserves how the weighted mean was obtained.
Answers to common follow-ups
Must weights add to 100?
No. Any consistent positive scale works because the weighted sum is divided by the weight total.
Can frequency counts be weights?
Yes. A value occurring five times can carry weight 5 without listing it five times.
What if every weight is equal?
The result equals the ordinary arithmetic mean.
May weights be decimals?
Yes. Proportions such as 0.2, 0.5, and 0.3 work directly.
What does a zero weight do?
It removes that value's contribution to both the numerator and denominator.