StatReason

Weighted Mean Calculator

Combine a set of values where some should count more than others, using explicit weights you provide.

What this answers

A weighted mean answers "what is the average value, when some observations should count more heavily than others?" A common example is averaging grades where each course carries different credit hours, or combining group averages where the groups have different sizes. A plain, unweighted mean would treat every entry equally, silently distorting the result whenever the weights genuinely differ.

How it is calculated

Each value is multiplied by its weight, those products are summed, and the total is divided by the sum of the weights themselves, not by the count of values. A weight of zero excludes that entry from the result entirely rather than treating it as a zero value, and this calculator reports how many zero-weight entries were excluded so that effect is never silent.

Worked example

For values 1 and 3 with weights 1 and 3: the weighted sum is (1 times 1) plus (3 times 3), which is 1 plus 9, equal to 10. The total weight is 1 plus 3, equal to 4. The weighted mean is 10 divided by 4, which is 2.5, pulled toward the value 3 because it carries three times the weight of the value 1.

Assumption audit

Calculated from your data: the total weight, whether any weights are zero, and whether the value and weight lists match in length.
Evidence to review: whether your chosen weights actually reflect what you intend (sample size, importance, credit hours), since a mismatched weighting scheme will produce a technically correct but misleading average.
You must verify: that a weight genuinely represents what you intend it to (such as a true sample size or a precision weight), not merely a preference score, since this calculator treats any nonnegative number you supply as a valid weight.

Common mistakes

Combining several group averages using a plain, unweighted mean of those averages is a frequent error: if the groups have different sizes, the correct combined average must weight each group average by its own group size, not treat every group equally regardless of how many observations it contains. Using the plain Mean Calculator on a set of group averages silently assumes every group is the same size, which is rarely true in practice.

Limitations

A weight is not automatically a sample size or a precision weight; this calculator uses whatever number you supply exactly as given. Negative weights are rejected since they would not correspond to a meaningful combination of values, and a weight of exactly zero removes that entry entirely rather than counting it as a value of zero.