Calculate a weighted average when some values matter more than others, with a full step-by-step solution.
A weighted mean (or weighted average) gives more influence to some values than others, based on an assigned "weight." It's used whenever different items in your data don't contribute equally to the overall result — for example, exam scores worth different percentages of a final grade, or portfolio returns weighted by investment size.
Unlike a simple mean, which treats every value equally, a weighted mean multiplies each value by its weight before averaging. This means values with larger weights count more toward the final result.
Weighted Mean = Σ(x·w) ÷ ΣwSuppose your final grade is 40% homework (score 90), 35% midterm (score 80), and 25% final exam (score 70). The weights (0.4, 0.35, 0.25) sum to 1, so the weighted mean is: (90×0.4) + (80×0.35) + (70×0.25) = 36 + 28 + 17.5 = 81.5.
A simple mean is really just a special case of the weighted mean where every value has an equal weight. If you enter a weight of 1 for every value, this calculator will return the same result as the average calculator.
No. The formula divides by the sum of the weights, so weights on any consistent scale will work correctly, whether they're percentages, decimals, or raw quantities like hours or units.
A simple mean treats every value equally. A weighted mean multiplies each value by its own weight first, so values with a higher weight have more influence on the final result.
Use a weighted mean whenever different values in your data should not count equally — for example, calculating a course grade from assignments worth different percentages, or a GPA where grades are weighted by course credit hours.
If every value has the same weight, the weighted mean gives exactly the same result as a simple arithmetic mean.