How this calculator works
A weighted average gives each value a share of the final result. Multiply every value by its weight, add the products and divide by the total of the weights. A value with weight 2 counts twice as much as one with weight 1, and a weight of zero removes a value entirely. If the weights add to 1 the division changes nothing, but weights do not have to be normalised; only their relative sizes matter.
Formula
Weighted average = (w₁x₁ + w₂x₂ + ... + wₙxₙ) / (w₁ + w₂ + ... + wₙ), with at least one weight above zero.
Worked example
For values 80, 90 and 70 with weights 1, 2 and 3, the numerator is 80 + 180 + 210 = 470 and the weights total 6, so the weighted average is 470/6 ≈ 78.333. The unweighted mean is 240/3 = 80.
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Frequently asked questions
What is the difference between a weighted average and a simple mean?
A simple mean gives every value the same weight. A weighted average lets some values count more, which is appropriate when entries come from groups of different sizes or carry different importance.
Do the weights need to add up to 1 or 100?
No. Dividing by the sum of the weights normalises them automatically. Scaling every weight by the same factor leaves the weighted average unchanged.
Can a weight be negative?
Mathematically a negative weight can be defined, but it makes short positions and odd cancellations possible and the result is no longer a weighted mean in the usual sense. This calculator accepts only non-negative weights.
When can a zero weight be useful?
A zero weight excludes a value without deleting it from the list, which is handy when a category is present but currently contributes nothing. At least one weight must remain above zero so the division is defined.