Statistics
Weighted average
Sum every value times its weight, then divide by the sum of weights. Weights may be percentages, counts, or ratios — only their relative size matters.
The Formula
Weighted Average = (v1 x w1 + v2 x w2 + v3 x w3) / (w1 + w2 + w3)
Sum every value times its weight, then divide by the sum of weights. Weights may be percentages, counts, or ratios — only their relative size matters.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| vi | Each value being averaged | number | Scores, returns, unit costs — anything you would otherwise average. |
| wi | Weight for that value | weight | Its relative importance. Use shares summing to 100, or any consistent proportional set. |
| vw | Weighted average | number | Always falls between the smallest and largest value in the set. |
What Each Symbol Means
vinumber
Each value being averaged
Scores, returns, unit costs — anything you would otherwise average.
wiweight
Weight for that value
Its relative importance. Use shares summing to 100, or any consistent proportional set.
vwnumber
Weighted average
Always falls between the smallest and largest value in the set.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate a weighted average page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Calculate A Weighted Average, filed under Math. Every number the guide produces comes from substituting into this one line.