How this instrument works
An ordinary mean treats every value as equally important, giving each one exactly 1 ⁄ n of the final say. A weighted average instead lets some values count for more than others by attaching a weight to each one: weighted average = (v₁w₁ + v₂w₂ + v₃w₃) ⁄ (w₁ + w₂ + w₃), the sum of every value multiplied by its own weight, divided by the total of all the weights. A larger weight pulls the result toward that value harder; a smaller weight barely moves it at all.
This is exactly how a course grade built from differently weighted assignments is computed — a final exam worth 40% of the grade should influence the overall figure four times as much as a homework set worth only 10%, and this calculation is precisely the tool that makes that happen correctly, where a plain mean of the raw scores would not.
When every weight is set equal to each other, the formula reduces exactly to the ordinary, unweighted mean — the weights cancel out of both the numerator and denominator proportionally, leaving the plain sum-divided-by-count result. This calculation is best understood as the more general tool, with a plain mean sitting inside it as the special case where nothing is actually weighted differently.
- Enter the first value and its weight into the Value 1 and Weight 1 fields.
- Enter the second value and its weight into the Value 2 and Weight 2 fields.
- Enter the third value and its weight into the Value 3 and Weight 3 fields.
- Read Weighted average: the sheet multiplies each value by its own weight, sums those products, and divides by the total weight.
Worked example — three values weighted 2, 3, and 1
Three values, 80, 90, and 70, carry weights of 2, 3, and 1 respectively. The result is (80×2 + 90×3 + 70×1) ⁄ (2+3+1) = (160+270+70) ⁄ 6 = 500 ⁄ 6 ≈ 83.33 — pulled closer to 90, the most heavily weighted value, than a plain unweighted mean of the same three numbers (which would land at exactly 80) would suggest.
As a check, set all three weights equal (1, 1, and 1) on the same three values: the figure becomes (80+90+70) ⁄ 3 = 80, exactly the ordinary mean — confirming that equal weights make this formula collapse back down to the plain calculation everyone already knows.
Questions
What is a weighted average?
It's a mean where each value counts according to its own assigned weight rather than equally. Values with larger weights pull the final figure toward themselves more strongly than values with smaller weights, unlike a plain mean, which gives every value the same say.
What is the formula for a weighted average?
weighted average = Σ(value × weight) ⁄ Σweight — multiply each value by its own weight, add those products together, then divide by the sum of all the weights. This normalizes the result back to a genuine mean rather than a raw, inflated total.
How is this different from a plain average?
A plain mean is the special case of this calculation where every weight happens to be equal — the weights cancel out proportionally, leaving the ordinary sum-divided-by-count result. This weighted version is the more general tool, needed whenever the values genuinely don't deserve equal influence.
Is a course grade a weighted average?
Yes, typically — assignments, quizzes, and exams usually carry different weights (say, 10%, 20%, and 40% of the final grade), and combining those component scores into one overall grade correctly requires exactly this calculation rather than a plain mean of the raw scores.
What happens if all the weights are zero?
The result is undefined, since dividing by a total weight of zero has no meaningful answer — at least one weight must be positive for a genuine weighted figure to exist.