Weighted Average Calculator

WA = Σ(value × weight) / Σ(weight). Generalizes the arithmetic mean.

Inputs

Result

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General calculation reads

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Jordan Ellenberg - math thinking
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The Joy of X
Steven Strogatz - accessible math
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Scientific calculator (Casio fx-991EX)
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How to use this calculator

  • Enter values + corresponding weights.
  • Weights need not sum to 1 (formula normalizes).

About this calculator

Weighted average: each value contributes proportionally to its weight. Used for: GPA (course credits = weights), portfolio returns (asset values = weights), survey responses with population adjustment, course grade with categories of different weights. If all weights equal, reduces to arithmetic mean.

Frequently asked

Weights sum to 1?+
Convenient but not required. Formula divides by Σweights, so any positive weights work.
Difference from arithmetic mean?+
AM treats all values equal. WA lets some values count more (or less). AM = WA when all weights are equal.
GPA example?+
3-credit A (4.0) + 4-credit B (3.0) + 1-credit A (4.0): (4×3 + 3×4 + 4×1)/(3+4+1) = 28/8 = 3.5.
Negative weights?+
Mathematically valid but unusual. Some applications (signed averages, optimization) use them.
Connection to expected value?+
Same formula. E[X] = Σ x × P(x) — values weighted by probability.

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