Weighted Mean Calculator
Weighted average of values with weights — grades, survey answers, prices by quantity — with each weight’s share, the simple mean and the weighted SD.
The weighted mean with the full Σ(value × weight) ÷ Σweight working, each row’s share of the total weight, the simple mean and a weighted standard deviation.
Example: Exam 85 at 40 %, homework 92 at 30 %, project 78 at 30 %: (3,400 + 2,760 + 2,340) ÷ 100 = 85.0, against a simple mean of 85.0 — weights need not add to 100.
Each value counts
as much as its weight.
The formula, what the weights may be, and the standard deviation convention used.
The mean
Multiply each value by its weight, add them up, divide by the sum of the weights: x̄w = Σ wᵢxᵢ / Σ wᵢ. The weights need not sum to 1 or 100 — each is divided by the total — and a value without a weight counts once. With equal weights this is the ordinary mean.
Reading the table
Each row shows its share of the total weight and its product, so the whole working can be checked by hand. Labels before a colon ("Exam: 85, 40") are kept for the table and ignored in the arithmetic.
Weighted SD
The standard deviation shown is √(Σ wᵢ(xᵢ − x̄w)² / Σ wᵢ), the population form with the weights read as frequencies or importances. Other conventions (reliability weights, an n − 1 correction) change the denominator; the formula is stated so you can tell which you need. Nothing leaves the browser; the same four anonymous usage counts as the rest of the site apply.
SOURCES
- Weighted arithmetic mean x̄w = Σ wᵢxᵢ / Σ wᵢ and the frequency-weighted standard deviation √(Σ wᵢ(xᵢ − x̄w)² / Σ wᵢ) (introductory statistics)
Last reviewed 20 September 2026. How results are checked: How we verify.