Weighted Mean Calculator
Calculate the weighted mean (weighted average) from values and their weights.
How to use this tool
- Enter values (comma-separated) and weights (comma-separated) in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your weighted mean and the full breakdown beneath it.
Weighted mean = Σ(value × weight) / Σ(weights). Useful for GPA calculations, portfolio returns, and graded assessments.
Formula
Weighted Mean = (Σ vᵢ × wᵢ) ÷ Σ wᵢ
Where vᵢ is each value and wᵢ is its corresponding weight. The sum of all (value × weight) products is divided by the total sum of weights.
How it works
This calculator computes the weighted mean by multiplying each value by its assigned weight, summing those products, then dividing by the total sum of weights. Unlike a simple average, the weighted mean allows certain data points to contribute more to the final result based on their importance or frequency. It assumes all weights are non-negative and that at least one pair of value and weight is provided.
Worked example
Worked example
- Values: 80, 90, 70 with weights: 1, 2, 3
- Multiply each value by its weight: 80×1 = 80, 90×2 = 180, 70×3 = 210
- Sum the products: 80 + 180 + 210 = 470
- Sum the weights: 1 + 2 + 3 = 6
- Divide: 470 ÷ 6 ≈ 78.3333
Weighted mean = 78.3333
Key terms
- Weighted mean
- An average where each value is multiplied by a weight reflecting its relative importance before summing, then divided by the total weight.
- Weight
- A numerical factor assigned to each data point to indicate how much it should influence the overall average.
- Simple mean
- An ordinary average where all values are treated as equally important (all weights are equal to 1).
- Numerator
- In the weighted mean formula, the sum of all (value × weight) products before dividing by total weight.
- Denominator
- The sum of all weights; dividing by this normalises the weighted sum into an average.
Frequently asked questions
- How is the weighted mean different from the regular mean?
- The regular mean treats all values equally. The weighted mean multiplies each value by its importance (weight) before summing. GPA calculation is a classic example: a 3-credit A contributes more than a 1-credit A.