# Weighted Average Calculator

> Find the weighted mean of a list of values with their weights, plus the sum of weights, the unweighted mean for comparison and the weighted standard deviation.

Category: Statistics & probability · Applies to: Worldwide · Last updated: 2026-10-29
Interactive calculator: https://calculators.geekmidst.com/calculators/weighted-average-calculator

A weighted average lets some values count more than others: multiply each value by its weight, add them up and divide by the total weight.

Also called: Weighted mean calculator.

## Inputs
- Values (default 80, 90, 70)
- Weights, same order (default 20, 30, 50)

## Results
- Weighted average
- Sum of weights
- Sum of value × weight
- Unweighted mean, for comparison
- Weighted standard deviation (population form)
- Number of values

## Formula

```
x̄_w = Σwᵢxᵢ ÷ Σwᵢ;  weighted SD = √(Σwᵢ(xᵢ − x̄_w)² ÷ Σwᵢ)
```

Where:
- xᵢ: value i
- wᵢ: weight of value i (non-negative)

## Worked example
1. Products: 80 × 20 = 1600, 90 × 30 = 2700, 70 × 50 = 3500; total 7800.
2. Total weight = 20 + 30 + 50 = 100.
3. Weighted average = 7800 ÷ 100 = 78, versus a simple mean of 80.

**Result:** Marks of 80, 90 and 70 weighted 20%, 30% and 50% average 78, lower than the simple mean because the lowest mark carries half the weight.

## What the result means

The weighted average is pulled toward the values with the most weight. If it differs a lot from the simple mean, the heavily weighted items are unusual. The weighted SD uses the population (frequency-weight) form, dividing by the total weight.

## Assumptions and limits
- Weights are relative importance or frequencies; only their proportions matter.
- For averaging rates or ratios (speeds, prices per unit), make sure the weights are the right denominator, such as time or quantity, or the result will be misleading.

## Questions

### Do the weights need to add up to 100 or 1?

No. The calculation divides by the total weight, so 2, 3, 5 gives the same answer as 20%, 30%, 50%.

### How do I average percentages from groups of different sizes?

Use each group’s size as its weight; that gives the overall percentage for all groups combined.

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Source: GM¹X CalcVerse — https://calculators.geekmidst.com/calculators/weighted-average-calculator