How to use this calculator
- Enter or choose values.
- Enter or choose weights, same order.
- The weighted average updates as you type. Use Copy result or Share to keep it.
Method
x̄_w = Σwᵢxᵢ ÷ Σwᵢ; weighted SD = √(Σwᵢ(xᵢ − x̄_w)² ÷ Σwᵢ)
- xᵢ
- value i
- wᵢ
- weight of value i (non-negative)
Worked example
- Products: 80 × 20 = 1600, 90 × 30 = 2700, 70 × 50 = 3500; total 7800.
- Total weight = 20 + 30 + 50 = 100.
- Weighted average = 7800 ÷ 100 = 78, versus a simple mean of 80.
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.