Weighted Mean Calculator
Weighted arithmetic mean using your explicit nonnegative weights. Scientific equation with no inferred weighting scheme.
In short
Weighted arithmetic mean using your explicit nonnegative weights. Scientific equation with no inferred weighting scheme.
Formula: Weighted mean = Σ(wᵢxᵢ) ÷ Σwᵢ.
What this calculator does
Weighted arithmetic mean using your explicit nonnegative weights. Scientific equation with no inferred weighting scheme. Formula, worked example, sources, FAQs and limitations included.
Use it to turn Observations, Nonnegative weights in observation order into a checked result you can compare, copy, or rerun with different assumptions.
The page shows the formula, a numeric worked example, and the assumptions that affect this statistics calculation.
Inputs and what they mean
- Observations
- — text value.
- Nonnegative weights in observation order
- — text value.
How to use it
- Enter each value in the unit shown next to the box (use the unit converter first if your numbers are in other units).
- Check the breakdown to see every intermediate step.
- Read the limitations before relying on the result.
Formula
Methodology type: scientific equation.
Methodology: NIST weighted mean; weights are explicit nonnegative user inputs, not inferred precision or probability.
Weights need not sum to one; multiplying all weights by the same positive constant leaves the result unchanged.
Weighted mean = Σ(wᵢxᵢ) ÷ Σwᵢ.
Inputs used: Observations, Nonnegative weights in observation order.
Worked example
Weighted mean
- (10 × 1 + 20 × 2 + 30 × 1) ÷ 4 = 20.
Reading the result
The headline figure is the main answer. Any breakdown underneath shows the parts that make it up, so you can check the working and see what changes when you adjust an input.
Limitations and assumptions
- No uncertainty or correlation model for the weights.
- Matching finite observations and weights only.
- For education and operational analysis only. No diagnosis, treatment recommendations, prescribing, dosing instructions, or reimbursement entitlement. Scientific calculations require appropriate laboratory verification; operational estimates do not replace local clinical, safety or financial policies.
- The result depends on the values you enter for this weighted mean calculator; it does not supply missing rates, rules, prices, dates, or assumptions for you.
Reference: NIST
Last reviewed:
Common questions
Must weights sum to one?
No. Division by total weight normalizes them.
Can weights be negative?
Not in this nonnegative weighted-mean model. Check the formula, example, and limitations on this page before using the result for a real statistics decision.
Are these inverse-variance weights?
Only if you deliberately enter appropriate inverse-variance weights; they are never inferred. Check the formula, example, and limitations on this page before using the result for a real statistics decision.
How do I use the Weighted Mean Calculator?
Enter the required values for Observations, Nonnegative weights in observation order. The calculator applies the formula on this page and shows the main result with any supporting breakdown so you can check the arithmetic.
What formula does the Weighted Mean Calculator use?
Weighted mean = Σ(wᵢxᵢ) ÷ Σwᵢ. The visible formula section above lists the calculation path and the edge cases the page handles, so the result can be checked without relying on the form alone.
Can the Weighted Mean Calculator be used for exact decisions?
Use it as a calculation aid, not as a substitute for checking the underlying rule, contract, policy, or professional advice that applies to your situation. When a result depends on local rules, personal details, prices, or dates, enter those values yourself and confirm them before acting.
Sources
Method based on NIST.
Cite this page
Free Calculator. (2026, October 23). Weighted Mean Calculator. https://freecalculator.tech/tools/weighted-mean-calculator
"Weighted Mean Calculator." Free Calculator, 23 Oct. 2026, https://freecalculator.tech/tools/weighted-mean-calculator.
Weighted Mean Calculator — Free Calculator, https://freecalculator.tech/tools/weighted-mean-calculator
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