# Weighted Mean Calculator

> Weighted arithmetic mean using your explicit nonnegative weights. Scientific equation with no inferred weighting scheme.

Page: https://freecalculator.tech/tools/weighted-mean-calculator
Last reviewed: 2026-10-23

## Formula

Weighted mean = Σ(wᵢxᵢ) ÷ Σwᵢ.

- 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.

## Inputs

- Observations
- Nonnegative weights in observation order

## Worked example: Weighted mean

(10 × 1 + 20 × 2 + 30 × 1) ÷ 4 = 20.
1. (10 × 1 + 20 × 2 + 30 × 1) ÷ 4 = 20.

## 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.

## 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.

## Sources

- NIST — https://www.itl.nist.gov/div898/software/dataplot/refman2/ch2/weigmean.pdf

## Cite this page

- APA: Free Calculator. (2026, October 23). Weighted Mean Calculator. https://freecalculator.tech/tools/weighted-mean-calculator
- MLA: "Weighted Mean Calculator." Free Calculator, 23 Oct. 2026, https://freecalculator.tech/tools/weighted-mean-calculator.
- Link: Weighted Mean Calculator — Free Calculator, https://freecalculator.tech/tools/weighted-mean-calculator