Calculator
Example data table
| # | Value |
|---|---|
| 1 | 12 |
| 2 | 15 |
| 3 | 18 |
| 4 | 20 |
| 5 | 22 |
| 6 | 22 |
| 7 | 25 |
| 8 | 27 |
| 9 | 30 |
| 10 | 31 |
This example matches the default values loaded in the calculator.
Example outputs (rounded)
- Mean: 22.2
- Population variance: 34.76
- Sample variance: 38.6222
Your results may differ if you change options.
Formula used
Unweighted variance
Let n be the number of values and x̄ be the mean.
- Population:
σ² = Σ(xᵢ − x̄)² / n - Sample:
s² = Σ(xᵢ − x̄)² / (n − 1)
Weighted variance
Let weights be wᵢ ≥ 0 and weighted mean be μw.
- Weighted mean:
μw = Σ(wᵢxᵢ) / Σwᵢ - Population:
σw² = Σ[wᵢ(xᵢ − μw)²] / Σwᵢ - Sample (unbiased):
sw² = Σ[wᵢ(xᵢ − μw)²] / (Σwᵢ − Σwᵢ²/Σwᵢ)
If the sample denominator is not positive, the calculator returns “—”.
Trimmed variance (if enabled) is computed after removing extremes, then applying the selected formula on the remaining values.
How to use this calculator
- Paste your values into the Data values box.
- Pick Sample for estimates, or Population for full data.
- Optional: enable Weights and paste a matching list.
- Optional: set Trim extremes to reduce outlier influence.
- Press Calculate variance to view results above the form.
- Use Download CSV or Download PDF to share outputs.