Calculator
Enter values as a list, or use value-frequency pairs for grouped data.
Formula used
Population mean
μ = (1 / N) · Σ xᵢ
For weighted data: μ = Σ(wᵢxᵢ) / Σwᵢ
Population variance and standard deviation
σ² = (1 / N) · Σ (xᵢ − μ)²
σ = √σ²
Weighted: σ² = Σ(wᵢ(xᵢ − μ)²) / Σwᵢ
This tool reports population statistics, meaning it divides by N (or Σw), not N − 1.
How to use this calculator
- Choose Values list for raw observations, or Value–frequency pairs for grouped data.
- Paste numbers using commas, spaces, or new lines. For pairs, enter one pair per line.
- Enable weights only when each value has a matching weight entry.
- Set rounding decimals for neat display and exports.
- Click Calculate. Results appear above the form with export buttons.
Example data table
Example dataset: 12, 15, 18, 20, 22, 25, 28, 30. Mean is 21.25, variance is 34.1875, and population standard deviation is about 5.8470.
| # | Value (x) | Deviation (x − μ) | Squared deviation |
|---|---|---|---|
| 1 | 12 | -9.25 | 85.5625 |
| 2 | 15 | -6.25 | 39.0625 |
| 3 | 18 | -3.25 | 10.5625 |
| 4 | 20 | -1.25 | 1.5625 |
| 5 | 22 | 0.75 | 0.5625 |
| 6 | 25 | 3.75 | 14.0625 |
| 7 | 28 | 6.75 | 45.5625 |
| 8 | 30 | 8.75 | 76.5625 |