Data: 2, 4, 4, 4, 5, 5, 7, 9
- Input
- 2, 4, 4, 4, 5, 5, 7, 9
- Expected output
- σ² = 4 (pop.), s² ≈ 4.57 (amostral)
σ = 2, s ≈ 2.14.
calculate variance of a dataset
Variance Calculator
Variance is the square of standard deviation: σ² = Σ(xᵢ−μ)²/N (population) or s² = Σ(xᵢ−x̄)²/(N−1) (sample).
Variance vs Standard Deviation
- Variance is in the original unit squared (e.g., kg²), which makes direct interpretation harder. Standard deviation (√variance) returns to the original unit.
Example
Safe use
- Input
- context + tool result
- Expected output
- interpreted with limits and next steps
Use the result as technical or educational support, keeping the tool limits explicit in the workflow.
Full tool FAQ
Population (σ) divides the sum of squared differences by N. Sample (s) divides by N−1 (Bessel's correction), giving an unbiased estimate of population variance when working with a sample.
Frequently asked questions
Why does variance use squared differences?
To prevent positive and negative deviations from cancelling (Σ(xᵢ−μ) = 0 always) and to penalize large deviations more.
Does this page replace official or professional review?
No. It helps explain the scenario and use the tool more safely, but real decisions should consider official sources, full context and qualified guidance when needed.