Simple data
- Input
- 2, 4, 4, 4, 5, 5, 7, 9
- Expected output
- σ = 2
Classic example with σ = 2.
population standard deviation
Population Standard Deviation
σ = √(Σ(xᵢ−μ)²/N). Use when data represents the complete population — not a sample.
When to use population standard deviation
- If you have all members of the universe (e.g., grades of an entire class, all daily temperatures for a month), use σ (division by N).
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
What if I only have a sample?
Use the sample standard deviation (s), which divides by N−1 (Bessel correction) to estimate σ without bias.
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.