Height of 5 people
- Input
- 170, 175, 160, 180, 165
- Expected output
- s ≈ 7.91
Sample deviation of 5 measurements.
sample standard deviation
Sample Standard Deviation
s = √(Σ(xᵢ−x̄)²/(N−1)). Use when data is a sample from the population — dividing by N−1 corrects the bias.
Why divide by N−1?
- Using the sample mean (x̄) to estimate μ costs one degree of freedom. Dividing by N−1 makes the sample variance an unbiased estimator (E[s²] = σ²).
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
Is the result more precise with more or fewer data?
More data always reduces estimation error. With large N, s ≈ σ.
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.