A familiar situation
Compare the spread of repeated measurements around their average in a lab or quality check.
How to use this calculator
- Enter values, standard deviation.
- Select Calculate to see the answer and its breakdown.
- Keep a scenario, change an input and compare the results.
Use consistent units and check the assumptions below before applying the result.
How standard deviation is calculated
Population deviation divides the sum of squared deviations from the mean by n. Sample deviation divides by n−1, applying Bessel’s correction when the list represents a sample. For 2, 4, 6, the mean is 4; population SD is √(8/3) ≈ 1.633, while sample SD is 2.
Population σ=√[Σ(x−μ)²/n]; sample s=√[Σ(x−x̄)²/(n−1)].For 2, 4, 6, the mean is 4; population SD is √(8/3) ≈ 1.633, while sample SD is 2.
Assumptions & useful context
The result depends on the values you enter and the method described above. Displayed numbers may be rounded; calculations use the unrounded values. Check that this model matches your situation before relying on it.
Frequently asked questions
Which choice should I use for a sample?
Choose sample when these observations estimate a wider population.
Why does sample mode require two values?
With one observation, n−1 is zero and sample variance cannot be estimated.