Standard Deviation Calculator
Compute sample (n−1) and population (n) standard deviation from a list of numbers.
Result
Sample σ (n−1)
1.888562
Population σ (n): 1.791647.
- Mean (μ)5.700000
- n10
- Sample variance (s²)3.566667
- Population variance (σ²)3.210000
- Sample std dev1.888562
- Population std dev1.791647
Step-by-step
- Mean = ([10 values]) / 10 = 5.7000.
- Squared deviations from mean computed for each value.
- Sample variance = sum_of_sq_dev / (n−1) = 32.1000 / 9 = 3.5667.
- Sample std dev = √sample-variance = 1.888562.
How to use this calculator
- Paste your numbers (commas, spaces, or newlines).
- Read both sample and population SD.
About this calculator
Standard deviation measures spread — how far values typically fall from the mean. Sample SD (divide by n−1) is the right choice when your data is a sample from a larger population; population SD (divide by n) when you have the entire population. The (n−1) correction (Bessel's correction) gives an unbiased estimate of the population variance.
Frequently asked
Sample (n−1) for almost everything in real life. Population (n) only when you literally have every value in the population.
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