This standard deviation calculator measures how spread out a number list is, with separate formulas for population and sample data.
Statistics
Standard Deviation Calculator
Calculate population or sample standard deviation and variance.
Calculator
About this calculator
Formula notes
Population σ = √(Σ(xᵢ−μ)²/N); sample s = √(Σ(xᵢ−x̄)²/(n−1)). Variance is the value before the square root.
Worked examples
- Example: 2, 4, 4, 4, 5, 5, 7, 9 has mean 5; population SD = 2 and sample SD ≈ 2.138.
- For values 2, 4, 4, 4, 5, 5, 7, and 9, the population mean is 5 and population standard deviation is 2.
How to use it
- Enter the numbers as a comma-separated list.
- Choose population or sample.
- Read mean, variance, and standard deviation together.
Frequently asked questions
Why does the sample version divide by n−1?
Bessel's correction removes the bias from estimating spread from a sample.
What does an SD of 2 mean for this list?
Values sit about 2 units from the mean on average in squared-distance terms.
Limits and interpretation
- Population and sample standard deviation use different divisors; choose based on what the listed observations represent.
- Standard deviation is sensitive to outliers and can be misleading for strongly skewed or multimodal data.