Standard Deviation Calculator
Paste a list of numbers to get the standard deviation, variance, and mean — choose sample (n−1) or population (n) — instantly, in your browser.
Paste a list of numbers to get the standard deviation, variance, and mean — choose sample (n−1) or population (n), depending on whether your data is a sample of a larger group or the entire group itself.
Formula
Standard deviation is the square root of variance. Variance is the average of the squared differences from the mean:
- Population variance:
σ² = Σ(x − mean)² ÷ n - Sample variance:
s² = Σ(x − mean)² ÷ (n − 1)
Worked example for the population 2, 4, 4, 4, 5, 5, 7, 9 (mean 5): sum of squared differences = 32; population variance = 32 ÷ 8 = 4; population standard deviation = √4 = 2.
FAQs
Should I use sample or population standard deviation?
Use population if your numbers represent the entire group you care about. Use sample if your numbers are a subset used to estimate the standard deviation of a larger group — sample standard deviation is slightly larger to account for the extra uncertainty of working from a subset.
Why do I need at least 2 numbers for sample mode?
Sample standard deviation divides by (n − 1); with only 1 data point that would mean dividing by zero, so the calculation is undefined until you add a second value or switch to population mode.