Standard deviation, sample or population
Enter a list of numbers and get the variance and standard deviation, with a toggle between dividing by n − 1 (sample) or n (population) — sample mode also shows a 95% margin of error for the true mean.
How to use
- Enter your numbers separated by commas, spaces or line breaks
- Press Calculate
- Switch between sample and population to see how the divisor changes the result
Common questions
Should I use "sample" or "population" mode?
Use sample (the default, dividing by n − 1) when your numbers are a subset drawn from something larger. Use population (dividing by n) only when your list genuinely is the entire population you care about, not a sample of it.
What does the 95% margin of error row mean?
It only appears in sample mode, and gives the range your true population mean is likely to fall within, based on your sample: x̄ ± 1.96 × s ÷ √n. It uses the normal (z) distribution, which slightly understates the range for a very small sample compared to a t-distribution.
What's the maximum list size?
2,000 numbers per calculation.