Ο Standard Deviation Calculator
Enter a list of numbers to calculate the mean, variance, and standard deviation for a population or sample.
Data Set
Result
How Standard Deviation Is Calculated
Standard deviation measures how spread out a set of numbers is from the mean. A low standard deviation means values cluster close to the mean; a high one means they're spread over a wider range.
Formulas
Population Variance: ΟΒ² = Ξ£(x β xΜ)Β² / n
Sample Variance: sΒ² = Ξ£(x β xΜ)Β² / (n β 1)
Standard Deviation: Ο (or s) = βvariance
Worked Example
The calculator loads with the data set 10, 12, 23, 23, 16, 23, 21, 16 (8 values) using the population setting. The sum is 144, giving a mean of 144 Γ· 8 = 18. Summing each value's squared difference from the mean and dividing by n gives a population variance of 24, so the population standard deviation is β24 β 4.899. The range (max 23 minus min 10) is 13.
Frequently Asked Questions
What's the difference between population and sample standard deviation?
Population standard deviation divides by n (the full data set), while sample standard deviation divides by nβ1, which corrects for bias when your data is only a sample of a larger population.
Which one should I use?
Use population standard deviation when your data represents the entire group you're interested in. Use sample standard deviation when your data is a subset used to estimate a larger population.
What input formats are supported?
You can separate numbers with commas, spaces, or new lines β the calculator parses all of these automatically and ignores invalid entries.