How spread out your data is
Standard deviation measures how far values typically sit from the mean. A small value means the data clusters tightly; a large one means it is widely scattered. This calculator returns both the sample and population standard deviations and variances, the mean, and the sum of squared deviations from one paste of numbers.
Sample versus population
Both start by squaring each values distance from the mean and adding them up. The population version divides that sum by n; the sample version divides by n minus 1. The n-minus-1 correction (Bessels correction) compensates for estimating the mean from the same sample, giving a less biased spread.
Which should I use?
Use the population formula only when your data is the entire group you care about. Use the sample formula — the more common case — when your numbers are a sample drawn from a larger population, which is why it leads here.
Related tools
For the averages themselves, use the mean median mode calculator; to see how unusual one value is, the z-score calculator.
Worked example
For 2, 4, 4, 4, 5, 5, 7, 9 the mean is 5 and the squared deviations sum to 32. The population variance is 32 over 8 = 4 (so population SD = 2), while the sample variance is 32 over 7, about 4.57 (sample SD about 2.14).
FAQ
Why square the deviations?
Squaring removes the sign so positive and negative gaps do not cancel, and it weights larger gaps more. Taking the square root at the end returns to the original units.
What does a standard deviation of zero mean?
Every value is identical — there is no spread at all.