Paste a data set, get sample and population standard deviation side by side, and save the exact list as a link.
Computed in your browser from the data above.
For the default seven-value set (12, 15, 17, 20, 22, 25, 18): the mean is 18.4286, the sum of squared deviations is 113.7143, sample variance is that sum divided by 6 (n minus 1), giving 18.9524 and a sample SD of 4.3534. Population variance divides the same sum by 7 instead, giving 16.2449 and a population SD of 4.0305.
Bessel's correction inflates the sample figure by a factor of the square root of n over n minus 1. That inflation shrinks fast as your data set grows:
With a handful of points, treating your data as the whole population instead of a sample of it can understate the spread by more than 10%. Past a few hundred points, the two numbers are nearly interchangeable. See the variance calculator for the squared version of this same figure, source data untouched.
Sample SD divides the sum of squared deviations by n minus 1 instead of n, and dividing by a smaller number always produces a bigger result. That correction, named after Friedrich Bessel, compensates for a sample's tendency to slightly underestimate how spread out the full population really is.
The population standard deviation comes out as exactly 0, correctly, since one point has no spread. The sample standard deviation also shows 0 here, but that's a display default rather than a real answer: with n minus 1 equal to zero, sample standard deviation is mathematically undefined, not actually zero. Enter at least two values for a meaningful sample figure.
Yes, disproportionately. The formula squares each deviation from the mean before averaging, so a point twice as far from the mean contributes four times the squared deviation, not twice. A single extreme value can move standard deviation more than several ordinary ones combined.
Yes. The data box accepts numbers separated by commas, spaces, or line breaks interchangeably, so pasting a column copied from a spreadsheet works without reformatting it first.