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Standard Deviation Calculator

Sample and population standard deviation, variance and mean from any list of numbers.

Separate with commas, spaces or new lines.

Sample vs. population: which one do you want?

If your numbers are the entire group you care about (every student in the class), use the population figure, which divides by n. If they are a sample standing in for something bigger (50 customers out of thousands), use the sample figure, which divides by n-1 to correct for the fact that samples underestimate spread. When in doubt, and in most homework, it's the sample one.

What the number means

Standard deviation is the typical distance of a value from the mean, in the same units as your data. For roughly bell-shaped data, about 68% of values fall within one standard deviation of the mean and 95% within two. Variance is just the standard deviation squared.