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Standard Deviation Calculator

Enter a list of numbers to instantly compute mean, standard deviation (population and sample), variance, min, max, range, sum, and count.

Separate values with commas, spaces, semicolons, or new lines.

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How to use the standard deviation calculator

Paste or type your data values separated by commas, spaces, or new lines. The calculator updates all statistics in real time. Population standard deviation assumes your data is the entire dataset; sample standard deviation assumes it is a sample from a larger population.

Population vs. sample standard deviation

Population std dev (sigma) divides by N. Sample std dev (s) divides by N-1 (Bessel's correction), which gives an unbiased estimate when your data is a sample. Use population when you have every data point; use sample when you are estimating from a subset.

FAQ

What is the difference between population and sample standard deviation?

Population std dev divides the sum of squared deviations by N. Sample std dev divides by N-1 to correct for bias when estimating the true population std dev from a sample. For large N the difference is small.

What is variance?

Variance is the squared standard deviation. It measures how spread out the values are around the mean. Standard deviation is the square root of variance and has the same units as the data.

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