What is standard deviation?

Standard deviation measures how spread out a set of numbers is around the mean. A small value means the numbers are clustered close together, and a large value means they are widely spread. It is the square root of the variance.

What is the difference between population and sample?

Use population standard deviation when your numbers are the whole group you care about. Use sample when they are a sample drawn from a larger group; it divides by one less than the count to correct for the smaller data set. The calculator shows both.

Variance is the average of the squared differences from the mean. Standard deviation is its square root, which brings the figure back to the original units, making it easier to interpret.

Standard Deviation Calculator

Measure how spread out your numbers are. Enter your values, separated by commas, spaces, or new lines, and the calculator shows the population and sample standard deviation, the variance, the mean, and the count. Use sample when your numbers are a sample from a larger group.

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Your numbers

sample standard deviation

Population SD0

Variance (sample)0

Mean0

Count0

How it works

The calculator finds the mean, then the squared difference of each number from the mean. The variance is the average of those squared differences. The standard deviation is its square root. Sample versions divide by one less than the count to allow for sampling.

Worked example

For 4, 8, 15, 16, 23, and 42, the mean is 18. The sample standard deviation is about 13.3 and the population standard deviation about 12.1, showing the numbers are quite spread out.

Related calculators

Average Calculator: the mean.
Median Calculator: the middle value.
Linear Regression Calculator: trends in data.
Probability Calculator: probabilities.

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