What is the difference between sample and population standard deviation?

Population deviation divides by the number of values. Sample deviation divides by one less, correcting the estimate when data is only a sample.

Can standard deviation be negative?

No. Standard deviation is the square root of variance, so it is always zero or positive.

What does a standard deviation of zero mean?

It means every value in the data set is identical, so there is no spread around the mean.

Math Calculators

Standard Deviation Calculator

Calculate population or sample standard deviation, variance and mean.

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Data values

Standard deviation

1.70782512766

Variance

2.91666666667

Mean

5.5

Glossary

Standard deviation: The typical distance of a value from the mean.
Variance: The average squared distance from the mean; standard deviation is its square root.
Mean: The average of all the values.
Population: Choose this when your data covers the entire group (divides by N).
Sample: Choose this when your data is a subset used to estimate a larger group (divides by N minus 1).

About the Standard Deviation Calculator

Standard deviation measures how spread out values are around their mean. A small value means the data points are clustered closely, while a larger value indicates more variation.

Choose population when your data includes every member of the group you want to describe. Choose sample when the values are a subset used to estimate a larger population.

The calculator reports standard deviation, variance and mean together so you can interpret both the original-unit spread and its squared variance.

Key features

Population and sample modes
Standard deviation and variance
Mean shown for context
Flexible list input

How to use

1Enter values separated by commas, spaces or new lines.
2Choose Population or Sample.
3Read the standard deviation, variance and mean.

Examples

Spread of a data set

Input: 2, 4, 4, 4, 5, 5, 7, 9

Output: Population standard deviation 2

A larger value means the numbers are more spread out from the mean.

Frequently asked questions

What is the difference between sample and population standard deviation?: Population deviation divides by the number of values. Sample deviation divides by one less, correcting the estimate when data is only a sample.
Can standard deviation be negative?: No. Standard deviation is the square root of variance, so it is always zero or positive.
What does a standard deviation of zero mean?: It means every value in the data set is identical, so there is no spread around the mean.

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