Should I use population or sample standard deviation?

Use population standard deviation when your data covers the entire group of interest, and sample standard deviation when your data is a subset used to estimate a larger population.

Standard Deviation Calculator

Q: What does a high standard deviation mean?

A high standard deviation means the data points are spread widely around the mean, indicating more variability in the data.

Calculate the mean, variance and standard deviation for a data set

Enter Numbers (comma or space separated)

Treat this data as a sample (uses n − 1 instead of n)

What is Standard Deviation?

Standard deviation measures how spread out a set of numbers is from its average (mean). A low standard deviation means values cluster tightly around the mean; a high standard deviation means they're more spread out. This calculator computes the mean, variance and standard deviation for any list of numbers, using either the population or sample formula.

How to Use the Standard Deviation Calculator

Enter your numbers, separated by commas or spaces.
Choose population or sample — check the box if your data is a sample of a larger population (this uses n − 1 in the formula, called Bessel's correction).
Read the results — mean, variance, standard deviation and more update instantly.

Formula Used

Population variance: σ² = Σ(x − mean)² ÷ n
Sample variance: s² = Σ(x − mean)² ÷ (n − 1)
Standard deviation is the square root of variance.

Example

For the data set 4, 8, 6, 5, 3, 9: the mean is 5.83. The population standard deviation is approximately 2.14, while the sample standard deviation (using n − 1) is approximately 2.32.

Frequently Asked Questions

Use population standard deviation if your data set includes every member of the group you care about. Use sample standard deviation if your data is a subset used to estimate a larger population — this is the more common case in surveys and experiments.

A high standard deviation means your data points are spread widely around the mean, indicating more variability. A low standard deviation means the values are clustered closely around the average.