How is standard deviation calculated?

The square root of variance, the average of squared differences from the mean.

What does standard deviation tell you?

How spread out values are from the mean — low means clustered, high means more spread out.

What's the difference between population and sample standard deviation?

Sample divides by (n−1) instead of n, correcting for bias when estimating from a smaller sample.

Standard Deviation & Mean Calculator

Find the mean, variance, and standard deviation of any list of numbers.

Enter Numbers (comma or space separated)

Data Type

Count (n)-

Sum-

Mean (Average)-

Variance-

Standard Deviation-

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What Is a Standard Deviation Calculator?

This calculator finds the mean (average), variance, and standard deviation of a set of numbers. Standard deviation measures how spread out the values are: a small value means the numbers are close to the mean, while a large value means they are spread widely.

Formulas

Given n values with mean x̄:

Mean: x̄ = (sum of values) / n
Population variance: σ² = Σ(x − x̄)² / n
Sample variance: s² = Σ(x − x̄)² / (n − 1)
Standard deviation is the square root of the variance.

How to Use This Calculator

Type or paste your numbers, separated by commas or spaces.
Choose whether your data is a full population or a sample drawn from a larger population.
Click Calculate to see the mean, variance, standard deviation, and more.

Worked Example

For the numbers 4, 8, 6, 5, 3, 9, 7: the mean is 42 / 7 = 6. The sample standard deviation works out to about 2.16. Paste "4, 8, 6, 5, 3, 9, 7" above to see the full breakdown.

Common Uses

Standard deviation is widely used in statistics, quality control, finance (measuring volatility), test score analysis, and scientific research to understand how consistent or variable a data set is.