Overview
Standard deviation measures how spread out values are around the mean. The larger it is, the more the numbers differ from each other. It is used in statistics, science and finance to assess volatility and consistency.
Formula
s = √(Σ(xᵢ − x̄)² ÷ (n − 1)) for a sample, and σ = √(Σ(xᵢ − μ)² ÷ n) for a population.
How it works
Enter the numbers
Separate them with commas or spaces.
Choose the data type
Sample if the numbers are part of a larger group, or population if they are all the values.
Read the results
You get the standard deviation, mean, variance and a data summary.
Worked examples
Example 1: sample
For 10, 12, 23, 23, 16, 23: the mean is 17.83 and the sample standard deviation is about 5.98.
Example 2: population
The same values as a full population give a standard deviation of about 5.46, because the denominator is n instead of n−1.
Frequently asked questions
What is the difference between sample and population standard deviation?
The sample version divides by n−1 to correct bias, while the population version divides by n. The difference shrinks as the sample grows.
What does a large standard deviation mean?
It means values are spread far from the mean and are less consistent. A small value means values are closer to the mean.
Are outliers influential?
Yes. Because deviations are squared, an outlier can have a strong effect. Inspect the data before relying on the result.
What unit does standard deviation use?
It uses the same unit as the original values. Variance is in squared units, which is why standard deviation is easier to interpret.
This calculator is for educational and informational purposes only and is not a substitute for professional advice.