Standard Deviation Calculator

About Standard Deviation Calculator

Standard Deviation Calculator computes population standard deviation (sigma), sample standard deviation (s), variance, and mean from a list of numbers. A deviation table shows each value, its distance from the mean, and its squared deviation, making the calculation transparent. Use population sigma when your data is the entire group, and sample s when it is a subset. Population standard deviation (sigma) divides the sum of squared deviations by n and is the correct choice when your data represents the entire group of interest. Sample standard deviation (s) divides by n-1 (Bessel correction) and is used when the data is a representative sample drawn from a larger population. The deviation table makes the step-by-step calculation visible so students and analysts can verify the result by hand.

How to use Standard Deviation Calculator

  1. Enter your numbers separated by commas or spaces
  2. See population and sample standard deviation, variance, and mean
  3. Review the deviation table to understand each value's contribution

Frequently Asked Questions

What is standard deviation?
Standard deviation measures how spread out values in a dataset are from their mean. A low standard deviation means values cluster closely around the mean; a high standard deviation means they are more spread out.
What is the difference between population and sample standard deviation?
Population standard deviation (sigma) divides by n and is used when you have data for the entire group. Sample standard deviation (s) divides by n-1 (Bessel correction) and is used when your data is a sample drawn from a larger population. The sample formula corrects for the tendency to underestimate spread in small samples.
How do I enter numbers?
Paste or type numbers separated by commas, spaces, semicolons, or newlines. The calculator parses them automatically.
When should I use population vs. sample standard deviation?
Use population standard deviation (sigma) when your data covers the entire group you are studying. Use sample standard deviation (s) when your data is a sample drawn from a larger population and you want to estimate the spread of the full population. In most real-world statistical analysis, sample s is the correct choice.
How do I interpret a standard deviation?
Standard deviation tells you how spread out values are from the mean. A low value means data points are clustered close to the average. A high value means they are more spread out. For a normal distribution, about 68% of values fall within one standard deviation of the mean and 95% within two.
Is Standard Deviation Calculator free and private?
Yes. Standard Deviation Calculator is completely free with no account required. All calculations run in your browser and nothing is uploaded or stored.
Does Standard Deviation Calculator work on mobile?
Yes. Standard Deviation Calculator is fully responsive and works in all modern browsers on desktop, mobile, and tablet.

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