Standard Deviation Calculator
Paste a list of numbers and choose sample or population to get the standard deviation and variance.
Result
- Sample variance
- 3.5
- Mean
- 5.5
- Count
- 6
- Sum of squared differences
- 17.5
How to use Standard Deviation Calculator
- Type or paste your numbers.
- Choose whether the data is a sample or the whole population.
- Read the standard deviation, variance and mean.
About this tool
Standard deviation measures how spread out numbers are around their mean. A small value means the numbers sit close to the mean. A large one means they are widely spread.
Use the sample version when your numbers are a sample from a larger group, which divides by n − 1. Use the population version when you have every value, which divides by n.
How it is calculated
Population: σ = √(Σ(x − mean)² ÷ n).
Sample: s = √(Σ(x − mean)² ÷ (n − 1)).
Worked examples
- 2, 4, 4, 4, 5, 5, 7, 9 (population): standard deviation 2, mean 5.
- 4, 8, 6, 5, 3, 7 (sample): standard deviation 1.870829, mean 5.5.
Tips for better results
- When unsure, sample is the usual choice.
- Variance is the square of the standard deviation.
Frequently asked questions
What is the difference between sample and population standard deviation?
The sample version divides by n − 1 to correct for a sample being less spread than the whole group. The population version divides by n.
What does a high standard deviation mean?
The values are spread widely around the mean.
Are my numbers saved or sent anywhere?
No. The calculation runs in your browser on your own device. Nothing you type is sent to Paul Digital or any other server.
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Privacy
The calculation runs in your browser on your own device. The numbers you type are not sent to Paul Digital or any other server. Results are estimates from the numbers you enter and are not financial, tax or legal advice.