Standard Deviation Calculator
Calculate population and sample standard deviation, variance, mean, and count from a list of numbers.
Standard Deviation Calculator
Answer
2
- mean = 5
- sum((x - mean)^2) = 32
- Population variance = 4
- Population standard deviation = sqrt(4) = 2
How to use the standard deviation calculator
The standard deviation calculator summarizes how spread out a data set is. It supports both population and sample formulas.
- Paste or type the data values separated by commas, spaces, or line breaks.
- Choose population or sample standard deviation.
- Review the mean, variance, standard deviation, and squared deviations.
Formula or method
Population: sigma = sqrt(sum((x - mean)^2) / n). Sample: s = sqrt(sum((x - mean)^2) / (n - 1)).
Worked examples
Population data
Problem: 2, 4, 4, 4, 5, 5, 7, 9
Solution: Mean is 5 and population standard deviation is 2.
Sample data
Problem: 10, 12, 23, 23, 16, 23, 21, 16
Solution: Use n - 1 in the denominator for sample standard deviation.