Standard Deviation Calculator
Find population and sample standard deviation, variance, and mean for a list of numbers. Fast and private.
Independently verified for accuracy
Calculator by Toolsloft ↗- Count
- 8
- Mean
- 5
- Population standard deviation
- 2
- Sample standard deviation
- 2.13809
- Population variance
- 4
- Sample variance
- 4.571429
Calculate the standard deviation of a set of numbers, both the population and the sample version, along with the mean and variance. Paste or type your values separated by commas, spaces, or new lines. Useful for statistics coursework, lab data, and quality checks.
How this is calculated
The mean is the sum divided by the count. Variance is the average of the squared differences from the mean: population variance divides by n, and sample variance divides by n minus 1, the Bessel correction. Each standard deviation is the square root of its variance. Sample figures need at least two values.
How to use
- Enter your numbers separated by commas, spaces, or line breaks.
- Read the mean and both variances.
- Read the population and sample standard deviation.
Examples
- Population:
2, 4, 4, 4, 5, 5, 7, 9 has a population deviation of 2 - Sample:
1, 2, 3, 4, 5 has a sample deviation of about 1.58
FAQ
- What is the difference between population and sample standard deviation?
- Population deviation divides by the number of values and is used when your data is the whole group. Sample deviation divides by that number minus one and is used when your data is a sample drawn from a larger group.
- Why is the sample deviation blank for one number?
- Sample standard deviation divides by the count minus one. With a single value that divisor is zero, so the sample figure is undefined and only the population figure is shown.