Find mean, variance and standard deviation of a data set.
Calculated locally in your browser.
How do you calculate standard deviation?
Variance is the average of the squared deviations from the mean, and standard deviation is its square root. Sample SD divides by n − 1, while population SD divides by n; use sample SD for a subset and population SD for the whole group. For 2, 4, 4, 4, 5, 5, 7, 9 the mean is 5 and the population standard deviation is 2.
Understanding your result
Use sample SD when your data is a sample of a larger group, and population SD when it is the whole group.
Formula and method
Variance is the average of squared deviations from the mean; standard deviation is its square root. Sample SD divides by n − 1, population SD by n.
Assumptions and limitations
It describes the spread of the numbers you enter and does not infer confidence intervals, run hypothesis tests or detect outliers for you. Choosing sample versus population standard deviation is your responsibility, as the two use different divisors and give slightly different answers.
Worked example
For 2, 4, 4, 4, 5, 5, 7, 9 the mean is 5 and the population standard deviation is 2.
How to use this tool
- Enter your numbers, separated by commas, spaces or new lines.
- Read the statistics.
Common mistakes to avoid
- Confusing sample and population standard deviation.
About the Standard Deviation Calculator
Compute the mean, variance and both population and sample standard deviation for a list of numbers.
Who should use this tool
Statistics students learning spread, researchers summarising data sets, teachers analysing test scores, and analysts who need the mean, variance and both sample and population standard deviation for a list of numbers without setting up a spreadsheet.
Benefits
- Returns mean, variance and standard deviation in one pass
- Gives both sample and population versions side by side
- Removes tedious squaring and summing by hand
- Accepts a full list of numbers at once
Practical use cases
- Summarising the spread of a set of test scores
- Reporting variability in an experiment's measured results
- Comparing consistency between two different data sets
- Teaching how variance and standard deviation are calculated
Frequently asked questions
Sample or population SD?
Use sample SD (n − 1) for a sample, and population SD (n) when you have the entire population.
Should I use sample or population standard deviation?
Use population standard deviation when your numbers are the entire group you care about, and sample standard deviation when they are a sample drawn from a larger population. Sample standard deviation divides by n minus 1 rather than n, giving a slightly larger, less biased estimate of the wider spread.
What is the difference between variance and standard deviation?
Variance is the average of the squared deviations from the mean, so it is measured in squared units. Standard deviation is simply the square root of the variance, which returns the figure to the original units and makes it far easier to interpret.