Standard deviation calculator
Paste your numbers and get the spread, mean, and variance.
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Standard deviation
What standard deviation tells you
Standard deviation measures how spread out a set of numbers is. A small value means the data clusters tightly around the average; a large value means it is widely scattered. Paste your numbers above and the calculator returns the mean, the variance, and both the population and sample standard deviation.
The formulas
population SD = √( Σ(x − mean)² ÷ n )
sample SD = √( Σ(x − mean)² ÷ (n − 1) )
Worked example
For 4, 8, 15, 16, 23, 42 the mean is 18, the sample standard deviation is about 13.49, and the population standard deviation is about 12.32. Variance is simply the standard deviation squared.
Frequently asked questions
How do I calculate standard deviation?
Find the mean, subtract it from each value and square the result, average those squares (the variance), then take the square root. The calculator does every step the moment you paste your data.
What is the difference between population and sample standard deviation?
Population standard deviation divides by n and is used when your data is the entire group. Sample standard deviation divides by n minus 1 and is used when your data is a sample of a larger group.
What is variance?
Variance is the average of the squared differences from the mean. Standard deviation is its square root, which puts the spread back into the original units.
What does a high standard deviation mean?
It means the values are spread far from the average. A low standard deviation means they are bunched close to the mean.
Which should I use, sample or population?
Use sample standard deviation when your numbers are a sample drawn from a bigger population, which is the most common case. Use population when you have data for every member of the group.