Calculate sample standard deviation.
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Population Standard Deviation Calculator
Quick answer
If values are 12, 15, 15, 18, 22, 27, 31, the population standard deviation is 6.4587.
Population standard deviation: σ = √( Σ(x − mean)² ÷ n ).
Enter your values
- 12
- 15
- 15
- 18
- 22
- 27
- 31
7 values
Population Standard Deviation
6.4587
How spread out the values are from the average — a larger number means more variation, a smaller one means the values sit close together.
You enter Values 12, 15, 15, 18, 22, 27 … (7 values). You get Population Standard Deviation 6.4587.
More in Dispersion
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DescriptiveOpenCalculate median.
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About the Population Standard Deviation Calculator
Standard deviation shows how far values typically sit from their mean, in the same unit as the data. Population standard deviation is used when your list is the whole group. A small value means the numbers are close together; a large one means they are spread out.
For 12, 15, 15, 18, 22, 27 and 31, the population standard deviation is about 6.46.
Population standard deviation
σ = √( Σ(x − mean)² ÷ n )
Things to keep in mind
- It is the square root of the population variance.
- In a bell-shaped distribution, about 68% of values lie within one standard deviation of the mean.
- For a sample, use the sample standard deviation, which divides by n − 1.
STATISTICS & PROBABILITY GUIDE
A quick guide to Population Standard Deviation
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How to Use the Population Standard Deviation Calculator
1
Enter Values
Provide your values.
2
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What is Population Standard Deviation?
This statistics & probability tool works out your population standard deviation instantly, so you don't have to do the math by hand.
“One quick calculation, so you always know your population standard deviation before you decide.”
What Affects Your Population Standard Deviation
Your population standard deviation depends on the values below.
Values
Changing your values changes your population standard deviation.
Example Result
Here's what you can expect from a population standard deviation calculation:
- Population Standard Deviation
- 6.4587
Frequently Asked Questions
- How to calculate population standard deviation?
- Fill in values in the Population Standard Deviation Calculator above and your population standard deviation is calculated instantly. Change any value to see how the result responds.
- What does an example population standard deviation calculation look like?
- If values are 12, 15, 15, 18, 22, 27, 31, the population standard deviation is 6.4587.
- Is this calculator free to use?
- Yes — every calculator on this site is completely free, with no sign-up or account required.
- How accurate is this calculator?
- It uses the standard formula and calculates on our server for every request, so results are precise for the values you enter.
- Is my data saved anywhere?
- No. Nothing you enter is stored or sent anywhere unless you choose to share a link with your values included.
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