Calculate population standard deviation.
DispersionOpen
Population Variance Calculator
Quick answer
If values are 12, 15, 15, 18, 22, 27, 31, the population variance is 41.7143.
Population variance: σ² = Σ(x − mean)² ÷ n.
Enter your values
- 12
- 15
- 15
- 18
- 22
- 27
- 31
7 values
Population Variance
41.7143
The average of the squared differences from the mean — the basis for standard deviation, in squared units.
You enter Values 12, 15, 15, 18, 22, 27 … (7 values). You get Population Variance 41.7143.
More in Dispersion
All Dispersion calculatorsCalculate sample variance.
DispersionOpenCalculate sample standard deviation.
DispersionOpenCalculate coefficient of variation.
DispersionOpenCalculate mean.
DescriptiveOpenCalculate median.
DescriptiveOpen
About the Population Variance Calculator
Variance measures how far values are spread out from their mean. Population variance is used when your list contains every member of the group you care about, not just a sample of it. It is the average of the squared distances from the mean.
For 12, 15, 15, 18, 22, 27 and 31, the mean is 20 and the population variance is about 41.71.
Population variance
σ² = Σ(x − mean)² ÷ n
Things to keep in mind
- Variance is in squared units; the standard deviation (its square root) is in the same unit as your data.
- If your values are only a sample of a larger group, use sample variance instead.
- A variance of zero means all the values are identical.
STATISTICS & PROBABILITY GUIDE
A quick guide to Population Variance
Use it to get an accurate population variance in seconds — free, with no sign-up.
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How to Use the Population Variance Calculator
1
Enter Values
Provide your values.
2
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What is Population Variance?
This statistics & probability tool works out your population variance instantly, so you don't have to do the math by hand.
“One quick calculation, so you always know your population variance before you decide.”
What Affects Your Population Variance
Your population variance depends on the values below.
Values
Changing your values changes your population variance.
Example Result
Here's what you can expect from a population variance calculation:
- Population Variance
- 41.7143
Frequently Asked Questions
- What is the difference between population and sample variance?
- Population variance divides by n, the number of values, because you have the whole group. Sample variance divides by n − 1 to correct the bias that comes from using a sample.
- How to calculate population variance?
- Fill in values in the Population Variance Calculator above and your population variance is calculated instantly. Change any value to see how the result responds.
- What does an example population variance calculation look like?
- If values are 12, 15, 15, 18, 22, 27, 31, the population variance is 41.7143.
- 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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