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Variance Calculator
Enter a data set to calculate its variance, the average squared distance from the mean. Both the sample variance (dividing by n − 1) and the population variance (dividing by n) are shown, along with the mean, the sum of squares and both standard deviations.
Divides by n − 1.
- Population variance (σ²)
- 8
- Mean
- 9
- Count (n)
- 7
- Sum of squared deviations
- 56
- Sample standard deviation (s)
- 3.0551
- Population standard deviation (σ)
- 2.8284
Saved setups
Save a set of inputs you reuse — your usual rate, your loan, your room sizes — and load it back in one tap.
Your recent calculations
Results you calculate here are kept on this device so you can come back to them.
Formula
How to use it
- Type or paste your data, separated by commas, spaces or new lines.
- Read the sample variance if the data is a sample, or the population variance if it is the whole group.
- Take the standard deviation if you want the spread in the original units.
Worked examples
The data set 6, 9, 14, 10, 5, 8, 11
- Sample variance (s²)
- 9.3333
- Population variance (σ²)
- 8
- Mean
- 9
- Count (n)
- 7
- Sum of squared deviations
- 56
- Sample standard deviation (s)
- 3.0551
The six faces of a die
- Sample variance (s²)
- 3.5
- Population variance (σ²)
- 2.9167
- Mean
- 3.5
- Sum of squared deviations
- 17.5
A worked example
For 6, 9, 14, 10, 5, 8, 11 the mean is 9. The deviations are −3, 0, 5, 1, −4, −1 and 2; squared, they are 9, 0, 25, 1, 16, 1 and 4, which total 56. The sample variance is 56 ÷ 6 = 9.333 and the population variance is 56 ÷ 7 = 8.
Variance versus standard deviation
Variance is in squared units — square dollars, square inches — which makes it hard to picture. Its square root, the standard deviation, is back in the original units and is the one usually quoted.
Variance is the one to use in calculations, though: the variances of independent quantities add, while standard deviations do not. In Excel and Google Sheets the functions are VAR.S and VAR.P.
Questions people ask
What is the variance of 6, 9, 14, 10, 5, 8, 11?
The sample variance is 9.333 and the population variance is 8.
What is the variance of a fair six-sided die?
35/12, about 2.917. Entering 1 through 6 gives this as the population variance.
Why divide by n − 1 for a sample?
Deviations are measured from the sample’s own mean, which sits closer to the data than the true mean does. Dividing by n − 1 corrects the resulting underestimate.