Variance Calculator
Paste your numbers to get the sample and population variance side by side.
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Variance Calculator by TheCalcTools
How the Variance Calculator works
Variance is the average squared distance of the values from their mean. Squaring makes every distance positive and gives more weight to values far from the mean.
The sum of squared deviations is divided by n − 1 for the sample variance or by n for the population variance. Its square root is the standard deviation, which is in the same units as the data.
The formula
Worked example
Using the default values shown in the calculator:
| Your data | 4, 8, 6, 5, 3, 7 |
|---|
- Mean = 33 ÷ 6 = 5.5.
- Squared deviations: 0.25, 6.25, 0.25, 0.25, 6.25, 2.25, sum 17.50.
- Sample variance = 17.50 ÷ 5 = 3.50; population variance = 17.50 ÷ 6 = 2.9167.
Result:
| Sample variance (s²) | 3.5000 |
|---|---|
| Population variance (σ²) | 2.9167 |
| Mean | 5.5000 |
| Sum of squared deviations | 17.5000 |
| Sample standard deviation | 1.8708 |
| Count | 6 |
Frequently asked questions
Why is variance in squared units?
Because the deviations are squared. If your data are in metres, the variance is in square metres. Take the square root to get the standard deviation in metres.
Can variance be negative?
No. It is a sum of squares divided by a positive number, so it is zero when all values are equal and positive otherwise.
Sources and further reading
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