Math
Variance Calculator
Compute population and sample variance, standard deviation, mean, and coefficient of variation for any list of numbers.
Numbers
Decimals and negative numbers are supported. Empty entries are ignored.
Use sample when your data is a subset of a larger group. Use population when it covers every value.
Sample variance
4.5714
Standard deviation: 2.1381
Count
8
Sum
40
Mean
5
CV %
42.76%
Min
2
Max
9
Range
7
Sum of (x - mean)²
32
Both variance methods
Population (÷ n)
4
SD: 2
Sample (÷ n - 1)
4.5714
SD: 2.1381
Step by step (mean = 5)
| Value (x) | Deviation (x - mean) | Squared deviation |
|---|---|---|
| 2 | -3 | 9 |
| 4 | -1 | 1 |
| 4 | -1 | 1 |
| 4 | -1 | 1 |
| 5 | 0 | 0 |
| 5 | 0 | 0 |
| 7 | 2 | 4 |
| 9 | 4 | 16 |
Frequently Asked Questions about the Variance Calculator
What is variance?
Variance measures how far a set of numbers spreads out around their mean. You subtract the mean from each value, square the result so positive and negative differences do not cancel, and average those squared differences. A small variance means values cluster tightly near the mean; a large variance means they are scattered widely.
What is the difference between population and sample variance?
Population variance divides the sum of squared deviations by n and is correct when your data covers every value in the group. Sample variance divides by n minus 1 (Bessel's correction) and is the right choice when your data is a subset drawn from a larger group, which fits most real surveys and experiments.
How is variance calculated step by step?
Find the mean. Subtract the mean from each value to get deviations. Square each deviation. Sum the squared deviations. Divide by n for population variance or by n minus 1 for sample variance. The calculator shows the deviations and squared deviations for the first 10 values so you can verify each step.
What is the coefficient of variation (CV)?
The coefficient of variation expresses standard deviation as a percentage of the mean: CV = SD / |mean| x 100. It lets you compare the relative spread of datasets with very different units or scales. CV is undefined when the mean is zero.
How are variance and standard deviation related?
Standard deviation is the square root of variance. Variance lives in squared units (dollars squared, kilograms squared) which is awkward to read, while standard deviation returns to the original units of your data. Both describe the same spread.