ClarityHow to use this tool
- Enter at least two observations, separated by commas or spaces.
- Use measurements of the same quantity and in the same unit.
- Calculate sample variance; use population variance instead when describing the complete population rather than estimating from a sample.
Input reference and sample values
Use the units and choices shown for each field. Sample values are provided for practice, not as recommendations.
| Input | Format and units | Sample |
|---|---|---|
| Numbers | Keep the structure and separators shown in the sample. Line breaks are retained in this input. | 2, 4, 6, 8 |
Result for these sample inputs
6.66666667
Select Try the example in the form to load these values and calculate them again. This replaces the current form inputs. Compare the result with the method and worked explanation below.
The method, explained
Sample variance = sum[(xi − sample mean)²]/(n − 1).
For 2, 4, 6, 8, the mean is 5. Squared deviations are 9, 1, 1, 9, which sum to 20. Sample variance is 20 / (4 − 1) = 6.6666667. Dividing by 4 instead gives population variance 5.
Understanding your result
Variance is expressed in squared input units. For measurements in metres, variance is in square metres; standard deviation is the square root of variance and returns to metres. Large deviations have a strong effect because they are squared.
What to keep in mind
Requires at least two finite observations. The n − 1 denominator estimates population variance from an appropriate random sample; it does not correct biased sampling, measurement errors or dependent observations.
Common questions
Why divide by n − 1?
Estimating the mean from the same sample uses one degree of freedom. Bessel’s correction adjusts the sum of squared deviations for this loss.
Can sample variance be negative?
No. Squared deviations are nonnegative. A zero variance means all entered observations are equal.
Methodology maintained by ClarityKit. How these tools are built and checked.