The Variance Calculator measures how widely values in a data set vary around their mean. Variance is a measure of dispersion used in statistics and is especially useful when comparing the spread of data sets.
Population and Sample Variance
For a population, variance is ΟΒ² = Ξ£(x β ΞΌ)Β² Γ· N. For a sample, the commonly used unbiased estimator is sΒ² = Ξ£(x β xΜ)Β² Γ· (n β 1). The denominator matters because a sample represents a larger population.
How to Use the Calculator
- Enter the observations in the data set.
- Choose the population or sample calculation when the calculator provides that option.
- Calculate the variance.
- Review the result together with the units and context of the original measurements.
Example
For the population values 2, 4, and 6, the mean is 4. The squared deviations are 4, 0, and 4, giving a total of 8. Dividing by 3 gives a population variance of 2.6667.
Interpreting Variance
A larger variance indicates greater dispersion around the mean. Because the deviations are squared, variance is expressed in squared units. Standard deviation is often easier to interpret because it returns the spread to the original measurement scale.