The variance is one of the measures of dispersion which is a measure of how much the values in the data set may differ from the average of the values. It is an average of the squares of the deviations from the average. The squaring of the deviations ensures that the negative and the positive deviations will not cancel each other out.

Variation formulas

The following formulas are used in this calculator to calculate the variance:

Parameter formula for the variance of a sample is:

$ s^2 ={\frac{1}{n-1} \sum_{i=1}^n (x_i-\bar{x})^2$

in which n is the sample size and x-bar is the sample average.

Parameter for the variance of an entire population is:

$ \sigma^2 =\frac{1}{N} \sum_{i=1}^N (x_i-\mu)^2$

Where N is the population size and μ is the population average.