Variance | Statistics

Variance is a measure of variability based on deviation from the mean. Variance is the average of the deviations squared.

All deviations is raised with the power of two before the mean of deviations is calculated. Variance is calculated on squared deviations because that eliminates negative numbers, two negative number times each other will be a positive number. The variance and the standard deviation is the most widely used measures of spread in statistics. There is a difference in the variance of a population and the variance for a sample. Variance from a population is the true variance. Variance calculated from a sample is an estimate of the variance in the population.

Variance for population: Total (deviations from the mean to the power of 2) / number of observations

Variance for a sample: (Total (deviations from the mean to the power of 2)) / (number of observations-1)

If we have three observations in a population of 2, 4 and 6, where 4 is the average. The variance is 2.66 (((2-4)^2 + (4-4)^2 + (6-4)^2) / 3). In a sample the variance had been 4 (((2-4)^2 + (4-4)^2 + (6-4)^2) / (3-1)). The variance is difficult to interpret, that is why we calculate the standard deviation of the variance.