(1) variance of the whole population of N items: ${\displaystyle \frac{1}{N}{\displaystyle \sum _{j=1}^N(x_j}-\overline{X}{)}^2}$

(2) variance of the sample of n observations: ${\displaystyle \frac{1}{n}{\displaystyle \sum _{j=1}^n(x_j}-\overline{X}{)}^2}$

(3) estimate of the variance of the population from a sample: ${\displaystyle \frac{1}{n-1}{\displaystyle \sum _{j=1}^n(x_j}-\overline{X}{)}^2}$

where ${\displaystyle \overline{X}}$ is the mean value of the items of observation ${\displaystyle x_j}$ considered