6 دادهٔ اولیه را به‌صورت زیر در نظر می‌گیریم:

${x_1},{x_2},...,{x_6}$

$\overline x  = \frac{{{x_1} + {x_2} + ... + {x_6}}}{6} \to \overline x  = 5 \to {x_1} + {x_2} + ... + {x_6} = 6 \times 5 = 30$

${\sigma ^2} = \frac{{{{({x_1} - 5)}^2} + {{({x_2} - 5)}^2} + ... + {{({x_6} - 5)}^2}}}{6}$

$ \to {\sigma ^2} = 3 \to {({x_1} - 5)^2} + {({x_2} - 5)^2} + ... + {({x_6} - 5)^2} = 18\,\,\,\,\,\,\,(1)$

حال بعد از اضافه کردن دو دادهٔ 7 و 3 داریم:

${x_1},{x_2},...,{x_6},3,7$

$\overline {x'}  = \frac{{{x_1} + {x_2} + ... + {x_6} + 3 + 7}}{8} = \frac{{30 + 10}}{8} = \frac{{40}}{8} = 5$

${\sigma '^2} = \frac{{{{({x_1} - 5)}^2} + {{({x_2} - 5)}^2} + ... + {{({x_6} - 5)}^2} + {{(3 - 5)}^2} + {{(7 - 5)}^2}}}{8} \to (1) \to $

${\sigma '^2}\frac{{18 + {{( - 2)}^2} + (2)}}{8} = \frac{{18 + 4 + 4}}{8} = \frac{{26}}{8} = 3/25$