Consider the numbers 1 ,2,3, 4, 5, 6,7 ,8, 9 and 10. If 1 is added to each number, the variance of the numbers so obtained is 

$\text{ Given numbers are }1,2,3,4,5,6,7,8,9\text{ and }10\text{ . }$

If 1 is added to each number, then observations will be 2, 3, 4, 5, 6,7 ,8, 9, 10 and 11.
$\begin{array}{c}\therefore \mathrm{\Sigma }{x}_i=2+3+4+\dots +11\\ =\frac{10}{2}[2\times 2+9\times 1]=5[4+9]=65\\ \text{ and }\mathrm{\Sigma }{x}_i^2=2^2+3^2+4^2+5^2+\dots +{11}^2\\ =\left(1^2+2^2+3^2+\dots +{11}^2\right)-\left(1^2\right)\\ =\frac{11\times 12\times 23}{6}-1=505\end{array}$

$\begin{array}{c}\therefore V=s^2=\frac{\mathrm{\Sigma }{x}_i^2}{n}-{\left(\frac{\mathrm{\Sigma }{x}_i}{n}\right)}^2=\frac{505}{10}-{\left(\frac{65}{10}\right)}^2\\ =50.5-(6.5{)}^2\\ =50.5-42.25\\ =8.25\end{array}$