If 1 is added to first 10 natural numbers, then variance of the numbers so obtained is
If 1 is added to first 10 natural numbers, then variance of the numbers so obtained is
8.25
3.87
6.5
2.87
Solution
We have to find variance of numbers $2,3,4, \ldots ., 11$.
Here $\overline{\mathrm{x}}=\frac{2+3+4+\ldots+11}{10}=\frac{65}{10}=6.5$
Variance $=\frac{\sum\left(\mathrm{x}_{\mathrm{i}}-\overline{\mathrm{x}}\right)^2}{\mathrm{n}}$
$\begin{aligned}
& =\frac{\left[(-4.5)^2+(-3.5)^2+(-2.5)^2+(-1.5)^2+(-0.5)^2+(0.5)^2+(1.5)^2+(2.5)^2+(3.5)^2+(4.5)^2\right]}{10} \\
& =\frac{2(20.25+12.25+6.25+2.25+0.25)}{10}=\frac{41.25}{5}=8.25
\end{aligned}$