Question

For the data $30,31,32,\dots ,45,46$. Evaluate variance.

Answer 1

Answer: 24

Mean $\Rightarrow \frac{30+31+32+\dots +45+46}{17}$
$=\frac{\frac{17}{2}(30+46)}{17}$
$\Rightarrow \bar{x}=38$
$\Rightarrow$ Variance $=\frac{1}{n}\Sigma (x-\bar{x}{)}^2$
$=\frac{1}{17}(8^2+7^2+6^2+\dots +1^2+0^2+1^2+2^2+\dots +3^2)$
$=\frac{1}{17}\times 2\left(1^2+2^2+\dots +8^2\right)$
$=\frac{2}{17}\times \frac{8(8+1)\cdot (2\times 8+1)}{6}$
$=\frac{2}{17}\times \frac{8\times 9\times 17}{6}=24$