Question

Variance of the distribution $73,77,81,85,...,113$ is

• A. $10$
• B. $160$
• C. $161$
• D. None of these

Answer 1

The correct option is C $161$

$73,77,\mathrm{81...113}$ are in A.P

where $a=73,d=4$

$\therefore 113=a+(n-1)d\Rightarrow 113=73+(n-1)4\Rightarrow 40=(n-1)4\Rightarrow 10=n-1\Rightarrow n=11$

$S=\frac{11}{2}(73+113)=1023$

$\overline{x}=\frac{1023}{11}=93$

Therefore variance $\frac{\sum {(x-\overline{x})}^2}{N}=161$