Mathematics - Statistics Question with Solution | TestHub

By using the formula of mean we get, $=\frac{\sum x_i}{50}=15\Rightarrow \sum x_i=750$

Now variance$=\frac{\sum x_i^2}{50}-{15}^2=2^2\Rightarrow \sum x_i^2=11450$

$\Rightarrow \underset{\left(\mathrm{new}\right)}{\sum x_i}=50\times 16=800$

So, $\underset{\left(\mathrm{new}\right)}{\sum x_i}-\sum x_i=800-750=50$

Hence, if wrong observation was $x$ then corrected one is $x+50$.
$\Rightarrow x+\left(x+50\right)=70\Rightarrow x=10$

Therefore, the correct observation $=60$.

Now, $\underset{\left(\mathrm{new}\right)}{\sum {x_i}^2}=11450-{\left(10\right)}^2+{\left(60\right)}^2=14950$

Therefore, variance of the correct set $=\frac{14950}{50}-{\left(16\right)}^2=299-256=43$.