Thank you for reporting, we will resolve it shortly
Q.
The mean of the data set comprising of $16$
observations is $16$. If one of the observatio $d$ three new observations valued $3,4$ and $5$ added to the data, then the mean of the resultant data is
$\frac{ a _{1}+ a _{2}+ a _{3}+\ldots \,\ldots+ a _{15}+16}{16}=16 \ldots \ldots(1)$
$\frac{ a _{1}+ a _{2}+ a _{3}+\ldots \,\ldots+ a _{15}+(3+4+5)}{18}=? ?\ldots \ldots(2)$
(1) $a _{1}+ a _{2}+ a _{3}+\ldots \ldots+ a _{15}=(16)^2 - 16$
now
(2) $\Rightarrow \frac{(16)^{2}-16+12}{18}$
$=\frac{256-4}{18}=\frac{252}{18}=14$
$\Rightarrow $ mean $=14$