Question

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

• A. 16.8
• B. 16
• C. 15.8
• D. 14

Answer 1

Answer: (D)

14

Answer 2

$\frac{ a _{1}+ a _{2}+ a _{3}+\ldots \,\ldots+ a _{15}+16}{16}=16 \ldots \ldots(1)$
$\frac{ a _{1}+ a _{2}+ a _{3}+\ldots \,\ldots+ a _{15}+(3+4+5)}{18}=? ?\ldots \ldots(2)$
(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 $=14$