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. 16.0
• C. 15.8
• D. 14.0

Answer 1

Answer: (D)

$\frac{a_1+a_2+a_3+\dots \dots +a_{15}+16}{16}=16\dots \dots (1)$
$\frac{a_1+a_2+a_3+\dots \dots +a_{15}+(3+4+5)}{18}=??\dots \dots (2)$
(1) $a_1+a_2+a_3+\dots \dots +a_{15}=(16{)}^2-16$
now
(2) $\Rightarrow \frac{(16{)}^2-16+12}{18}$
$=\frac{256-4}{18}=\frac{252}{18}=14$
$\Rightarrow$ mean $=14$