Question

The number of observations in a group is 40. If the average of first 10 is 4.5 and that of the remaining 30 is 3.5, then the average of the whole group is

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

$\frac{x_1+x_2+....+x_{10}}{10}=4.5$
$\Rightarrow x_1+x_{12}+....+x_{10}=45$
$And\frac{x_{11}+x_{12}+....+x_{40}}{30}=3.5$
$\Rightarrow x_{11}+x_{12}+....+x_{40}=105$
$\therefore x_1+x_2+....+x_{40}=150$
$\therefore \frac{x_1+x_2+....+x_{40}}{40}=\frac{150}{40}=\frac{15}{5}$