Question

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

• A. $\frac{1}{5}$
• B. $\frac{15}{4}$
• C. $4$
• D. $8$

Answer 1

The correct option is B

$\frac{15}{4}$

$\frac{x_1+x_2+\dots \dots +x_{10}}{10}=4.5$
$\Rightarrow x_1+x_2+\dots \dots x_{10}=45x_{11}+x_{12}+\dots \dots +x_{40}$
$=105$
$\therefore x_1+x_2+\dots \dots +x_{40}=150$
$\therefore \frac{x_1+x_2+\dots \dots +x_{40}}{40}=\frac{150}{40}=\frac{15}{4}$