Question

Mean of $x_1$ and $x_2$ is 4 and that of $x_1,x_2,x_3$ and $x_4$ is 16, the mean of $2x_1,2x_2–a,x_3,2a,x_4–a$ is

• A. 14
• B. 7.2
• C. 14.4
• D. 7

Answer 1

The correct option is C 14.4

Mean of $x_1$ and $x_2=4$
$\Rightarrow \frac{x_1+x_2}{2}=4$
$\Rightarrow x_1+x_2=8$ .........(i)

Also, mean of $x_1,x_2,x_3$ and $x_4$ is 16
$\Rightarrow \frac{x_1+x_2+x_3+x_4}{4}=16$
$\Rightarrow x_1+x_2+x_3+x_4=64$
$\Rightarrow 8+x_3+x_4=64$ [from(i)]
$\Rightarrow x_3+x_4=56$ ........(ii)
Mean of $2x_1,2x_2-a,2a,x_4-a$

$=\frac{2x_1+(2x_2-a)+x_3+2a+(x_4-a)}{5}$

$=\frac{2(x_1+x_2)+x_3+x_4}{5}$

$=\frac{2\times 8+56}{5}$ [from (i) and(ii)]

$=\frac{16+56}{5}$

$=\frac{72}{5}$

$=24.4$

Hence, the correct answer is option c.