Question

The highest score of certain data exceeds its lowest score by 16 and coefficient of range is $\frac{1}{3}$. Find the sum of the highest score and the lowest score

• A. 36
• B. 48
• C. 24
• D. 18

Answer 1

The correct option is B 48

Let the highest score of certain data is $h$ and its lowest score is $l$
Given, coefficient of range is $\frac{1}{3}$.
According to given statement:
$h=l+16$
$\Rightarrow h-l=16$
$\Rightarrow h=16+l$ .........(i)
Since, Cofficient of range = $\frac{h-l}{h+l}$
$\therefore \frac{1}{3}=\frac{h-l}{h+l}$
$\Rightarrow 3h-3l=h+l$
$\Rightarrow 2h-4l=0$
by using (i). we get:
$2(16+l)-4l=0$
$\Rightarrow 32-2l=0$
$\Rightarrow l=16$
By substitute the value of $l$ in (i). we get
$h=16+16=32$
The sum of the highest score and the lowest score = $h+l$
=$32+16=48$
$\therefore$ Option B is correct.