Question

Marks obtained by $40$ students in a short assessment is given below, where $a$ and $b$ are two missing data.

Marks	$5$	$6$	$7$	$8$	$9$
No. of students	$6$	$a$	$16$	$13$	$b$

If the mean of the distribution is $7.2$, find $a$ and $b$.

Answer 1

The total number of students is $40$.

$\therefore 6+a+16+13+b=40$

$\Rightarrow a+b=15...\left(1\right)$

The mean of the given data is $\frac{5\times 6+6a+7\times 16+8\times 13+9b}{40}$

$\Rightarrow \frac{30+6a+112+104+9b}{40}=7.2$

$\Rightarrow 246+6a+9b=288$

$\Rightarrow 6a+9b=42$

$\Rightarrow 2a+3b=14...\left(2\right)$

From $\left(1\right)$, we get $b=15-a$. Substitute this value in $\left(2\right)$

$\therefore 2a+3(15-a)=42$

$\Rightarrow 2a+45-3a=42\Rightarrow a=3$

$\therefore b=15-a=15-3=12$