In a test, the marks obtained by $\displaystyle 100$ students (out of $\displaystyle 50$) are given below : Marks obtained : $\displaystyle 40$-$\displaystyle 50$ Find the mean marks of the students.

Marks Obtained	Number of students \(\displaystyle \left(\mathbf{f}_{\mathbf{i}}\right)\)	\(\displaystyle \mathbf{x}_{\mathbf{i}}\)	\(\displaystyle \mathbf{f}_{\mathbf{i}} \mathbf{x}_{\mathbf{i}}\)
$\displaystyle 0$-$\displaystyle 10$	$\displaystyle 12$	$\displaystyle 5$	$\displaystyle 60$
$\displaystyle 10$-$\displaystyle 20$	$\displaystyle 23$	$\displaystyle 15$	$\displaystyle 345$
$\displaystyle 20$-$\displaystyle 30$	$\displaystyle 34$	$\displaystyle 25$	$\displaystyle 850$
$\displaystyle 30$-$\displaystyle 40$	$\displaystyle 25$	$\displaystyle 35$	$\displaystyle 875$
$\displaystyle 40$-$\displaystyle 50$	$\displaystyle 6$	$\displaystyle 45$	$\displaystyle 270$
Total	$\displaystyle 100$		$\displaystyle 2400$

Marking-scheme solution