Question

Using the information given in the table below, calculate the mean marks of the students.

Marks	less than $10$	less than $20$	less than $30$	less than $40$	less than $50$
No. of students	$7$	$19$	$32$	$42$	$50$

Answer 1

Given data

Marks Less than $10$ Less than $20$ Less than $30$ Less than $40$ Less than $50$

No. of students $7$ $19$ $32$ $42$ $50$

Marks Class interval of marks No. of students($f_i$) Mid marks($x_i$) $f_i{x}_i$

Less than $10$ $0-10$ $7$ $5$ $35$

Less than $20$ $10-20$ $19$ $15$ $34$

Less than $30$ $20-30$ $32$ $25$ $800$

Less than $40$ $30-40$ $42$ $35$ $1470$

Less than $50$ $40-50$ $50$ $45$ $2250$

$\sum f_i=150$

$\sum f_i{x}_i=4589$

We know mean$\left(\overline{x}\right)=\frac{\sum f_i{x}_i}{\sum f_i}=\frac{4589}{150}=30.59$

(Rounded to decimal)

$\cong 30.6$

$\therefore$ Mean marks of the students$\cong 30.6$.