Question

The following table gives the marks obtained by $100$ students in a class test.

Marks	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$
Number of Students	$12$	$18$	$27$	$20$	$17$	$6$

Find the mean marks scored by a student in class test.

Answer 1

Step 1: Completing the table

The sum of the number of students and the product of mid-values and the number of students is computed.

It is filled in the table as below,

Marks	Mid values $\left(x_i\right)$	Number of Students $\left(f_i\right)$	$\left(f_i{x}_i\right)$
$0-10$	$5$	$12$	$60$
$10-20$	$15$	$18$	$270$
$20-30$	$25$	$27$	$675$
$30-40$	$35$	$20$	$700$
$40-50$	$45$	$17$	$765$
$50-60$	$55$	$6$	$330$
Total		$\sum _{}{f}_i=100$	$\sum _{}\left(f_i{x}_i\right)=2800$

Step 2: Finding mean

The formula to find the mean is $Mean\left(\overline{x}\right)=\frac{\sum _{}\left(f_i{x}_i\right)}{\sum _{}{f}_i}$.

where $\sum _{}{f}_i$ is the total frequency and $x_i$ is the mid-values of the clas-intervals.

To find the mean marks scored by a student in-class test, apply the mean formula

$$\begin{gathered} \Rightarrow \overline{x}=\frac{2800}{100} \\ \therefore \overline{x}=28 \end{gathered}$$

Hence, the mean marks scored by a student in-class test is $28$ marks.