Question

The marks obtained by 40 class X students in a math paper of 50 marks, are presented in the table. Find the mean using direct method.
$\begin{array}{cc}\text{Marks obtained}& \text{Number of students}\\ 0-10& 3\\ 10-20& 4\\ 20-30& 13\\ 30-40& 15\\ 40-50& 5\end{array}$

• A. 28.7
• B. 25.2
• C. 26.4
• D. 29.9

Answer 1

The correct option is A 28.7

Class mark for a class interval
$=\frac{\text{upper class limit}+\text{lower class limit}}{2}$

e.g: for the first class interval of 0-10
= $\frac{0+10}{2}$
= 5

Similarly the class mark for each class interval can be found. Look at the table.
$\begin{array}{cccc}\text{Class interval}& \text{Number of students}\left(f_i\right)& \text{Class mark}\left(x_i\right)& f_i{x}_i\\ 0-10& 3& 5& 15\\ 10-20& 4& 15& 60\\ 20-30& 13& 25& 325\\ 30-40& 15& 35& 525\\ 40-50& 5& 45& 225\\ Total& \sum f_i=40& & \sum f_i{x}_i=1150\end{array}$
$Mean=\frac{\sum f_i{x}_i}{\sum f_i}=\frac{1150}{40}=28.75$