Question

The marks obtained by 40 students in class X of a certain school in a math paper of maximum marks '100' are presented in the table. Find the mean using direct method.

$$\begin{array}{cccccc}ClassInterval& 0-10& 10-20& 20-30& 30-40& 40-50\\ Numberofstudents& 3& 4& 13& 15& 5\end{array}$$

• A. 28.75
• B. 25.2
• C. 26.4
• D. 29.9

Answer 1

The correct option is A 28.75

Class mark for first class interval = 5

Similarly the class mark for each class interval can be found. Look at the table.

$$\begin{array}{cccc}ClassInterval& Numberofstudents\left(f_i\right)& Classmark\left(x_i\right)& f_i{x}_i\\ 0-10& 3& 5& 15\\ 10-20& 4& 15& 60\\ 20-30& 13& 25& 325\\ 30-40& 15& 35& 525\\ 40-50& 5& 45& 225\\ Total& \sum f_i=40& & \sum f_i{x}_i=1150\end{array}$$

$\therefore Mean=\frac{\sum f_i{x}_i}{\sum f_i}$
$=\frac{5\times 3+15\times 4+25\times 13+35\times 15+45\times 5}{40}$

$=\frac{1150}{40}$

$=28.75$