Question

The following table shows marks secured by 140 students in an examination:
$\begin{array}{cc}\text{Marks}& \text{Number of students}\\ 0-10& 20\\ 10-20& 24\\ 20-30& 40\\ 30-40& 36\\ 40-50& 20\end{array}$
Calculate mean marks by the step deviation method.

Answer 1

$\begin{array}{ccccc}\text{Class interval}& \text{Frequency}\left(f_i\right)& \text{Class mark}\left(x_i\right)& u_i=\frac{(x_i-25)}{10}& f_i{u}_i\\ 0-10& 20& 5& -2& -40\\ 10-20& 24& 15& -1& -24\\ 20-30& 40& 25(=a)& 0& 0\\ 30-40& 36& 35& 1& 36\\ 40-50& 20& 45& 2& 40\\ Total& \sum f_i=140& & & \sum f_i{u}_i=12\end{array}\text{Mean}=a+10\times \frac{\sum f_i{u}_i}{\sum f_i}=25+10\times \frac{12}{140}=25.86$