Question

Calculate $\frac{\sum f_i{u}_i}{\sum f_i}$ for the given data using step-deviation method.
$\begin{array}{ccccc}\text{Class interval}& \text{Frequency}\left(f_i\right)& \text{Class mark}\left(x_i\right)& d_i=x_i-a& u_i=\frac{d_i}{h}\\ 0-100& 40& 50& -200& -2\\ 100-200& 39& 150& -100& -1\\ 200-300& 34& 250& 0& 0\\ 300-400& 30& 350& 100& 1\\ 400-500& 45& 450& 200& 2\end{array}$

• A. $0$
• B. $250$
• C. $\frac{1}{188}$
• D. 100

Answer 1

The correct option is C $\frac{1}{188}$

$\begin{array}{cccccc}\text{Class interval}& \text{Frequency}\left(f_i\right)& \text{Class mark}\left(x_i\right)& d_i=x_i-a& u_i=\frac{d_i}{h}& f_i{u}_i\\ 0-100& 40& 50& -200& -2& -80\\ 100-200& 39& 150& -100& -1& -39\\ 200-300& 34& 250& 0& 0& 0\\ 300-400& 30& 350& 100& 1& 30\\ 400-500& 45& 450& 200& 2& 90\\ \text{Total}& \sum f_i=188& & & & \sum f_i{u}_i=1\end{array}$

$\frac{\sum f_i{u}_i}{\sum f_i}=\frac{1}{188}$