Question

Calculate the mean of the following distribution using step - deviation method.

$\begin{array}{cc}\text{Class Interval}& \text{Frequency}\\ 30-40& 10\\ 40-50& 6\\ 50-60& 8\\ 60-70& 12\\ 70-80& 5\\ 80-90& 9\end{array}$

• A. 58.6
• B. 59.6
• C. 54
• D. 60

Answer 1

The correct option is B 59.6

$\begin{array}{ccccc}\text{Class Interval}& \text{Frequency}\left(f_i\right)& x_i& u_i=\frac{x_i-a}{h}& f_i{u}_i\\ 30-40& 10& 35& -3& -30\\ 40-50& 6& 45& -2& -12\\ 50-60& 8& 55& -1& -8\\ 60-70& 12& 65=a& 0& 0\\ 70-80& 5& 75& 1& 5\\ 80-90& 9& 85& 2& 18\\ & \sum f_i=50& & & \sum f_i{u}_i=-27\end{array}$

$\therefore \text{Mean}=a+h\frac{\sum f_i{u}_i}{\sum f}$
$=65+10\times \frac{(-27)}{50}=65-5.4=59.6$