Question

Prepare a continuous grouped frequency distribution from the following data.

$\begin{array}{cc}\text{Mid-Point}& \text{Frequency}\\ 5& 4\\ 15& 8\\ 25& 13\\ 35& 12\\ 45& 6\end{array}$

Also, find the size of class intervals.

Answer 1

Here, we see that the difference between two mid-points is, 15 - 5 i.e., 10.
It means the width of the class interval is 10.
Let the lower limit of the first class interval be a.
Then, its upper limit = a + 10
Now, mid value of the first class interval = 5
$\Rightarrow$ mid value $=\frac{\text{Lower limit + Upper limit}}{2}$
$\Rightarrow 5=\frac{a+a+10}{2}\Rightarrow 2a+10=10$
$\Rightarrow 2a=0\Rightarrow a=0$
So, the first class interval is 0 - 10.
Now, we prepare a continuous grouped frequency distribution table is given below.

$\begin{array}{ccc}\text{Mid-point}& \text{Class interval}& \text{Frequency}\\ 5& 0-10& 4\\ 15& 10-20& 8\\ 25& 20-30& 13\\ 35& 30-40& 12\\ 45& 40-50& 6\end{array}$

The size of the class interval is 10.