Question

Convert the given frequency distribution into a continuous grouped frequency distribution.

$\begin{array}{cc}\text{Class interval}& \text{Frequency}\\ 150-153& 7\\ 154-157& 7\\ 158-161& 15\\ 162-165& 10\\ 166-169& 5\\ 170-173& 6\end{array}$

In which intervals would 153.5 and 157.5 be included?

Answer 1

It is clear that the given table is in inclusive (discontinuous) form. So, we first convert it into exclusive form.
Now, consider the classes 150 - 153, 154 - 157.
$\therefore$ Lower limit of 154 - 157 = 154
And upper limit of 150 - 153 = 153
Required difference = 154 - 153 = 1
So, half the difference
$=\frac{1}{2}=0.5$
So, we subtract 0.5 from each lower limit and add 0.5 to each upper limit. The table for continuous grouped frequency distribution is given below.

$\begin{array}{cc}\text{Class interval}& \text{Frequency}\\ 149.5-153.5& 7\\ 153.5-157.5& 7\\ 157.5-161.5& 15\\ 161.5-165.5& 10\\ 165.5-169.5& 5\\ 169.5-173.5& 6\end{array}$

Thus, 153.5 and 157.5 included in class intervals 153.5 - 157.5 and 157.5 – 161.5 respectively.