Question

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

Class interval	Frequency
150 – 153	7
154 – 157	7
158 – 161	15
162 – 165	10
166 – 169	5
170 – 173	6

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.

Lower limit of 154 – 157 = 154 and upper limit of 150 – 153 = 153

Required difference = 154 – 153 = 1

So, half the difference = `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:

Class interval	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

Thus, 153.5 and 157.5 would use in the class intervals 153.5 – 157.5 and 157.5 – 161.5, respectively.