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

Answer:-

To convert inclusive class interval into an exclusive class interval:
(1) Find the difference between the upper limit of the class interval and the lower limit of the next class interval.
For example, the upper limit of the class interval 150-153 is 153. The lower limit of the next class interval 154-157 is 154. The difference is 154-153=1

(2) Subtract half of the difference from the lower limit of the class interval and add half of that difference to the upper limit of a class interval.

Half of 1 is 0.5. Hence add 0.5 to the upper limit and subtract 0.5 from the lower limit for each class interval.
Thus, we get:-

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

153.5 is included in the class interval 153.5 - 157.5 and 157.5 is included in the class interval 157.5 - 161.5.