Question

If (1-100), (101-200), (201-300), (301-400), (401, 500), and (501, 600) are the class interval of a frequency distribution, then the truth class width is:
a.) 99
b.) 99.5
c.) 100
d.) 100.5

Answer 1

Hint: We will first define the true class width for the class intervals and then we will compute the class width for the given class intervals i.e. (1-100), (101-200), (201-300), (301-400), (401, 500), and (501, 600) using the methods. Class width for the continuous limit i.e. (0-10), (10-20), (20-30) etc. is equal to (upper limit – lower limit) for any class interval.

Complete step by step answer:
Let us first define the true class width. True class width or class width is the number of points in the class interval i.e. in the class interval (0-10), (10-20), (20-30), (30,40) class width is equal to (10-0) = 10. But this is true only for continuous limits.
In (1-100), (101-200), (201-300), (301-400), (401, 500), and (501, 600), the limits are not continuous, so at first, we will make the limits continuous.
For the class interval (1-100), the upper limit of the class interval will be equal to average of upper limit of (1-101) and lower limit of (101-200) i.e. upper limit will become equal to: $\dfrac{100+101}{2}=100.5$
So, class interval is (0.5-100.5)
For the class interval (101-200), lower limit will be equal to average of the lower limit of (101-200) and upper limit of (0-100) i.e. lower limit will become equal to: $\dfrac{100+101}{2}=100.5$
And, the upper limit of the class interval will be equal to average of upper limit of (101-200) and lower limit of (201-300) i.e. upper limit will become equal to: $\dfrac{200+201}{2}=200.5$
So, the class interval (101-200) will become equal to (100.5-200.5)
Similarly, class interval (201-300) will become $\left( \left( \dfrac{200+201}{2} \right)-\left( \dfrac{300+301}{2} \right) \right)$ = (200.5-300.5)
Similarly, class interval (401-500) will become (400.5-500.5)
And, class interval (501-600) will become (500.5-600.5)
Now, we will tabulate the class interval:

Class Interval with non-continuous limit.	1-100	101-200	201-300	301-400	401-500	501-600
Class Interval continuous limit	0.5 -100.5	100.5-200.5	200.5-300.5	300.5-400.5	400.5-500.5	500.5-600.5

Hence, our new continuous class interval is (0.5-100.5), (100.5-200.5), (200.5-300.5), (400.5-500.5), (500.5-600.5).
Now, we know that class width for continuous class interval i.e. (0.5-100.5), (100.5-200.5), (200.5-300.5), (400.5-500.5), (500.5-600.5) is given (upper limit – lower limit) of any class interval.
So, class width is equal to (200.5-100.5) = 100.

So, the correct answer is “Option c”.

Note: For non-continuous limits we can also directly find the class width by directly subtracting the lower limit of two consecutive class intervals. This will also always give us always the correct answer. There is no need to class interval continuous.