Question

Define the following term: class size.

Answer 1

Hint:
Here, we need to explain the meaning of the term ‘class size’. We will define the class size and mention its formula. Then, using an example of an inclusive series, and an example of exclusive series, we will show how class size can be calculated.

Complete step by step solution:
Class size is the difference between the upper limit and the lower limit of a class interval. It is also known as class width.
The formula to calculate the class size of a class interval is the upper limit of the class interval $$-$$ lower limit of the class interval.
For example:
(A) The following tables represent an exclusive series.

Class Interval	Frequency
10 – 30	5
30 – 50	1
50 – 70	8
70 – 85	6
85 – 90	7

In the class interval 10 – 30, the upper limit is 30 and the lower limit is 10.
Therefore, the class size of the class interval 10 – 30 is $$30-10=20$$.
Similarly, we get
Class size of the class interval 30 – 50 is $$50-30=20$$.
Class size of the class interval 50 – 70 is $$70-50=20$$.
Class size of the class interval 70 – 85 is $$85-70=15$$.
Class size of the class interval 85 – 90 is $$90-85=5$$.
(B)
Now, let us see an example of an inclusive series.
The class size is the difference between the true upper limit and the true lower limit.
The following table shows an inclusive series.

Class Interval	Frequency
10 – 19	5
20 – 29	1
30 – 39	8
40 – 49	6
50 – 59	7

Here, we cannot say that the class size of the interval 10 – 19 is 9, because this is an inclusive series.
We will convert this series to an exclusive series, where the upper limit of a class interval is equal to the lower limit of the next class interval.
Therefore, the inclusive series becomes the following exclusive series.

Class Interval	Frequency
$$9.5$$ – $$19.5$$	5
$$19.5$$ – $$29.5$$	1
$$29.5$$ – $$39.5$$	8
$$39.5$$ – $$49.5$$	6
$$49.5$$ – $$59.5$$	7

The class limits in the new class intervals $$9.5$$ – $$19.5$$,$$19.5$$ – $$29.5$$, $$29.5$$ – $$39.5$$, $$39.5$$ – $$49.5$$, and $$49.5$$ – $$59.5$$ are the true class limits.
Now, the class size of the class interval $$9.5$$ – $$19.5$$ is $$19.5-9.5=10$$.

Note:
We have used the terms ‘inclusive series’ and ‘exclusive series’ in the solution.
An inclusive series is the one where the class intervals include both upper limit and lower limits. For example: In the inclusive series in the example given, 10 – 19 includes all the numbers between 10 and 19, including 10 and 19 also.
An exclusive series is the one where the class intervals include both upper limit and lower limits. In an exclusive series, the upper limit of a class interval is equal to the lower limit of the next class interval. For example: In the exclusive series in the example given, $$9.5$$ – $$19.5$$ includes all the numbers between $$9.5$$ and $$19.5$$, including $$9.5$$ but not $$19.5$$.