Question

Explain the meaning of the following term: true class limits.

Answer 1

Hint: Here, we will use an example to convert an inclusive series to exclusive series, and show what true class limits mean. When an inclusive series is converted into exclusive series, the new upper and lowers limits are called the true class limits.

Complete step-by-step answer:
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

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.
To convert 10 – 19, we will halve the difference of the upper limit of the class interval 10 – 19 and the lower limit of the next class interval 20 – 29, and add it to the upper limit, and subtract it from the lower limit.
The difference in the upper limit of the class interval 10 – 19 and the lower limit of the next class interval 20 – 29 is \[20 - 19 = 1\]. The half of this difference is \[0.5\].
We will add \[0.5\] to the upper limit 19, and subtract it from the lower limit 10.
Thus, the new class interval is \[9.5\] – \[19.5\].
Similarly, we can convert the other class intervals to \[19.5\] – \[29.5\], \[29.5\] – \[39.5\], \[39.5\] – \[49.5\], and \[49.5\] – \[59.5\].
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.
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 \[19.5\].