Explanation of the Rule

This rule is based on the concept of class intervals or class width in a frequency distribution table. Class interval refers to the range of values that are grouped together to form a class. For example, if we have a frequency distribution table for the heights of students in a class, the class interval could be 150-160 cm, 160-170 cm, etc.

The class boundaries are the numbers that separate one class from another. For example, if we have a class interval of 150-160 cm, the class boundaries would be 149.5 and 160.5. The lower class boundary is always the midpoint between the lower limit of the class and the upper limit of the previous class. Similarly, the upper class boundary is always the midpoint between the upper limit of the class and the lower limit of the next class.

In the case of the rule mentioned in the question, all class boundaries except the first and the last are located at the midpoint between the upper limit of a class and the lower limit of the next higher class. This means that if we have class intervals of 150-160 cm, 160-170 cm, 170-180 cm, etc., the class boundaries would be 154.5, 164.5, 174.5, etc.

This rule is commonly used in statistical analysis to create frequency distribution tables, histograms, and other graphs that show the distribution of data. By using class boundaries that are located midway between classes, we can create a more accurate representation of the data and avoid overlapping of the classes.

Example

To illustrate this rule, let's consider the following frequency distribution table for the weights of students in a class:

| Weight (kg) | Frequency |
|-------------|-----------|
| 50-60 | 5 |
| 60-70 | 10 |
| 70-80 | 15 |
| 80-90 | 8 |
| 90-100 | 2 |

Using the rule, we can calculate the class boundaries as follows:

- The lower class boundary of the first class (50-60) is 49.5.
- The upper class boundary of the last class (90-100) is 100.5.
- For the second class (60-70), the class boundaries are 59.5 and 70.5.
- For the third class (70-80), the class boundaries are 69.5 and 80.5.
- For the fourth class (80-90), the class boundaries are 79.5 and 90.5.

Using these class boundaries, we can create a histogram that accurately represents the distribution of weights in the class.