**The Difference Between the Upper and Lower Limit**

The difference between the upper and lower limit of a data set is known as the class size. This term is commonly used in statistics and is an essential concept when organizing data into frequency distributions or histograms.

**Understanding the Class Size**

To understand the concept of class size, let's first define some related terms:

1. **Upper Limit**: The highest value in a particular class or group.
2. **Lower Limit**: The lowest value in a particular class or group.
3. **Class Interval**: The range between the upper and lower limits, which defines a specific class or group.

The class size refers to the difference between the upper and lower limits, or in other words, the width of each class interval. It provides information about the range of values included in a particular class.

**Example**

Suppose we have a data set of students' heights in centimeters and want to create a frequency distribution. The data set includes the following values:

154, 162, 168, 173, 159, 165, 170, 166, 161, 157

To organize this data into a frequency distribution, we need to determine the class intervals and their corresponding frequencies. Let's choose a class size of 5.

1. **Determine the Range**: The range is the difference between the highest and lowest values in the data set. In this case, the range is 173 - 154 = 19.

2. **Determine the Number of Classes**: Divide the range by the class size to determine the number of classes. In this case, 19 ÷ 5 = 3.8. Since we can't have a fraction of a class, we round up to the nearest whole number. Thus, we choose 4 classes.

3. **Determine the Class Intervals**: Divide the range by the number of classes to determine the size of each class interval. In this case, 19 ÷ 4 = 4.75. Since we can't have a decimal as a class interval, we round up to the nearest whole number. Thus, each class interval will be 5.

4. **Determine the Upper and Lower Limits**: Start with the lowest value in the data set (154) as the lower limit of the first class. Add the class interval to the lower limit to determine the upper limit of the first class. Repeat this process for each subsequent class.

- First class: Lower limit = 154, Upper limit = 154 + 5 = 159
- Second class: Lower limit = 159, Upper limit = 159 + 5 = 164
- Third class: Lower limit = 164, Upper limit = 164 + 5 = 169
- Fourth class: Lower limit = 169, Upper limit = 169 + 5 = 174

Therefore, the class intervals for this data set are: 154-159, 159-164, 164-169, and 169-174.

**Conclusion**

In summary, the class size refers to the difference between the upper and lower limits of a data set. It helps determine the width of each class interval when organizing data into frequency distributions or histograms. By understanding the class size, we can effectively analyze and interpret data in a meaningful way.