Which of the following best describes the difference between a $\mathrm{class}\mathrm{boundary}$ and a $\mathrm{class}\mathrm{limit}$ in a $\mathrm{frequency}\mathrm{distribution}$?

• A. Class boundaries are only used for qualitative data, while class limits are used for quantitative data.
• B. Class limits are used to calculate the $\mathrm{mean}$, while class boundaries are used to calculate the $\mathrm{median}$.
• C. A $\mathrm{class}\mathrm{limit}$ defines the smallest and largest data values that can belong to a class, while a $\mathrm{class}\mathrm{boundary}$ is the value that separates adjacent classes.
• D. A $\mathrm{class}\mathrm{boundary}$ is always greater than the $\mathrm{class}\mathrm{limit}$ for the same class.

Answer: (C)

Verified step by step guidance

1. Step 1: Understand the concept of class limits. Class limits define the smallest and largest data values that can be included in a particular class interval. For example, if a class interval is 10-19, then 10 is the lower class limit and 19 is the upper class limit.
2. Step 2: Understand the concept of class boundaries. Class boundaries are the values that separate one class interval from the next without any gaps. They are typically found by averaging the upper class limit of one class and the lower class limit of the next class.
3. Step 3: Recognize that class boundaries help to avoid gaps between classes in a frequency distribution, ensuring continuous intervals. For example, if one class ends at 19 and the next starts at 20, the class boundary would be 19.5, which lies between the two classes.
4. Step 4: Compare class limits and class boundaries. Class limits are the actual data values that define the range of a class, while class boundaries are the values that separate classes and are used to create continuous intervals.
5. Step 5: Conclude that the best description is: 'A class limit defines the smallest and largest data values that can belong to a class, while a class boundary is the value that separates adjacent classes.' This distinguishes the role of each in organizing data.