In the context of frequency distributions, what is the main difference between class limits and class boundaries?

• A. Class limits are the smallest and largest data values that can belong to a class, while class boundaries are the values that separate classes without gaps.
• B. Class limits and class boundaries are interchangeable terms that mean the same thing.
• C. Class boundaries are used to calculate the $\mathrm{mean}$, while class limits are used to calculate the $\mathrm{median}$.
• D. Class limits are always decimals, while class boundaries are always whole numbers.

Answer: (A)

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. They essentially mark the range of values that belong to that class.
2. Step 2: Understand the concept of class boundaries. Class boundaries are the values that separate one class from the next without leaving any gaps between classes. They are used to ensure continuous intervals when data is grouped.
3. Step 3: Recognize that class limits are typically the actual data values or integers that define the class intervals, while class boundaries may include decimal values to eliminate gaps between classes.
4. Step 4: Note that class boundaries are calculated by finding the midpoint between the upper limit of one class and the lower limit of the next class. This ensures that classes are adjacent without overlapping or gaps.
5. Step 5: Conclude that the main difference is that class limits specify the range of data values within a class, whereas class boundaries define the precise points that separate classes continuously.