Why shouldn’t classes overlap when summarizing continuous data in a frequency or relative frequency distribution? Choose the correct answer below: A. Classes shouldn’t overlap so that the class width is as small as possible. B. Classes shouldn’t overlap so that they are open-ended. C. Classes shouldn’t overlap so there is no confusion as to which class an observation belongs. D. Classes shouldn’t overlap so that the distribution is not skewed in one direction
The Correct Answer and Explanation is:
Correct Answer: C. Classes shouldn’t overlap so there is no confusion as to which class an observation belongs.
When summarizing continuous data in a frequency or relative frequency distribution, it is essential that classes do not overlap. The purpose of organizing data into classes is to make it easier to understand and interpret patterns or trends in large datasets. If classes overlap, it becomes unclear where certain data values should be placed, which can lead to misinterpretation and inaccuracies in the frequency count.
For example, if one class is defined as 10 to 20 and the next as 20 to 30, then a value of 20 could belong to either class. This causes confusion and inconsistency when tallying frequencies. To avoid this problem, class boundaries should be clearly defined so that each observation falls into one, and only one, class. A common method is to make the lower boundary inclusive and the upper boundary exclusive, such as 10 to less than 20, and then 20 to less than 30. This rule ensures that each data value has a unique position in the distribution.
Overlapping classes also affect the accuracy of visual data representations like histograms. If a data point can appear in more than one class, the frequency count will be unreliable, and the shape of the distribution could be misleading.
Avoiding overlap is not about minimizing class width, making classes open-ended, or avoiding skewness. These are separate concerns. The main issue with overlapping classes is the potential for confusion and misclassification, which compromises the clarity and reliability of the data analysis. Therefore, it is a best practice to create distinct, non-overlapping class intervals when summarizing continuous data.
