Why shouldn’t classes overlap when summarizing continuous data in a frequency or relative frequency distribution?
The Correct Answer and Explanation is:
Correct Answer:
Classes should not overlap when summarizing continuous data in a frequency or relative frequency distribution because overlapping classes can cause confusion and ambiguity about which class a particular data value belongs to. This would lead to incorrect classification of data and potentially distort the results of the analysis.
Explanation
When summarizing continuous data in a frequency or relative frequency distribution, it is essential that the classes do not overlap. Continuous data refers to numerical values that can take any value within a given range, including decimals or fractions. Because these values can be very close to each other, clearly defined and distinct class intervals are needed to ensure that every data point is categorized accurately and without uncertainty.
If classes overlap, a single data point could logically belong to more than one class. For example, if one class is labeled 10 to 20 and another is 20 to 30, it is unclear where the value 20 should go. Should it be counted in the first class or the second? This ambiguity introduces the risk of either double-counting a value or missing it entirely. The result is a distribution that does not accurately reflect the true nature of the dataset.
To avoid this issue, non-overlapping class intervals are used, typically by using less-than or greater-than symbols in one of the boundaries. For instance, one might define the classes as 10 to less than 20, 20 to less than 30, and so on. This way, each value can be placed into exactly one class with no overlap and no confusion.
Non-overlapping classes improve the clarity of the distribution, allowing analysts to summarize, compare, and interpret data with confidence. They also help in creating accurate graphical representations, such as histograms or frequency polygons, which depend on precise class boundaries to convey meaningful patterns in the data.
