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 to avoid confusion and ensure that each data value is counted in one and only one class.
Explanation:
When constructing a frequency or relative frequency distribution for continuous data, it is essential to create distinct, non-overlapping classes. Overlapping classes introduce ambiguity because it becomes unclear where certain data points belong. For example, if two classes are defined as 10–20 and 20–30, a value of 20 could fall into either class. This overlap causes uncertainty in classification, making the data summary inaccurate.
To maintain clarity, class boundaries must be defined in a way that ensures every possible data value fits into one unique class. This is typically achieved by using intervals such as 10–19.9 and 20–29.9, or by specifying the boundary with inequality symbols like 10 ≤ x < 20 and 20 ≤ x < 30. Such definitions eliminate ambiguity by assigning each value to exactly one class, which is crucial for consistent analysis.
Non-overlapping classes help preserve the integrity of statistical results. Accurate frequency counts depend on precise categorization. If data points are double-counted or not counted at all due to class overlaps, the resulting distribution misrepresents the data. This misrepresentation can lead to faulty conclusions, especially in further analysis such as calculating mean, median, or constructing histograms.
Moreover, non-overlapping intervals are vital in data visualization. A histogram built from overlapping classes would show incorrect frequencies and distort the overall shape of the data distribution. Proper class construction enhances both the clarity and effectiveness of the data summary.
In conclusion, classes must not overlap in a frequency distribution to ensure accuracy, avoid confusion, and support valid interpretation of continuous data.
