In the context of interpreting a graph related to confidence intervals, why might the $\mathrm{percentages}$ shown not add up to $100\%$?

• A. Because the graph is displaying cumulative frequencies, not $\mathrm{percentages}$.
• B. Because confidence intervals always require the $\mathrm{percentages}$ to sum to less than $100\%$.
• C. Because $\mathrm{percentages}$ in statistics are never expected to add up to $100\%$.
• D. Because the categories may overlap, causing some data points to be counted in more than one category.

Answer: (D)

Verified step by step guidance

1. Understand that percentages typically add up to 100% when categories are mutually exclusive and collectively exhaustive, meaning each data point belongs to exactly one category.
2. Recognize that in some graphs, especially those involving confidence intervals or overlapping categories, data points can belong to more than one category, causing overlaps.
3. When categories overlap, the percentages represent proportions of the total data that fall into each category, but some data points are counted multiple times across categories.
4. This overlap means the sum of the percentages can exceed 100%, because the percentages are not mutually exclusive parts of a whole.
5. Therefore, the percentages shown in such graphs do not add up to 100% because the categories overlap, not because of cumulative frequencies or any rule about confidence intervals.