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Jordan compared 10 books at the school library. The following table shows the number of chapters and the total number of pages for each book.

Number of Chapters 2 7 8 12 14 15 17 18 19 20
Total Pages 21 72 84 92 87 141 190 185 198 210

Which of the following representations is most appropriate to show the relationship between the number of chapters and the total pages of a book?
line graph titled school library, with the x axis labeled number of chapters ranging from 0 to 38 and the y axis labeled total pages ranging from 0 to 450 with points at 2 comma 21, 7 comma 72, 8 comma 84, 12 comma 92, 14 comma 87, 15 comma 141, 17 comma 190, 18 comma 185, 19 comma 198, and 20 comma 210
scatter plot titled school library, with the x axis labeled number of chapters ranging from 0 to 38 and the y axis labeled total pages ranging from 0 to 450 with points at 2 comma 21, 7 comma 72, 8 comma 84, 12 comma 92, 14 comma 87, 15 comma 141, 17 comma 190, 18 comma 185, 19 comma 198, and 20 comma 210
line graph titled school library, with the x axis labeled number of chapters ranging from 0 to 20 and the y axis labeled total pages ranging from 0 to 275 with points at 2 comma 21, 7 comma 72, 8 comma 84, 12 comma 92, 14 comma 87, 15 comma 141, 17 comma 190, 18 comma 185, 19 comma 198, and 20 comma 210
scatter plot titled school library, with the x axis labeled number of chapters ranging from 0 to 20 and the y axis labeled total pages ranging from 0 to 275 with points at 2 comma 21, 7 comma 72, 8 comma 84, 12 comma 92, 14 comma 87, 15 comma 141, 17 comma 190, 18 comma 185, 19 comma 198, and 20 comma 210

1 answer

To determine the most appropriate representation for showing the relationship between the number of chapters and the total pages of the books, we should consider the properties of the data:

  1. Nature of the Data: The relationship between the number of chapters (a discrete variable) and total pages (a continuous variable) can be effectively represented using a scatter plot, as this type of graph shows individual data points and their correlation without assumed connectivity between the points.

  2. Axes Ranges: Since the maximum number of chapters is 20 and the maximum number of pages is 210, both axes should be limited to these ranges for clarity.

  3. Graph Titles: Including a descriptive title helps understand the context of the data being represented.

Based on these considerations, the most appropriate representation is:

Scatter plot titled school library, with the x axis labeled number of chapters ranging from 0 to 20 and the y axis labeled total pages ranging from 0 to 275 with points at (2, 21), (7, 72), (8, 84), (12, 92), (14, 87), (15, 141), (17, 190), (18, 185), (19, 198), and (20, 210).

This option provides a clear view of the individual relationships without implying a linear progression, within the appropriate ranges.