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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?
1. 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
2.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
3.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
4.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 the relationship between the number of chapters and the total pages of the books, we need to consider the type of data and the nature of the relationship.

  1. Line Graphs: Best suited for showing trends over time or continuous data. In this case, the number of chapters and total pages are discrete values, and the relationship is not a continuous trend.

  2. Scatter Plots: Ideal for visualizing the relationship between two variables, especially when the relationship might not be linear. The points can be plotted to see if they form any pattern.

Given this information, the scatter plot allows us to effectively visualize the relationship between the number of chapters and total pages, without implying a continuous line connecting the points, which may misrepresent the relationship.

Now let's evaluate the options considering the correct scale:

  • Scatter Plot Option 2 (with a range of the x-axis from 0 to 38 and the y-axis from 0 to 450) provides sufficient range but is too large for the actual data points.
  • Scatter Plot Option 4 (with a range of the x-axis from 0 to 20 and the y-axis from 0 to 275) is more focused and appropriate for the actual data values.

Therefore, the best choice is:

4. 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).