Michael's teacher asked the students in his class to gather data about the number of pages in the chapters of the books they are currently reading.
Michael used the data about the chapters in his book to create the line plot shown below.
Altogether, Michael's class gathered information about the number of pages in the 204 different chapters in all of the books being read by the class. His teacher created the box-and-whisker plot shown below to display the data.
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This question has 3 parts. Be sure to complete all parts.
A
Type your response in the box.
What is an example of a question that the data displays can be used to answer about Michael's book but not about all the books being read by the class? Answer the question, and explain why it cannot be answered about all the books.What is the interquartile range of the data from Michael's book? Explain how you found this value and what it indicates about the book.Michael thinks there are twice as many chapters in the books read by the class with fewer than 11 pages than there are chapters with more than 18 pages because the left whisker of the box-and-whisker plot is twice as long as the right whisker.Explain why Michael is not correct. As part of your explanation, find the approximate number of chapters with page counts in each interval and describe how you found those numbers.
A
An example of a question that the data displays can be used to answer about Michael's book but not about all the books being read by the class is: "How many pages are in Chapter 4 of Michael's book?" This question can be answered by looking at the position of the fourth data point on Michael's line plot but cannot be answered about all the books, since we do not have individual chapter information for every book in the class.
B
To find the interquartile range of the data from Michael's book, we first need to find the values of Q1 (first quartile) and Q3 (third quartile). In the line plot, since the number of chapters is not given, we can only provide a rough estimate. We estimate that Q1 is around 6-7 pages, and Q3 is around 13-14 pages. The interquartile range (IQR) is the difference between Q3 and Q1, so IQR ≈ 13-6 = 7 pages or 14-7 = 7 pages. The interquartile range indicates the spread of the middle 50% of the data or chapter lengths in Michael's book.
C
Michael is not correct because the length of the whiskers does not necessarily indicate the number of chapters within that range. Instead, it shows the distribution of the data. To find the approximate number of chapters with page counts in each interval, we need to look at the percentage of chapters within those intervals.
Looking at the box-and-whisker plot of the entire class, we can estimate the following:
- About 25% of chapters have fewer than 11 pages, as this is the range covered by the left whisker.
- We can see that about 25% of chapters have more than 18 pages, as this is the range covered by the right whisker.
To find the approximate number of chapters in each interval, we multiply the percentage by the total number of chapters:
- Chapters with fewer than 11 pages: 0.25 * 204 ≈ 51 chapters
- Chapters with more than 18 pages: 0.25 * 204 ≈ 51 chapters
So, there are roughly the same number of chapters with fewer than 11 pages as there are chapters with more than 18 pages. This error happened because Michael misconceived the length of the whiskers as a representation of the number of chapters rather than the spread of the data.