Question
In her free time, Isabelle likes to read. She kept track of the number of pages in each book she read last summer. This box plot shows the results.
Book pages
the values are
100
150
200
250
300
350
What fraction of the books had 200 or fewer pages?
Book pages
the values are
100
150
200
250
300
350
What fraction of the books had 200 or fewer pages?
Answers
GPT-4o mini
To determine the fraction of books that had 200 or fewer pages using a box plot, we would need to look at the quartiles and the distribution depicted in the box plot.
In a typical box plot:
- The smallest value (minimum) is at the leftmost end of the box plot.
- The first quartile (Q1) is shown at the left edge of the box.
- The median (Q2) is shown within the box.
- The third quartile (Q3) is at the right edge of the box.
- The largest value (maximum) is at the rightmost end.
For a box plot indicating ranges of 100, 150, 200, 250, 300, and 350 pages, we want to focus on the position of 200 pages within this range.
Here’s the general approach:
1. If 200 is equal to the first quartile (Q1), that means 25% of the books have pages less than or equal to 200.
2. If 200 is positioned between Q1 and the median (Q2), then you must estimate the percentage of books that fit in that range.
Assuming the box plot shows that 200 falls at Q1, we have 25% of the books with pages of 200 or fewer pages.
However, if Q2 is around 200 and a few more books are also within that number, we must also include those. This way, we would need information about the distribution of pages from Q2 to Q3 to determine the exact fraction.
For the most accurate representation, you would likely graph the distribution based on the quartiles from the box plot. If you can share more specifics, the fraction could be adjusted accordingly.
In conclusion, if we assume that 200 pages correspond with Q1 in the box plot, then about **25%** of the books have 200 or fewer pages. Adjust this estimate based on additional details.
In a typical box plot:
- The smallest value (minimum) is at the leftmost end of the box plot.
- The first quartile (Q1) is shown at the left edge of the box.
- The median (Q2) is shown within the box.
- The third quartile (Q3) is at the right edge of the box.
- The largest value (maximum) is at the rightmost end.
For a box plot indicating ranges of 100, 150, 200, 250, 300, and 350 pages, we want to focus on the position of 200 pages within this range.
Here’s the general approach:
1. If 200 is equal to the first quartile (Q1), that means 25% of the books have pages less than or equal to 200.
2. If 200 is positioned between Q1 and the median (Q2), then you must estimate the percentage of books that fit in that range.
Assuming the box plot shows that 200 falls at Q1, we have 25% of the books with pages of 200 or fewer pages.
However, if Q2 is around 200 and a few more books are also within that number, we must also include those. This way, we would need information about the distribution of pages from Q2 to Q3 to determine the exact fraction.
For the most accurate representation, you would likely graph the distribution based on the quartiles from the box plot. If you can share more specifics, the fraction could be adjusted accordingly.
In conclusion, if we assume that 200 pages correspond with Q1 in the box plot, then about **25%** of the books have 200 or fewer pages. Adjust this estimate based on additional details.