A group of 15 students were assigned a novel to read during class. The data below represents the number of pages each student read.
8, 8, 10, 11, 12, 12, 13, 14, 16, 16, 18, 18, 18, 20, 24
Which of the following box plots correctly summarizes the data?
A.
The end of the first whisker is at 8, the box starts at 12, the line inside the box is at 16, the box ends at 18, and the end of the second whisker is at 24.
B.
The end of the first whisker is at 8, the box starts at 11, the line inside the box is at 14, the box ends at 18, and the end of the second whisker is at 24.
C.
The end of the first whisker is at 8, the box starts at 11, the line inside the box is at 16, the box ends at 18, and the end of the second whisker is at 24.
D.
The end of the first whisker is at 8, the box starts at 11, the line inside the box is at 14, the box ends at 20, and the end of the second whisker is at 24.
C.
The end of the first whisker is at 8, the box starts at 11, the line inside the box is at 16, the box ends at 18, and the end of the second whisker is at 24.
To summarize the data using a box plot, we need to understand the key components: the minimum, lower quartile (Q1), median, upper quartile (Q3), and maximum.
First, let's sort the data in ascending order:
8, 8, 10, 11, 12, 12, 13, 14, 16, 16, 18, 18, 18, 20, 24
Now, let's find the corresponding values:
Minimum: 8
Lower quartile (Q1): The median of the lower half of the data. In this case, it's the median of the values from 8 to 14. The median of these values is 12.
Median: The median of the entire data. In this case, it's the median of all the values, which is 14.
Upper quartile (Q3): The median of the upper half of the data. In this case, it's the median of the values from 16 to 24. The median of these values is 18.
Maximum: 24
Now that we have these values, let's compare them to the options provided:
A. The end of the first whisker is at 8, the box starts at 12, the line inside the box is at 16, the box ends at 18, and the end of the second whisker is at 24. This option is incorrect because the line inside the box should represent the median, which is 14 in this case, not 16.
B. The end of the first whisker is at 8, the box starts at 11, the line inside the box is at 14, the box ends at 18, and the end of the second whisker is at 24. This option is incorrect because the box should end at the upper quartile, which is 18 in this case, not at 20.
C. The end of the first whisker is at 8, the box starts at 11, the line inside the box is at 16, the box ends at 18, and the end of the second whisker is at 24. This option is incorrect because the line inside the box should represent the median, which is 14 in this case, not 16.
D. The end of the first whisker is at 8, the box starts at 11, the line inside the box is at 14, the box ends at 20, and the end of the second whisker is at 24. This option is correct because it accurately represents the minimum, Q1, median, Q3, and maximum of the data.
Therefore, the box plot that correctly summarizes the data is option D.