The given box plots show the number of text messages Paul and Sally received each day on their cell phones.
Select the true statement.
A.
The interquartile range of Paul's data is less than the interquartile range of Sally's data.
B.
The median of Paul's data is equal to the median of Sally's data.
C.
The median of Paul's data is greater than the median of Sally's data.
D.
Paul's data has a larger overall spread than Sally's data.
To determine the correct statement, we need to analyze the given box plots. Box plots display the five-number summary of a dataset: minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum.
It is important to note that "interquartile range" refers to the range of the middle 50% of the data, which is the difference between the first and third quartiles (Q3 - Q1).
Now, let's examine each statement:
A. The interquartile range of Paul's data is less than the interquartile range of Sally's data.
- To verify this, compare the lengths of the boxes in each box plot. If Paul's box plot is narrower than Sally's, it means that his interquartile range is smaller. Conversely, if Paul's box plot is wider, it means his interquartile range is larger.
B. The median of Paul's data is equal to the median of Sally's data.
- Check the positions of the medians on each box plot. If Paul's median is at the same value as Sally's median, then this statement is correct.
C. The median of Paul's data is greater than the median of Sally's data.
- Compare the positions of the medians. If Paul's median is further to the right (higher values) than Sally's median, this statement is true.
D. Paul's data has a larger overall spread than Sally's data.
- Observe the whiskers of each box plot. If Paul's whiskers stretch further away from the box (indicating more extreme values) compared to Sally's whiskers, then this statement is correct.
By carefully examining the given box plots, you will be able to determine which statement is true.
To determine the correct statement, we need to analyze the given box plots.
Looking at the box plots, we can see that the box for Paul's data is wider than the box for Sally's data. This indicates that the interquartile range (IQR) of Paul's data is larger than the IQR of Sally's data.
Therefore, the correct statement is:
A. The interquartile range of Paul's data is less than the interquartile range of Sally's data.