Question

a sociologist collected data from a sample of people on their highest level of education and the number of times they visited any fast - food restaurant during the previous week. the data are summarized in the boxplots. visits by highest education level based on the boxplots, which of the following statements must be true? a the number of people surveyed at the more than four - year college level is greater than the number of people surveyed at the high school level. b the proportion of people surveyed from the first quartile to the third quartile at the four - year college level is less than the respective proportion at the community college level. c the interquartile range (iqr) for the number of visits at the more than four - year college level is less than the iqr for the number of visits at the community college level. d the maximum number of visits at the community college level is greater than the maximum number of visits at the high school level. e the median number of visits at the four - year college level is greater than the median number of visits at the high school level.

Explanation:

Step1: Recall box - plot properties

A box - plot shows the minimum, first quartile ($Q_1$), median ($Q_2$), third quartile ($Q_3$), and maximum of a data set. The inter - quartile range (IQR) is $IQR = Q_3 - Q_1$.

Step2: Analyze each option

Option A

The box - plot does not give information about the number of people surveyed in each group. We cannot compare the number of people surveyed at different education levels from the box - plot alone. So, option A is incorrect.

Option B

The proportion of data in each quartile is 25% for each part of the box ($Q_1$ to $Q_2$ and $Q_2$ to $Q_3$) and 25% in each of the whiskers. We cannot compare the proportion of people at the first and third quartiles between different education levels just by looking at the box - plot. So, option B is incorrect.

Option C

The IQR for the four - year college level is the length of the box for the four - year college group, and for the community college level is the length of the box for the community college group. From the box - plot, the length of the box (IQR) for the four - year college level is less than the length of the box (IQR) for the community college level. So, the inter - quartile range (IQR) for the number of visits at the four - year college level is less than the IQR for the number of visits at the community college level. This option is correct.

Option D

The maximum value for the high school level is not lower than the maximum value for the community college level. The end of the upper whisker for the high school level is not lower than the end of the upper whisker for the community college level. So, option D is incorrect.

Option E

The median (the line inside the box) for the high school level is not greater than the median for the four - year college level. The median for the high school level is lower than the median for the four - year college level. So, option E is incorrect.

Answer:

C. The interquartile range (IQR) for the number of visits at the four - year college level is less than the IQR for the number of visits at the community college level.