Question

time spent traveling home
box plot with time axis labeled 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40
it took della 28 minutes or less to travel home on at least half the days.
the median amount of time it took della to travel home was 30 minutes.
the range of the different amounts of time it took della to travel home was 40 minutes.
it took della between 26 and 32 minutes to travel home on only one - quarter of the days.

Explanation:

To determine the correct statements about the box - and - whisker plot for the time Della spent traveling home, we analyze each statement:

Statement 1: "It took Della 28 minutes or less to travel home on at least half the days."

In a box - and - whisker plot, the median (the line inside the box) represents the middle value of the data set. If the median is at 28 minutes (from the plot, the line inside the box is at 28), this means that at least half of the data points (days) are less than or equal to the median. So, it is true that it took Della 28 minutes or less to travel home on at least half the days.

Statement 2: "The median amount of time it took Della to travel home was 30 minutes."

Looking at the box - and - whisker plot, the line inside the box (which represents the median) is at 28 minutes, not 30 minutes. So, this statement is false.

Statement 3: "The range of the different amounts of time it took Della to travel home was 40 minutes."

The range of a data set is calculated as the maximum value minus the minimum value. From the plot, the minimum value is 20 minutes and the maximum value is 40 minutes. The range is $40 - 20=20$ minutes, not 40 minutes. So, this statement is false.

Statement 4: "It took Della between 26 and 32 minutes to travel home on only one - quarter of the days."

In a box - and - whisker plot, the inter - quartile range (IQR) is the range of the middle 50% of the data. The lower quartile (Q1) is at 26 and the upper quartile (Q3) is at 32. The data between Q1 and Q3 represents 50% (or half) of the data, not one - quarter. So, this statement is false.

Answer:

It took Della 28 minutes or less to travel home on at least half the days.