Question

the box and whisker chart represents the time (minutes) arizonians spent travelling to work.
which of the following statements are correct?
1 the median time is 30 minutes.
2 half of the people travel at least 15 minutes.
3 the quickest travel time is 10 minutes.
4 none of the people travel at least 15 minutes.

Explanation:

Step1: Recall box - plot concepts

In a box - plot, the median is the line inside the box. The lower whisker gives the minimum value (excluding outliers), and the upper whisker gives the maximum value (excluding outliers). The lower quartile (\(Q_1\)) is the left - hand side of the box, and the upper quartile (\(Q_3\)) is the right - hand side of the box.

Step2: Analyze each option

• Option A:

The median is the line inside the box. From the box - plot, the median is \(30\) minutes. So, the statement “The median time is \(30\) minutes” is correct.

• Option B:

The lower quartile (\(Q_1\)) is \(20\) minutes. The number of people who travel at least \(15\) minutes: Since \(Q_1 = 20\) minutes, more than \(25\%\) (because \(15<20\)) of the people travel at least \(15\) minutes. In a box - plot, \(25\%\) of the data is below \(Q_1\). So, the statement “Half of the people travel at least \(15\) minutes” is incorrect.

• Option C:

The lower whisker is at \(10\) minutes. So, the statement “The quickest travel time is \(10\) minutes” is correct.

• Option D:

The lower whisker is at \(10\) minutes. So, the statement “No one or people travel at least \(15\) minutes” is incorrect.

Answer:

A. The median time is \(30\) minutes; C. The quickest travel time is \(10\) minutes.