Question

the box and whisker chart represents the time (minutes) arizonians spent travelling to work
which of the following statements are correct?
a the median time is 30 minutes.
b half of the people travel at least 15 minutes.
c the quickest travel time is 10 minutes.
d most of the people travel at least 15 minutes.

Explanation:

Step1: Recall box - and - whisker plot properties

In a box - and - whisker plot, the left - hand side of the box is the lower quartile (\(Q_1\)), the line inside the box is the median (\(Q_2\)), and the right - hand side of the box is the upper quartile (\(Q_3\)). The left - most whisker represents the minimum value and the right - most whisker represents the maximum value.

Step2: Analyze each option

• Option A:

The line inside the box (median) is at \(30\) minutes. So, the median time is \(30\) minutes.

• Option B:

The left - hand side of the box (lower quartile \(Q_1\)) is at \(15\) minutes. \(25\%\) of the data is less than \(Q_1\) and \(75\%\) of the data is greater than or equal to \(Q_1\). So, half of the people do not travel at least \(15\) minutes.

• Option C:

The left - most whisker (minimum value) is not at \(10\) minutes.

• Option D:

Since \(Q_1 = 15\) minutes, \(75\%\) of the data is greater than or equal to \(15\) minutes. So, most (more than half) of the people travel at least \(15\) minutes.

Answer:

A. The median time is 30 minutes; D. Most of the people travel at least 15 minutes.