Question

The box plots show a random sample of wait times for two rides at a water park.

The median wait time for Speed Slide is
2 minutes longer than the median
wait time for Wave Machine. The IQR for
both rides is 6 minutes.
Express the difference in the medians as a
multiple of the IQRs.
The difference in the medians is
the IQR.
times
Wait Times for Rides
Speed Slide
Wave Machine
5 7
11
9
Time (min)
7
4
13
8
5
9
6
+
15
8

Answer 1

1/3

Explanation:

You want to know the ratio of the difference in median wait times to the IQR for the box plots shown.

Medians

The median is the line in the middle of the box. The medians are ...

• Speed Slide: 11 min
• Wave Machine: 9 min

The difference in median wait times is 11 -9 = 2 min.

IQR

The IQR is the difference between the upper end of the box and the lower end. The IQRs are ...

• Speed Slide: 12 -6 = 6 min
• Wave Machine: 14 -8 = 6 min

Ratio

The ratio of the difference in medians to the IQR is ...

(median difference) / (IQR) = (2 min)/(6 min) = 1/3

The difference in medians is 1/3 times the IQR.

__

Additional comment

The problem already tells you the difference of medians and the IQR, so all you need to do is express than as a ratio.

difference = k × IQR

k = difference/IQR = 2/6 = 1/3

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