Question

the box plots show the average gas mileage, in miles per gallon, of cars and minivans tested by a certain company. which correctly compares the interquartile ranges? the interquartile range for cars is about 8 mpg, and the interquartile range for minivans is about 7 mpg. the interquartile range for cars is about 24 mpg, and the interquartile range for minivans is about 19 mpg. the interquartile range for cars is about 7 mpg, and the interquartile range for minivans is about 3 mpg. the interquartile range for cars is about 12 mpg, and the interquartile range for minivans is about 12 mpg.

Explanation:

Step1: Recall IQR formula

The inter - quartile range (IQR) is \(Q_3 - Q_1\), where \(Q_3\) is the third - quartile and \(Q_1\) is the first - quartile.

Step2: Identify \(Q_1\) and \(Q_3\) for minivans

For minivans, \(Q_1\approx18\) and \(Q_3\approx25\). Then \(IQR_{minivans}=Q_3 - Q_1\approx25 - 18 = 7\).

Step3: Identify \(Q_1\) and \(Q_3\) for cars

For cars, \(Q_1\approx24\) and \(Q_3\approx32\). Then \(IQR_{cars}=Q_3 - Q_1\approx32 - 24 = 8\).

Answer:

The interquartile range for cars is about 8 mpg, and the interquartile range for minivans is about 7 mpg.