Question

The box plots show the average gas mileage of cars and minivans tested by a certain company.

2 box plots. The number line goes from 14 to 34. For cars, the whiskers range from 21 to 33, and the box ranges from 22 to 29. A line divides the box at 24. For minivans, the whiskers range from 14 to 26, and the box ranges from 18 to 21. A line divides the box at 19.

Josef says that the range for the car data is greater than the range for the minivan data because the box in the box plot for the car data is wider. Which explains Josef’s error?
A. Josef confused the range and the interquartile range.
B. Josef confused the range and the median.
C. Josef should have compared the medians and minimum values.
D. Josef should have compared the medians and maximum values.

Answer 1

B, Josef is confused about the range and the interquartile range.

Explanation:

You have to make the box plot using the numbers given

Find the IQR *interquartile range* and the difference between the max and the minimum numbers.

For the cars the IQR is: 6

The range for the cars is: 12

The IQR of the minivan is: 3

The range of the minivan is: 12

The ranges are the same but IQR of the cars is bigger, that's where Josef got confused.