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

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?

Given:
                                      car               minivan
minimum number           21                 14
1st quartile                     22                   18
2nd quartile/median       24                   19
3rd quartile                     29                   21
maximum number         33                   26

josef is wrong. the range of the box plot is not determined by the size of the box. the range is computed by deducting the minimum number from the maximum number.

the range of car: 33 - 21 = 12
the range of minivan: 26 - 14 = 12

the range of both box plot are the same.

josef must have referred to the interquartile range. interquartile range is solved by deducting 1st quartile from the 3rd quartile.

iqr of car = 29 - 22 = 7
iqr of minivan = 21 - 18 = 3

as can be seen in the by the formation of the box, the iqr of the car  data is greater than the iqr of the minivan data.