Question

This year at the state fair they held two hot dog eating contests. The first contest had 19 contestants and the winner would be the person that ate the most regular-sized hot dogs in 15 minutes. The second contest had 23 contestants and the winner would be the person that ate the most jumbo-sized hot dogs in 15 minutes. The data from both contests are shown in the box-and-whisker plots above. Using the box-and-whisker plots, the results for the____-sized hot dog contest has greater variability. The difference in the medians of the two contests is approximately _____times the interquartile range.

Answer 1

*regular-sized hot dog contest has greater variability

*The difference in the medians of the two contests is approximately 2 times the interquartile range.

Explanation:

Variability of the data from both contests can be compared using the range or interquartile range of each set of data from both contests.

The greater the value of the range or interquartile range, the greater the variability.

Range for regular-sized hot dog contest = 32 - 17 = 15

Range for Jumbo-sized hot dog contest = 22 - 8 = 14

Interquartile range for regular-sized hot dog contest = 27 - 22 = 5

Interquartile range for jumbo-sized hot dog contest = 16 - 11 = 5

Median for regular-sized hot dog contest = 23

Median for jumbo-sized hot dog contest = 14

The difference in the median of both contests = 23 - 14 = 9, which is approximately 2 times the interquartile range (5)

Thus, results for the regular-sized hot dog contest has greater variability, be side its range is 5, which is greater than that for jumbo-sized contest.

The difference in the medians of the two contests is approximately 2 times the interquartile range.

The interquartile range of both contests is 5. The median difference between both contests is 9, it is approximately 2 times 5. (i.e. 9/5 = 1.8 ≈ 2).