Question

The following back-to-back stem plots compare the ages of players from two minor-league hockey teams ($1/7=17$ years)

Which of the following cannot be justified from the plots?

a. Team A has the same number of players in their $30s$as does Team B.

b. The median age of both teams is the same.

c. Both age distributions are skewed to the right.

d. The range of age is greater for Team A

e. There are no outliers by the$1.5IQR$ rule in either distribution.

Short answer

The answer is option (e) There are no outliers by the $1.5IQR$rule in either distribution.

Step-by-step solution

Given information

The given data is

Explanation

Back-to-back stem plots that compare the ages of players from two minor league hockey teams are provided in the question. As a result, we can see from the selections that,

Option (a) is justified since the plot has equal values on the left and right sides, indicating that both teams have the same number of players, i.e. $25$.

(b) Because the median is the middle value of the sorted data set, and the data are sorted in the plot, we can compute it from the plot.

Option (c) is justified since the skewness of the distribution is visible in the plots, as most of the values are near the top of the plot, indicating that the distribution is right-skewed.

Option (d) is justified since the range is the difference $i=$between the smallest and largest observation, and the smallest and largest observations can be calculated as the data is ordered by the plots.

Option (e) cannot be justified because we will have to perform some computations first, as the $1.5IQR$rule stipulates that outliers are located above or below the third quartile. As a result, option (e) is the proper choice.