Question

Catherine and Ana suspect that athletes (i.e., students who have been on at least one varsity team) typically have a faster reaction time than other students. To test this theory, they gave an online reflex test to 33 varsity athletes at their school and 29 other students. Here are parallel boxplots and numerical summaries of the data on reaction times (in milliseconds) for the two groups of students. Write a few sentences comparing the distribution of reaction time for the two types of students.

Short answer

The varsity distribution has a right skewed distribution, whereas the other distribution is roughly symmetric.

The varsity distribution's centre is lower than the student distribution's centre.

Both distributions appear to have a similar spread.

The Varsity distribution contains one outlier, whereas the other distribution contains two.

Step-by-step solution

Step 1. Given information.

Here are parallel boxplots and numerical summaries of the data on reaction times (in milliseconds) for the two groups of students.

Step 2. A few sentences comparing the reaction time distributions of the two types of students

The varsity distribution is skewed to the right due to the boxplot's box lying to the left between the whiskers. Because the box of the boxplot lies roughly in the middle between the whiskers of the boxplot, the other distribution is roughly symmetric.

Center: The varsity distribution's centre is lower than the student distribution's centre because the line in the box of the boxplot (representing the median) is further to the left in the varsity distribution. Furthermore, the mean and median for the other distribution are both higher than for the varsity distribution.

Spread: Because the width between the whiskers of the boxplots is roughly the same for both distributions, they appear to have roughly the same spread.

Unusual characteristics: The Varsity distribution has one outlier, whereas the other distribution has two. In the boxplots, outliers are denoted by a *.

As a result:

The varsity distribution has a right skewed distribution, whereas the other distribution is roughly symmetric.

The varsity distribution's centre is lower than the student distribution's centre.

Both distributions appear to have a similar spread.

The Varsity distribution contains one outlier, whereas the other distribution contains two.