## Double Box-and-Whisker Plots

### Topic

Comparing the Salaries of NBA players to WNBA and MLS players

### Vocabulary

- Box-and-whisker plots
- Double box-and-whisker plots
- Median
- Quartile
- Dispersion of data

### Student Exploration

#### How can you use a double box-and-whisker plot to compare the salaries of NBA and WNBA players? How can you use a double box-and-whisker plot to compare the salaries of MLS and NBA players?

Create a double box-and-whisker plot for the salaries of National Basketball Association (NBA) and Women’s National Basketball Association (WNBA) players. The NBA and WNBA are highest levels of professional basketball in the United States. Use the websites below for determining the salaries of the top twenty highest paid players in both leagues.

Then create a double box-and-whisker plot for the Major League Soccer (MLS) and NBA players. The MLS is the highest level of professional soccer in the United States and Canada. Use the websites below for determining the salaries of the top twenty highest paid players in the MLS.

http://www.draftexpress.com/nba-player-salaries/

http://womensbasketballonline.com/wnba/rosters/salary.htm

http://www.mlsplayers.org/salary_info.html

- 1. Compare the box-and-whisker plots for the NBA and WNBA players’ salaries.
- 2. Compare the box-and-whisker plots for the MLS and NBA players’ salaries.

*Here is an example of a double box-and-whisker plot for the 2011-2012 seasons for the top 20 highest paid players’ salaries in the MLS and NBA.*

*NBA Top 20 Highest Salaries (in red)*

*Maximum: 25244493, Q3: 18714150, Medium: 17104485, Q1: 15691000, and Minimum: 15032144*

*MLS Top 20 Highest Salaries (in blue)*

*Maximum: 6500000, Q3: 900000, Medium: 4075000, Q1: 323750, and Minimum: 250000*

*A comparison of the two box-and-whisker plots and the data that they represent could include the following observations. Both box-and-whisker plots are skewed to the left, indicating that of the twenty highest paid players in both the MLS and NBA the salaries are not evenly distributed and that most players’ salaries are in the higher portion of each range. This NBA data is even more strongly skewed to the left, showing that the NBA salaries are distributed even less evenly and that most of the players are in the highest part of the salary range. The MLS has a larger salary range than the NBA, as its box plot is wider. The salaries for the NBA are much higher than the MLS as the values of the two box plots do not intersect.*

A basketball.

A soccer ball.

### Extension Investigation

- 3. What does the first double box-and-whisker plots for the NBA and WNBA players’ salaries show about the distribution of the data? Explain and give specific examples.
- 4. What does the graph show about the salaries of NBA and WNBA players? Explain your reasoning.
- 5. What does the second double box-and-whisker plots for the MLS and NBA players’ salaries show about the distribution of the data? Explain and give specific examples.
- 6. What does the graph show about the salaries of MLS and NBA players? Explain your reasoning.
- 7. What are the advantages of presenting the athletes’ salary data in a box-and-whisker plot graph? Explain.
- 8. Suppose a salary is chosen at random. Based on the box plots, what is the approximate probability that the salary falls between the median and third quartile for the NBA, WNBA and MLS? Explain your reasoning.
- 9. Scan and upload your graph to the CK-12’s website to share with other students! You can also use educreations.com to record your discussion of your double box-and-whisker plots and then upload your video to the CK-12’s website!

### Resources Cited

http://www.draftexpress.com/nba-player-salaries/

http://womensbasketballonline.com/wnba/rosters/salary.htm

http://www.mlsplayers.org/salary_info.html

### Connections to other CK-12 Subject Areas

- Measures of Central Tendency and Dispersion
- Median
- Box-and-Whisker Plots

Photos from:

http://pixabay.com/en/photos/?q=basketball

http://pixabay.com/en/black-outline-soccer-silhouette-34898/