## Using NBA Statistics for Box and Whisker Plots

• Lesson
6-8
1

In this lesson, students use information from NBA statistics to make and compare box and whisker plots. The data provided in the lesson come from the NBA, but you could apply the lesson to data from the WNBA or any other sports teams or leagues for which player statistics are available.

Students will make 3 box and whisker plots for sets of data about basketball players. They will make 1 box and whisker plot for the players’ weights, and 2 box and whisker plots for height. One will include the tallest player, and one will not. The effects of changing one piece of the data will be addressed.

Students can work in groups or pairs throughout this activity, but make sure that they all record their own information on their own activity sheet.

### Background Knowledge

Students should be familiar with interpreting and constructing a box and whisker plot. Use the first example on the activity sheet, in which the weights of the players are analyzed as a warm up or a whole-class activity. The concepts of minimum, maximum, median, upper quartile and lower quartile may need to be reviewed.

Students may find it helpful to use graphing calculators to display the box and whisker plots, if they are available. Instructions for graphing on the TI-83/84 are available here.

### Gathering Data

Students gather data to complete 2 tables, but make 3 box and whisker plots on the activity sheet.

Explain to students that, for this lesson, we will only gather data for the team members who have numbers. Professional teams have practice players who don't have numbers, but we won't be using them for statistics in this lesson in order to keep the sample size down.

• Internet Option: Tell students that they can look up the roster of the Houston Rockets at the official page (use a simple search engine to provide students the URL). Have students record the names, weight, and height of the players who have numbers.
• Non-Internet Option: Give students a copy of the Houston Rockets roster. Have them record the data for the players who have a number
NBA Player Statistics

For each of the numbered players on the Houston Rockets, write down their name and weight on the activity sheet. Find the minimum, maximum, lower quartile, upper quartile and median for the numbers.

Show students how to construct a box and whisker plot from the data. If you are using TI-83/84 these instructions can help. The box and whisker plot students generate should resemble this:

Next, students should gather data on the height of the numbered players. The heights are given in feet and inches and need to be converted to inches. The conversion formula is the number of feet times 12 plus the number of inches. Check that students know how to do this by asking them to convert 6’8”, 5’6”, and 7’3” into inches. Write an example on the board for students to use as a reference. This will help ensure that they focus on the constructing and analyzing of a box and whisker plot rather than on converting the player’s height.

Ask students to record the height of each player in inches. Ask students to check their answers with a partner, and to check with you when they think they are finished. Monitor that students are recording the heights properly. Consider keeping a list of converted heights handy to give it to or read to any student who is struggling.

### Analyzing the Data

Check the box and whisker plots that the students have made. The first height graph (Question 3 on the Activity Sheet) should include all of the "numbered" players. Make sure students record the minimum, maximum, lower quartile, upper quartile, and median. Before students move on to Question 4, ask them to compare their first plot with their neighbors’ plots to see if they agree on what the plot should look like. Have a plot ready to show if there is unresolved disagreement. This will allow you to be sure that all students have constructed the plot properly. The aim here is to compare 2 plots, so accuracy is important. Without accurate plots, no analysis can occur.

The second box and whisker plot of heights (Question 4) excludes the height of Yao Ming (the tallest player). Again, make sure students record the minimum, maximum, lower quartile, upper quartile, and median.

Students are to compare the 2 height plots and then write about what changed and what stayed the same. They need to identify which statistics changed and explain why some of the statistics changed while others did not.

If a group finishes early, ask them to predict what happens to the box and whisker plot for players’ weights when Yao Ming is removed. Ask them if they think they will have the same observations as they did for the players' heights. Have them check their predictions by constructing the additional plot.

When students have finished, lead a whole-group discussion to read and read and answer Questions 5 to 8 on the Activity Sheet. Have students explain the changes they observed. Record and display their specific reasons to help the class critique the reasoning of others. Talk about any misconceptions and emphasize why changes occurred or did not occur. You may need to add your own reasons to the list if students are not coming up with valid reasons on their own.

Ask the whole class to write down what they think might happen to the mean height when Yao Ming is removed from the data.

After students have predicted the changes, ask them to calculate the mean height with and without Yao Ming. Students should find that the median doesn't change, but the mean changes drastically when Yao Ming is excluded.

Assessment Options

1. Ask students to use the Houston Rockets data to make weight box and whisker plots with and without Yao Ming. Then ask the same questions as used in the activity.
2. Make 2 box and whisker plots for the Denver Nuggets. In this case they could do one that includes Chucky Atkins (the shortest player on the team)and one that does not. Then ask the same questions as used in the activity.
3. Make 2 height box and whisker plots for an NBA team of the students’ choice. Answer the same questions as used in the activity.

Extensions

1. Students could use another team’s roster and eliminate the tallest or shortest player as suggested in the Assessment Options section.
2. Ask students to use the Rockets data again to make a new plot, but this time eliminate player(s) with the median height. What differences do they observe between the plots?
3. If Internet access is available, students could research to determine the shortest player in the NBA, and then find that player’s roster.

Questions for Students

Use these questions to compare the height plots.

1. What happened to the medians? Explain why.
2. What happened to the maximums? Explain why.
3. What happened to the first and third quartiles? Explain why.
4. What happened to the mean? Explain why.
5. How does the plot change if the shortest player is removed?
6. Suppose the height of a player near the middle of the ordered list is removed instead of Yao Ming. How will the statistics change?
7. What effect does Yao Ming have on the range and the mode?
8. Suppose the heights of Yao Ming and just 4 other numbered players are used to make a box and whisker plot. What effect does removing Yao Ming from the data have on the plot?

Teacher Reflection

• How effective was it to have students compare their plots with each other to determine if there was agreement on the shape of the plot? What can you do to make this strategy more effective so students don’t rely on you as the authority?
• What student misconceptions did you anticipate, and how did you address them?
• What advantages, if any, are there in using a graphing calculator with this lesson?
• How might you use a lesson like this be teach students about other types of graphical representations?
• Did you find it necessary to make adjustments while teaching the lesson? If so, what adjustments did you make? Were they effective?

### Learning Objectives

In this lesson, students will:

• Collect data on the height of the Houston Rockets' players.
• Create box and whisker plots.
• Compare and analyze different box and whisker plots.

### NCTM Standards and Expectations

• Understand relationships among units and convert from one unit to another within the same system.
• Formulate questions, design studies, and collect data about a characteristic shared by two populations or different characteristics within one population.
• Select, create, and use appropriate graphical representations of data, including histograms, box plots, and scatterplots.
• Discuss and understand the correspondence between data sets and their graphical representations, especially histograms, stem-and-leaf plots, box plots, and scatterplots.