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
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.
Students gather data to complete 2 tables, but make 3 box and whisker plots on the activity sheet.
Box and Whisker 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,
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.
Questions for Students
Use these questions to compare the height plots.
- What happened to the medians? Explain why.
- What happened to the maximums? Explain why.
- What happened to the first and third quartiles? Explain why.
- What happened to the mean? Explain why.
- How does the plot change if the shortest player is removed?
- Suppose the height of a player near the middle of the ordered
list is removed instead of Yao Ming. How will the statistics change?
- What effect does Yao Ming have on the range and the mode?
- 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?
- 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?
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.
Common Core State Standards – Mathematics
Grade 6, Stats & Probability
Display numerical data in plots on a number line, including dot plots, histograms, and box plots.