Who Wins?
Mean versus Median
Subject: Mathematics
Grades: 6-8
Ages: 11-14
Lesson Objective
In middle school, students learn how to calculate mean and median but often have difficulty describing differences in these two values and determining the most appropriate measure of center to use in a given situation. This lesson uses InspireData® to bring data about students and basketball players to life. Students will examine the connection between data distribution and measures of central tendency.
Teacher Instructions
- Begin class by asking students to estimate the average height of students in the class. What about the average height of professional basketball players? Inform students that they will be using data about themselves and famous basketball players to investigate two measures of central tendency, the mean and the median. Direct students to determine their age in months, height to the nearest inch and number of siblings. If necessary, provide measuring tools so that students can help each other find accurate heights.
- Access the Athletes and Us database from the InspireData Starter Screen>Databases>Mathematics. This database is a Web Resource and will only be available with an Internet connection. Examine the data contained in the Sample Data tab to show students the type of table they will be building. Explain that their data will be added to data about four basketball players.
- Select the Database Template tab to begin entering student data. Data can be entered directly into the table or with the Survey or e-Survey tools. For more information, refer to InspireData Starter Screen>Learn to Use>Documentation>Handouts>Learn to Use Surveys.
Note: To limit height measurements to one unit (inches or centimeters), simply delete a field in Table View.
- Open the database containing the compiled survey data. Demonstrate how to create a Stack Plot of Height (inches or centimeters). Label the icons by the Name field. Ask students to describe the distribution of heights. Do any heights stand apart from the rest? Do you see any evidence of clustering? In what range do most heights fall? Refer to InspireData Starter Screen>Learn to Use>Documentation>Handouts>Learn to Use Stack Plots and Learn to Use Plots for more information about stack plot and labeling icons.
- Add the Median and the Mean to the Height stack plot. Discuss the meaning of both measures of central tendency in the context of the distribution of heights. Why is the mean height larger than the median height? What impact do the basketball players have on either of these measures? Demonstrate how to use the Notes Area to record the mean, median and several observations about their meaning in the context of heights before capturing a Slide. For information on adding the median and mean, go to the Help menu or see the User’s Manual. Refer to InspireData Starter Screen>Learn to Use>Documentation>Handouts>Learn to Use Slides Shows for more information about creating slides.
- Exclude the basketball players from the stack plot. This also excludes the heights of the basketball players from the mean and median calculations. Elicit observations from students about the new mean and median values. Why are they closer together? How did the outliers impact the value of the mean? Use the Notes Area to record the mean, median and student observations before capturing a Slide. For information on excluding data, go to the Help menu or see the User’s Manual.
- Break students into as many groups as there are computers available and have them access the database containing the compiled survey data. Ask each group to explore the distribution of the other two numerical fields, Number of Siblings and Age in Months by answering the questions below
Note: Students might want to change the intervals on the axes. This can be done by selecting Step below the axis and entering a new value.
a. For the field Age in Months, complete the following:
i. Create a Stack Plot, Label by Name and select to show the Mean and Median.
ii. Use the Notes Area to record both measures, observations about any differences in the values and any reasons for those differences. Capture a Slide.
iii. Exclude the data from the basketball players.
iv. Use the Notes Area to record the new Mean and Median values. How much did these values change, if any? Why? Record observations and then Capture a Slide.
v. Select View All from the Plot menu before moving on to subtopic b.
b. For the field Number of Siblings, complete the following:
i. Create a Stack Plot, Label by Name and select to show the Mean and Median.
ii. Use the Notes Area to record both measures, observations about any differences in the values and any reasons for those differences. Capture a Slide.
iii. Exclude the data from the basketball players.
iv. Use the Notes Area to record the new Mean and Median values. How much did these values change, if any? Why? Record observations and then Capture a slide.
- Convene as a class, display the plots and discuss student observations. Which is the best measure of the center for Height? Number of Siblings? Age in Months? How does the distribution of a plot determine the most appropriate measure of the center of a data set? What impact do outliers have? Ask students why the median is used as a measure of income rather than the mean. What impact do people like Bill Gates have on these values?
Assessment
- Student groups can present their slides and observations. They can be assessed on the quality of their observations and their presentation skills.
- Assess how well students understand measures of center by their contributions to the whole-class discussions.
Lesson Adaptations
- Ask students to research the age, height and siblings of several basketball players before coming to class. This will require students to determine age in months based on the athlete’s date of birth and perform any conversions to get height in inches or centimeters.
- Assign completion of the e-Survey as homework so the completed database is ready for analysis when class begins.
- This lesson can be extended by asking students to research other sets of data with potential outliers. They can use InspireData to plot the data, determine the mean and median and choose the most appropriate measure of center.
