This activity introduces students to the term median. They learn that the median describes the middle value in an ordered list of data, and that it can capture what we consider typical for the data in some cases.

Students learn about the median through a kinesthetic activity. They line up in order of the number of letters in their name. Then, those at both ends of the line count off and sit down simultaneously until one or two people in the middle remain standing. If one person remains standing, that person has the median number of letters. If two people remain standing, the median is the mean or the average of their two values. 

Students then practice identifying the median of other data sets, by analyzing both tables of values and dot plots.

Select a few students to share their responses to the questions about number of siblings and Elena's travel times. Focus the discussion on the median as another measure of the center of a data set and whether it captures what students would estimate to be a typical value for each data set.

Emphasize to students that the median is a value and not an individual. For example, if the last person standing in the class has 10 letters in their name, the median is the number 10 and not the person standing. If there is another student who has 10 letters in their name, they might have switched places with the last person standing when lining up initially. Although the person standing could change, the median remains the same value of 10.

At this point, it is unnecessary to compare the mean and the median. Students will have many more opportunities to explore the median and think about how it differs from the mean in the upcoming activities.

In this lesson, students study distributions using dot plots and a histogram for which the mean and median can be the same, close, or far apart, and make conjectures about how the distributions affect the mean and median (MP7). Along the way, students recognize that the mean and median are equal or close when the distribution is roughly symmetrical and are farther apart when the distribution is non-symmetrical.

Students sort different distributions during this activity. A sorting task gives students opportunities to analyze representations, statements, and structures closely and to make connections (MP2, MP7).

As students work, encourage them to refine their descriptions of the distributions using more precise language and mathematical terms (MP6).

Use the whole-class discussion to reinforce the idea that the distribution of a data set can tell us which measure of center best summarizes what is typical for the data set. Briefly review the answers to the statistical questions, and then focus the conversation on the last questions (how students knew which measure of center to use in each situation). Select a couple of students to share their responses. Discuss:

• “For data sets with non-symmetrical distributions, why does the median turn out to be a better measure of center?” (Non-symmetrical data sets often have unusual values that pull the mean away from the center of data. The median is less influenced by these values.)
• “Does it matter which measure we choose to describe a typical value? For example, in Card F, would it matter if we said that a typical age for the people who went on the field trip to D.C. was about 21 years old?” (Yes, it does matter in some cases. In that example, it wouldn’t really make sense to say that 21 years is a typical age because the vast majority of the people on the trip were teenagers.)

Use Critique, Correct, Clarify to give students an opportunity to improve a sample written response to the question, “When are median and mean likely to be close?”, by correcting errors, clarifying meaning, and adding details. 

• Display this first draft:
• “They’re the same when most of the points are in the middle.”
• Ask, “What parts of this response are unclear, incorrect, or incomplete?” As students respond, annotate the display with 2–3 ideas to indicate the parts of the writing that could use improvement.
• Give students 2–4 minutes to work with a partner to revise the first draft. 
• Display and review these criteria: 
• Specific words and phrases: “symmetric” or “approximately symmetric” distributions
• Select 1–2 individuals or groups to read their revised draft aloud slowly enough to record for all to see. Scribe as each student shares, then invite the whole class to contribute additional language and edits to make the final draft even more clear and more convincing.