This activity introduces students to histograms. By now, students have developed a good sense of dot plots as a tool for representing distributions. They use this understanding to make sense of a different form of data representation. The data set shown on the first histogram is the same one from the preceding Warm-up, so students are familiar with its distribution. This allows them to focus on making sense of the features of the new representation and comparing them to the corresponding dot plot.

At this point students do not yet need to see the merits or limits of histograms and dot plots. Students should recognize, however, how the structures of the two displays are different (MP7) and start to see that the structural differences affect the insights we are able to glean from the displays.

Ask a few students to briefly share their responses to the first set of questions to make sure that students are able to read and interpret the graph correctly.

Then direct students' attention to the reference created using Collect and Display. Ask students to share their comparison of dot plots and histograms. Invite students to borrow language from the display as needed, and update the reference to include additional phrases as they respond. (For example, “The histogram is less precise, but you can still see the distribution. The center and spread appear similar in both.”)

If not already mentioned by students, highlight that, in a histogram:

• Data values are grouped into intervals or “bins” and represented as vertical bars.
• The height of a bar reflects the combined frequency of the values in that bin.
• A histogram uses a number line.

In this activity, students use histograms to compare two groups by studying the shape, center, and spread of each distribution. Although histograms are not precise, often they can be enough to make a general comparison of groups.

Use Stronger and Clearer Each Time to give students an opportunity to revise and refine their response to the questions about describing the distribution of heights of basketball and baseball players. In this structured pairing strategy, students bring their first draft response into conversations with 2–3 different partners. They take turns being the speaker and the listener. As the speaker, students share their initial ideas and read their first draft. As the listener, students ask questions and give feedback that will help clarify and strengthen their partner’s ideas and writing.

If time allows, display these prompts for feedback:

• “$\underline{\hspace{.5in}}$ makes sense, but what do you mean when you say $\underline{\hspace{.5in}}$?”

• “Can you describe that another way?”

• “How do you know $\underline{\hspace{.5in}}$ ? What else do you know is true?”

Close the partner conversations, and give students 3–5 minutes to revise their first draft. Encourage students to incorporate any good ideas and words they got from their partners to make their next draft stronger and clearer. If time allows, invite students to compare their first and final drafts. Select 2–3 students to share how their drafts changed and why they made the changes they did.

After Stronger and Clearer Each Time, highlight the fact that students are using approximations of center and different adjectives to characterize a distribution or a typical height and that, as a result, there are variations in our descriptions. In some situations, these variations might make it challenging to compare groups more precisely.

If time allows, remind students that this type of analysis uses trends to compare groups, not individuals. There are some baseball players that are taller than some basketball players in these groups, so we cannot determine which sport each person plays based on their height.