Students may struggle to know how to place numbers that lie on the boundary between intervals. For example, students may not know if a value like 60 should be included in the interval 50–60 or 60–70. Explain to students that the lower boundary value is included in the interval, and the upper boundary value is not. For example, the interval 60–70 includes all the values that are greater than or equal to 60 and less than 70.

The purpose of this discussion is to make sure that students know how to create and begin to interpret histograms.

Use Stronger and Clearer Each Time to give students an opportunity to revise and refine their responses when explaining the differences between the two histograms. 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 their partners clarify and strengthen their ideas and writing.

Consider displaying these prompts for feedback:

• “What do you mean when you say . . . ?”
• “Can you describe that another way?”
• “How do you know . . . .”

Close the partner conversations, and give students 3–5 minutes to revise their first draft. Encourage students to incorporate any good ideas and words that they get from their partners to make their next draft stronger and clearer.

Here is an example of a second draft: “The second histogram shows a little more detail than the first histogram.”

As 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, consider asking these questions for discussion about creating and interpreting these histograms.

• “Where did you put the 60? In the 50–60 interval or 60–70 interval?” (Tell students that we use the convention of including the 60 in the 60–70 interval. The interval 60–70 means all the values greater than or equal to 60, but less than 70. The interval 50–60 means all values greater than or equal to 50 but less than 60.)
• “What information is easily seen in a histogram?” (The shape of the distribution as well as estimates for the measure of center and measure of variability.)
• “According to each histogram, what appears to be the typical number of days it takes a tomato plant to produce tomatoes?” (Using the first histogram, it appears that the typical number of days is somewhere between 60 and 80. Looking at the second histogram, it appears that the typical number of days could be between 75 and 80.)
• “What information is not seen in a histogram?” (You are not able to see the actual values. You know only the number of values within an interval rather than the values themselves.)

For students who have difficulty calculating the median, remind them that the median is the middle of a sequential data set. For students who have difficulty finding Q1 and Q3, ask them how many groups we should have if we are splitting the data into “quarters.” The data should be divided into four equal groups. The median of the lower half of the values is Q1, and the median of the upper half of the values is Q3.

The goal is to make sure that students understand the five-number summary and to help them think informally about the median as a measure of center. Here are some questions for discussion.

• “What information is easily seen in the box plot?” (The minimum value, quartiles including the median, and the maximum value. This also highlights the interquartile range and the range.)
• “According to the box plot, what is the typical number of days it takes a tomato plant to produce fruit?” (The typical number of days is 71 because the median of the data is 71 days.)