Lesson 4

This warm-up serves two purposes. It prompts students to determine when a dot plot is an appropriate representation and allows students to practice organizing data into a frequency table. The table completed in this activity will be used in the following activity in this lesson. 

Arrange students in groups of 2. Give students 2 minutes to complete the activity with a partner, and then another 1–2 minutes for them to compare their frequency tables with another group.  

Ask a couple of students to share their responses to the first question and poll the class for their agreement or disagreement.

After organizing the data set into a frequency table in the warm-up, students now represent the information graphically. The drawing of the plot should be fairly straightforward. The emphasis here is on using a graphical representation to study and comment on the data distribution, and to reinforce how it allows us to make observations that are difficult to make by looking at lists and tables.

As students work, identify those who describe distributions not only in terms of individual categories or values (e.g. “four people did not order any toppings”) but also characterize them in broader terms (e.g. “almost all customers in the data set ordered 2 or fewer toppings”). Invite them to share during the discussion following the activity.

Keep students in groups of 2. Give students 4–5 minutes of quiet work time and 1–2 minutes to share their responses with a partner. 

Display a completed dot plot for all to see. Solicit as many observations or comments about the distribution as time permits. The goal of this discussion is to allow students to hear as many ways to describe distributions as possible. Be sure to select previously identified students to make observations that succinctly capture the distributions. 

In the previous activity, students commented on distributions on a dot plot and had opportunities to hear different ways to describe distributions. In this activity, they begin to think about how to characterize a distribution as a whole, in terms of its center and spread. Students learn that we can give a general description of a distribution by identifying a location that could be the center of the data, and by noting how alike or different the data points are. 

Note that at this point “center” and “spread” can only be identified and described informally, via visual observation and intuitive reasoning about how data points are distributed. The lack of precise ways to identify center and spread helps to cultivate the need for more formal measures later.

In this activity, students evaluate and critique another's reasoning (MP3).

Keep students in groups of 2. Ask students to read the question in the stem, “How many hours do you generally spend on homework each week?” Then, ask students to explain why this is a statistical question. This is a statistical question because it can be answered by collecting data, and we can expect variability in the data.

Give them 6–7 minutes of quiet time to work on the first three questions, and then 4–5 minutes to share their responses with their partner and to complete the last two questions together. Be sure to leave at least 5 minutes for a whole-class discussion.

Students may not recall how to find a percentage. Remind them that a percentage can be found if we know the size of a part and that of a whole. If needed, prompt them to determine the size of the entire data set. 

Ask a couple of students to share their thinking on what number of hours would be a good description of homework time for this group of students and why. Then, select a couple of other students to discuss how alike or different the lengths of homework time are.

Explain that sometimes it helps to describe a set of data generally, or to characterize it as a whole. One way to do that is by finding a value that describes the whole set reasonably well, or a value whose location can be considered the “center” of a distribution. Ask students:

• “Where on the dot plot would you consider the center of the data? What is the value of that center?”

Another way to characterize a data set is by describing its “spread,” or the variability in the data points. The wider the spread (the more dispersed the data points are on a dot plot), the more variable or different they are. The narrower the spread (the more clustered together), the more alike they are. Ask students:

• “Based on the dot plot, how would you describe the spread of the students’ homework time? Are the amounts of time they spend on homework alike or different?”

Tell students that we will continue to explore center and spread in upcoming lessons.