In this activity, students use a list of data to complete a frequency table and draw a dot plot. The drawing of the dot 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 (like “four people did not order any upgrades”) but also characterize them in broader terms (like “almost all customers in the data set ordered two or fewer upgrades”). Invite them to share during the discussion following the activity.

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 this activity, students 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).

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. Ask students to share what they found to be the center of the distribution and whether that was a good description of the set as a whole.

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:

• “Do you agree with this statement? ‘In general, these students spend roughly the same number of hours doing homework.’” (I disagree. Most of the data spreads out from 0 to 9 hours. There is a student who does not do homework at all, and there are several who spend 8–9 hours per week.)
• “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?” (Students spend anywhere from 0 to 9 hours on homework, but most students spend 1–6 hours. The difference between 1 hour of homework and 6 hours of homework seems like a lot based on how much time there is after school, so the amounts of time seem different.)