All of the information from this section about scatter plots comes into play as students analyze data about animal body and brain weights. Students begin with a table of data and create a scatter plot. After seeing the scatter plot, students pick out any outliers and fit a line to the scatter plot. Finally, the slope of the line is estimated and its meaning interpreted in context (MP2).

In the digital version of the activity, students use an applet to analyze and fit a linear model to the data. The applet allows students to drag two points on a line around the graph to find a good linear model. Use the digital version if available to allow students to try different models easily.

The goal of this discussion is to ensure students can make sense of the data given all the tools from this unit.

Consider asking some of the following questions:

• “Which data did you consider outliers?” (human and chimpanzee)
• “How did you determine your fitted line?” (I tried to get some points on either side of the line so that it would go through the middle of the points.)
• “Let’s assume the trend you found continues past the end of the scatter plot. A Tyrannosaurus rex is a dinosaur that is estimated to have a body weight of about 8,000 kg. What do you expect its brain weight to be?” (About 8,000 g, or 8 kg)

Based on the fossils of Tyrannosaurus rex and what they understand about the dinosaur’s anatomy, scientists believe that their brains would’ve weighed about 1 kilogram. The trend does not appear to continue, at least not in a linear way.

In this activity students create another scatter plot to analyze the data they collected about books in a previous lesson (MP4). A suggested linear model is compared to the data and a particular point is identified in both the scatter plot and data table.

Although the scatter plots are left to students to organize, the only linear model considered is , where represents the weight in ounces and represents the number of pages. If possible, identify any groups who have axes switched to bring up in the discussion.

In the digital version of the activity, students use an applet to create a scatter plot and draw the linear model. The applet allows students to input the data into a table and create a scatter plot. Use the digital version if available to allow students to focus on analyzing the scatter plot without worrying about construction.

The goal of this activity is for students to use the methods they have learned in this unit to explore data they have collected. To highlight some of the main points, select 2–3 students to respond to each question:

• “What is the slope of the line that best fits the data?” (Answers vary based on class data, but should be close to .)
• If any groups had axes switched, select these groups to show their scatter plots. "How can the the line be changed if the axes are different?" (We could switch the and then divide by on each side to get .)
• “What does it mean about a books that is represented by a point is above the line ? What does it mean about a book represented by a point below the line?” (Depending on the axes, a point above the line represents a book with pages that weigh more than ounces on average. Below the line, the books have pages that weigh less than ounces on average.)
• “Suppose you measure pages and weight for a lot of books in the library. When you make a scatter plot, you notice 2 groups of data the seem to line up like parallel lines. What could this mean? Why do you think there may be these clusters?” (It may mean there are hardback books and paperback books. Because the weight of the cover is included, that could bring up the average for that type of book.)