• As students discuss and identify misleading features in graphs, including distortion of axis scales, use of multidimensional pictographs, and use of convenient domains, there is a key opportunity to highlight how important labels are for visual representations. This will help students find value in making precise labels for their own data visuals, rather than thinking of labeling as a trivial detail.
• For each misleading graph, asking “what would be a better way to represent this data?” provides students with agency and the opportunity for creative thinking to reinforce the key concepts of the lesson.
• Students will manually create a few graphs of their own in this lesson, and it’s good to emphasize that they should be able to do so. However, instructors can foreshadow that students will spend much more time in this course analyzing pre-drawn graphs or creating graphs with technology. Offering students this glimpse into the future may be helpful in creating the vision for the course as focused on analysis and critical thinking, rather than manual procedures. It will remain students’ responsibility, however, to recognize and avoid creating graphs that are misleading.

First, download this lesson's slide deck and handout key to see the prompt and sample responses for the Lesson Starter. Then, check out the additional background notes below.

Instructional routine: Notice & Wonder. The lesson handout provides a Notice & Wonder T-frame for students to capture their notes and ideas. It is important that students recognize the difference between a noticing (observation) and a wondering (question that comes to mind). You can find more background on implementing a Notice & Wonder here.

Purpose & Background: The goal of this Lesson Starter is to open the course with questioning sources and images, in an accessible way. The graph that students analyze is one that we return to later in the lesson: a data visualization describing basketball player Kobe Bryant. Specifically, the graph shows the average number of shots that Kobe made per game (9.8) and the average number of assists he had per game (5.0) in the 2009-2010 NBA season. In basketball, an “assist” occurs when a player passes the ball to a teammate, who then scores. However, for the Lesson Starter, none of this background information is given. Students are only given the two basketballs and the axes, with scales and labels. The goal for the Lesson Starter is get students questioning and thinking about this graphic, which will help prime them for the later discussion of this graph in context. As such, none of the context about Kobe Bryant or the exact values for shots/assists should be revealed during the Lesson Starter phase of the lesson.

First, download this lesson's handout key and read through its Discussion Question section. Then, check out our model discussion norms and the additional background notes below.

• It is important to set the stage for discussion beginning on Day 1. Taking the time to develop a conversation and demonstrate appreciation for all inputs will lay the foundation for more complex contexts later in the course.
• Beyond the features mentioned in the lesson handout key, there are additional oddities among the graphs in the Discussion Question. For example, the time intervals on the x-axis aren’t uniform. Neither graph is fully labeled with a title or x-axis label. No information is given as to whether the dollar amounts have been adjusted for inflation (they haven’t). Students may also surface these ideas during class conversation.
• The data for the graphs was compiled by CouponBirds, based on publicly available ticket price information for major U.S. tours and from Pollstar (a data aggregator for the global concert industry). Dollar amounts are not adjusted for inflation. To see inflation-adjusted amounts, check out the graph created by CouponBirds.

• Because the key focus of this lesson is to see and recognize how images can be misleading, slides of the Practice problems with larger images and better contrast have been provided.
• Additional misleading graphs are offered here (with accompanying slides here). These graphs contain more serious contexts. Those provided in the main lesson were selected to support discussion that’s suitable for the first days of school. In classrooms with an established culture and discussion protocols in place, the additional graphs may provide opportunities for deeper discussion.

• A key focus of this course is to work with statistics in ways that will be useful beyond the classroom. Therefore, rather than labels, keys, and titles for graphs being viewed as a checklist required for a grade, they should be recognized as components for communication. The graphs in this lesson set the stage for that perspective by showing examples of how poor labeling can be used to mislead.
• One of the most prominent scholars of data visualization is Edward Tufte. This lesson covers much of the same content from his principles of data visualization. However, one additional principle not covered in this lesson is the “data-ink ratio.” The idea behind the data-ink ratio is to maximize the proportion of ink in a data visual that represents data. According to this principle, every feature on a graph should be used intentionally, without decoration or unnecessary “chart junk” (as Tufte called it). Graphs should be as simple as possible, including only the features needed for representing the data. For example, the practice of using pictures in place of simple bars (e.g. the basketball pictograph from the lesson) is often considered “chart junk.”
• With software advances, it has become easier to utilize animation alongside data visuals. The scholar Hans Rosling has a prominent TED talk showing how animation can be used with scatterplots to tell more compelling data stories. Instructors and students can try their own hand at animating updated versions of the same dataset on the gapminder website.