The U.S. Department of Education does a survey of colleges every year. Students will use this data to test a conjecture they have about colleges. Tell students that the data characteristics include:

• College ownership: public, private non-profit, or private for-profit
• Average SAT scores of admitted students
• Acceptance rate
• Number of enrolled students
• Average cost of attendance
• Median earnings 10 years after graduation

Task Statement 1 has four more categories (highest degree awarded, graduation rate, percentage earning more than a high school graduate, and median ACT score), which also can be included in this discussion if students use that task statement.

Ask students to identify the type of data for each characteristic (for example, categorical, percent, mean, or count). Once all the types are identified, ask students: "Which characteristics are related to each other? How are they related?" Record each idea for all to see. Ask students why they think a pair of categories is related in the way they propose, to increase investment in finding the answer, but students do not need to have well-supported reasons at this time.

If students have trouble generating ideas or do not bring up a variety of ideas, introduce a few more. Here are some examples:

• The more selective the college, the higher the average SAT score of the people who are accepted.
• Private for-profit colleges cost more on average but also have a wider range of expenses, because they need to make money and also attract a lot of students.
• Public schools are larger than private schools.

Once enough ideas have been suggested, ask students: “If these relationships exist, how could we see them in the data? How could we present the data to show that they’re true?” Give students quiet think time, and then invite them to share one of their ideas with a partner. Then ask students to share their ideas with the class. Ensure that a variety of ways of presenting data are discussed. Here are some examples:

• The more selective the college, the higher the average SAT score of the people who are accepted: Make a scatter plot of admission rate versus average SAT score.
• Private for-profit colleges cost more on average, but also have a wider range of expenses: Make a box-and-whisker plot of expenses for each type of college.
• Public schools are larger than private schools: Make a two-way frequency table of school ownership (public or private) versus school size (small, medium, and large, defined by ranges of numbers of enrolled students).