Modeling Prompt

The US 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 these are some of the characteristics we have information on:

• 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, completion rate, percent of white students, and median ACT score), which can also be included in this discussion if students will be using that task statement.

Ask students to identify what type of data each of these is (for example, categorical, percent, mean, or count). Once all the types are identified, ask "Which of these characteristics might be related to each other? How are they related?" Write down 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. However, students do not need to have well-supported reasons at this time.

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

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

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