options: Understand independence and conditional probability and use them to interpret data.

Interpret linear models.

Investigate chance processes and develop, use, and evaluate probability models.

Understand and evaluate random processes underlying statistical experiments.

Use probability to evaluate outcomes of decisions.

Develop understanding of statistical variability.

Draw informal comparative inferences about two populations.

Summarize and describe distributions.

Calculate expected values and use them to solve problems.

Summarize, represent, and interpret data on a single count or measurement variable.

Summarize, represent, and interpret data on two categorical and quantitative variables.

Make inferences and justify conclusions from sample surveys, experiments, and observational studies.

Use random sampling to draw inferences about a population.

Use the rules of probability to compute probabilities of compound events in a uniform probability model.

Investigate patterns of association in bivariate data.
problem_activity: Activity
After organizing the data set into a frequency table in the warm-up, students now represent the information graphically. The drawing of the 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 (e.g. “four people did not order any toppings”) but also characterize them in broader terms (e.g. “almost all customers in the data set ordered 2 or fewer toppings”). Invite them to share during the discussion following the activity.
Launch
Keep students in groups of 2. Give students 4–5 minutes of quiet work time and 1–2 minutes to share their responses with a partner.
Action and Expression: Develop Expression and Communication.
Invite students to talk about their ideas with a partner before writing them down. Display sentence frames to support students when they explain their ideas. For example, “I notice that . . .,” or  “I know _____ because . . .”
Supports accessibility for: Language; Organization
Student Facing
Use the tables from the warm-up to display the number of toppings as a dot plot. Label your drawing clearly.
[IMG]
Use your dot plot to study the distribution for number of toppings. What do you notice about the number of toppings that this group of customers ordered? Write 2–3 sentences summarizing your observations.
Student Response
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Student Facing
Are you ready for more?
Think of a statistical question that can be answered with the data about the number of toppings ordered, as displayed on the dot plot. Then answer this question.
Student Response
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Activity Synthesis
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.


correct_option_index: 7