options: Summarize and describe distributions.

Investigate patterns of association in bivariate data.

Understand and evaluate random processes underlying statistical experiments.

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

Calculate expected values and use them to solve problems.

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

Use probability to evaluate outcomes of decisions.

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

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

Develop understanding of statistical variability.

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

Draw informal comparative inferences about two populations.

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

Interpret linear models.

Use random sampling to draw inferences about a population.
problem_activity: Activity
In this activity, students extend their thinking about distribution shapes to using the shape to justify making a decison from a set of repesentations. In previous lessons, students matched distribution shapes to situations. Students practice applying the situations when they choose a representation and are able to eliminate the others. This activity prepares students to compare specific measures of several distribution shapes in a later lesson.
Student Facing
Restaurant A
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Restaurant B
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Restaurant C
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Restaurant D
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Each histogram represents the number of star ratings for a different restaurant. The ratings range from 0–4, with 0 representing a very poor experience and 4 representing an excellent experience. For each question, explain your reasoning.
Which restaurant do reviewers like the most?
Which restaurant do reviewers like the least?
Which restaurant received mostly mixed reviews?
Which restaurant would you choose to try?
Student Response
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Activity Synthesis
Discuss how students use the data distribution shapes to choose their answers. Here are sample questions to promote class discussion:
“How did you determine at which restaurant you would eat?” (I thought the restaurant with the highest ratings is the one at which I would want to eat.)
“How can you tell which restaurant has the best ratings?” (I can tell which one has the best ratings by looking for the histogram with the greatest frequency of 4 or 4-star ratings indicated by tall bars on the right side of the histogram.)
“How does shape influence your decisions?” (Shape influences my decisions because as I am looking for the amount of ratings, I am looking at how tall the bars are on each histogram. The skewed histograms show me that reviewers tend to agree that the restaurant is either very good or very bad. The uniform shape shows me that the restaurant has an equal amount of each rating, which might mean the experience is somewhat random. The bimodal shape shows me that reviewers are split on the restaurant, with some rating the quality very good while others are rating it as very poor.)


correct_option_index: 5