options: Calculate expected values and use them to solve problems.

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

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

Investigate patterns of association in bivariate data.

Use random sampling to draw inferences about a population.

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

Develop understanding of statistical variability.

Use probability to evaluate outcomes of decisions.

Understand and evaluate random processes underlying statistical experiments.

Summarize and describe distributions.

Interpret linear models.

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

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

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

Draw informal comparative inferences about two populations.
problem_activity: Task
Students were asked to report how far (in miles) they each live from school. The following distances were recorded.
|    | Student  | Distance |
|----|----------|----------|
| 1  |   Zane   |   0.4    |
| 2  | Jackson  |   0.5    |
| 3  | Benjamin |   1.0    |
| 4  | Bethany  |   1.0    |
| 5  |   Joe    |   2.4    |
| 6  |  Noelle  |   2.7    |
| 7  |  Tianye  |   3.0    |
| 8  | Anthony  |   3.2    |
| 9  |  Amanda  |   4.1    |
| 10 | Michaela |   4.2    |
| 11 | Miranda  |   4.4    |
| 12 |  Joseph  |   5.0    |
| 13 |   John   |   7.5    |
1.  Summary statistics for the distances are given below.
| Min | Q1  | Median | Q3  | Max | Mean |
|-----|-----|--------|-----|-----|------|
| 0.4 | 1.0 |  3.0   | 4.3 | 7.5 | 3.03 |
Construct a box plot for the distances and describe the main features of the distribution.
2.  John currently lives furthest from school. Would you consider his distance from school (7.5 miles) to be ”unusual"? Explain.
3.  John’s family is considering moving to a house that is 10 miles from school. How will this move affect the summary statistics? Change John’s distance from 7.5 miles to 10 miles and complete the table based on this new data.
| Min | Q1 | Median | Q3 | Max | Mean |
|-----|----|--------|----|-----|------|
|     |    |        |    |     |      |
Has the mean increased, decreased or remained unchanged? Has the median increased, decreased or remained unchanged? Explain how John’s move has affected these measures of center.
4.  Construct a boxplot of the distances after John's move. Would you consider John's new distance from school (10 miles) to be "unusual" now? Explain.
5.  A data point can be considered an “outlier” if it is more than 1.5 times the IQR above Q3 or more than 1.5 times the IQR below Q1. Using this description of an outlier, was John’s distance from school considered an outlier before the move? How about after the move? Support your answer with appropriate work.
6.  Zane lives closest to school. Using the description of an outlier given in question 5, is his distance considered an outlier?


correct_option_index: 12