options: Number Systems and Quantity: students learn to understand the complex number system and reason quantitatively.

Statistics & Probability: students learn to analyze and produce data distributions, and build understanding of univariate and bivariate data. They learn to interpret data, make statistical inferences, justify conclusions, understand rules of probability, and use probability to make decisions.

Modeling: students learn to choose and use appropriate mathematics and statistics to analyze real-world empirical situations, improve decisions, and report on their conclusions and the reasoning behind them.

Measurement & Data: students learn to work with data and measure attributes such as time, money, length, area, and volume. They may learn to compare measurements to operations and convert between different units of measure.

Geometry: students learn to classify geometric figures by their properties, and understand and compare the relationships between them. Students develop and use formulas to compute lengths, areas, and volumes, and they use transformations to generate new shapes and compare existing ones. Geometry can be studied with and without coordinates.

Number & Operations in Base Ten: students learn to work with the base-ten system and build place value understanding.

Number & Operations - Fractions: students learn to understand fractions as numbers and may work with them using addition, subtraction, multiplication, and division.

Ratios & Proportional Relationships: students learn to recognize, describe, represent, and reason with ratios, rates, proportional relationships, and percent.

Operations & Algebra: students learn to solve problems using algebraic thinking and operations such as addition, subtraction, multiplication, and division. They may learn to identify and explain arithmetic patterns, evaluate or manipulate numerical expressions, and reason with equations and inequalities.

Counting & Cardinality: students learn to know number names and the count sequence, count to tell the number of objects, and compare numbers.

Functions: students learn to define, use, and evaluate functions to model relationships between quantities.
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: 1