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# Massachusetts Comprehensive Assessment System

## 2014, Grade 8 Mathematics

 Question 11: Open-Response Reporting Category: Statistics and ProbabilityStandard: Mathematics.8.SP.1.04 - Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores? A principal surveyed 75 seventh-grade and eighth-grade students. She asked them if they prefer to obtain the news from the Internet or to obtain the news from television. She created a table to display the data, as shown below.How many seventh-grade students responded to the survey? Show or explain how you got your answer.What is the relative frequency of seventh-grade students who prefer to obtain the news from the Internet to all the seventh-grade students surveyed? Show or explain how you got your answer.What is the relative frequency of eighth-grade students who prefer to obtain the news from the Internet to all the eighth-grade students surveyed? Show or explain how you got your answer.Is there evidence in the principalâ€™s survey that eighth-grade students prefer to obtain the news from the Internet more than seventh-grade students do? Explain your reasoning.

### Scoring Guide and Sample Student WorkSelect a score point in the table below to view the sample student response.

ScoreDescription
4 The student response demonstrates an exemplary understanding of the Statistics and Probability concepts involved in interpreting a two-way table summarizing data on two categorical variables collected from the same subjects and uses relative frequencies calculated for rows or columns to describe possible association between the two variables.
4
3 The student response demonstrates a good understanding of the Statistics and Probability concepts involved in interpreting a two-way table summarizing data on two categorical variables collected from the same subjects and uses relative frequencies calculated for rows or columns to describe possible association between the two variables. Although there is significant evidence that the student was able to recognize and apply the concepts involved, some aspect of the response is flawed. As a result the response merits 3 points.
2 The student response demonstrates a fair understanding of the Statistics and Probability concepts involved in interpreting a two-way table summarizing data on two categorical variables collected from the same subjects and uses relative frequencies calculated for rows or columns to describe possible association between the two variables. While some aspects of the task are completed correctly, others are not. The mixed evidence provided by the student merits 2 points.
1 The student response demonstrates a minimal understanding of the Statistics and Probability concepts involved in interpreting a two-way table summarizing data on two categorical variables collected from the same subjects and uses relative frequencies calculated for rows or columns to describe possible association between the two variables.
0 The student response contains insufficient evidence of an understanding of the Statistics and Probability concepts involved in interpreting a two-way table summarizing data on two categorical variables collected from the same subjects and uses relative frequencies calculated for rows or columns to describe possible association between the two variables to merit any points.

Note: There are 2 sample student responses for Score Point 4.

### Grade 8 Mathematics

Question 11:
Question 20:

Return to the MCAS 2014 Student Work Directory

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