Massachusetts Comprehensive Assessment System

2019, Grade 8 Mathematics

Question 15: Constructed-Response

Reporting Category: Statistics and Probability
Standard: Mathematics.8.SP.A.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?
Item Description: Interpret a two-way table to answer statistical questions about categorical data collected from the same subjects.

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Scoring Guide and Sample Student Work

Select a score point in the table below to view the sample student response.

Score	Description
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. The student determines the number of students in a category, calculates relative frequencies, and uses relative frequencies to analyze the validity of a 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. 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. 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.
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 to merit any points.

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

Grade 8 Mathematics

Question 5: Functions

Question 15: Statistics and Probability

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Last Updated: March 11, 2024