




Massachusetts Comprehensive Assessment System
2016, Grade 8 Mathematics
Question 21: OpenResponse 

Reporting Category: Statistics and Probability Standard: 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 twoway table. Construct and interpret a twoway 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?

An athletic director wants to add either tennis or gymnastics to the physical education program at her school. She surveyed the seventhgrade students and eighthgrade students to determine whether they preferred tennis or gymnastics. Some of the data from the survey is listed below. A total of 255 students were surveyed.
 120 of the students surveyed are seventhgraders.
 72 of the seventhgraders surveyed chose tennis.
 62 of the eighthgraders surveyed chose gymnastics.
In your Student Answer Booklet, copy the table exactly as shown below.  Use the data from the survey to complete your table. Show or explain how you got your answers.
 Based on your table, what percentage of the eighthgraders chose tennis? Show or explain how you got your answer.
 Among those students who chose gymnastics, what is the relative frequency of seventhgraders? Show or explain how you got your answer.
 In which grade did a higher percentage of students choose tennis? Show or explain how you got your answer.

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 understanding that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a twoway table, and constructing and interpreting a twoway table summarizing data on two categorical variables collected from the same subjects. 
4 
3 
The student response demonstrates a good understanding the Statistics and Probability concepts involved in understanding that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a twoway table, and constructing and interpreting a twoway 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 understanding that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a twoway table, and constructing and interpreting a twoway 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 understanding that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a twoway table, and constructing and interpreting a twoway 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 understanding that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a twoway table, and constructing and interpreting a twoway 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 11: Functions
 Question 21: Statistics and Probability
Return to the MCAS 2016 Student Work Directory
Last Updated: August 1, 2002


