




Massachusetts Comprehensive Assessment System
2016, Grade 10 Mathematics
Question 41: OpenResponse 

Reporting Category: Statistics and Probability Standard: 10.D.1  Select, create, and interpret an appropriate graphical representation (e.g., scatterplot, table, stemandleaf plots, boxandwhisker plots, circle graph, line graph, and line plot) for a set of data and use appropriate statistics (e.g., mean, median, range, and mode) to communicate information about the data. Use these notions to compare different sets of data. Standard: Mathematics.S.ID.2.05  Summarize categorical data for two categories in twoway frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.* 
The table below shows the distribution of eye color and hair color for the 60 students in a chorus.  How many students in the chorus have brown hair? Show or explain how you got your answer.
 What fraction of the students with blond hair have hazel eyes? Show or explain how you got your answer.
 What percentage of all the students have both green eyes and red hair? Show or explain how you got your answer.
 What percentage of all the students have green eyes or red hair? 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 summarizing categorical data for two categories in twoway frequency tables and interpreting relative frequencies in the context of the data. The student interprets data from a table and calculates percentages based on the data. 
4 
3 
The student response demonstrates a good understanding of the Statistics and Probability concepts involved in summarizing categorical data for two categories in twoway frequency tables and interpreting relative frequencies in the context of the data. 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 summarizing categorical data for two categories in twoway frequency tables and interpreting relative frequencies in the context of the data. 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 summarizing categorical data for two categories in twoway frequency tables and interpreting relative frequencies in the context of the data. 
0 
The student response contains insufficient evidence of an understanding of the Statistics and Probability concepts involved in summarizing categorical data for two categories in twoway frequency tables and interpreting relative frequencies in the context of the data to merit any points. 
Note: There are 2 sample student responses for Score Point 4.
Grade 10 Mathematics
 Question 17: Algebra and Functions
 Question 20: Geometry
 Question 21: Number and Quantity
 Question 36: Algebra and Functions
 Question 41: Statistics and Probability
 Question 42: Geometry
Return to the MCAS 2016 Student Work Directory
Last Updated: September 30, 2018


