




Massachusetts Comprehensive Assessment System
2017, Grade 10 Mathematics
Question 21: OpenResponse 

Reporting Category: Statistics and Probability Standard: 10.D.2  Approximate a line of best fit (trend line) given a set of data (e.g., scatterplot). Use technology when appropriate. Standard: CCSS.Math.Content.HSSID.B.6  Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.* 
The table below shows the number of fulltime employees at eight guitarproduction companies and the number of guitars produced by each company last year.
Guitar ProductionNumber of Full Time Employees  3  5  6  8  8  10  13  18  Number of Guitars Produced  98  189  235  309  336  412  494  692  On the grid in your Student Answer Booklet, copy the title, the axes, and the labels exactly as shown below.
 On your grid, create a scatterplot using the data from the table.
 On your scatterplot, draw a line of best fit for the data.
 Write an equation that represents the line of best fit you drew in part (b). Show or explain how you got your answer.
 Use your equation to estimate the number of fulltime employees needed if a company plans to produce 1000 guitars in a year. 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 representing data on two quantitative variables on a scatterplot and describing how the variables are related. The student draws a line of best fit and creates an equation for a set of data and uses the equation to make a prediction. 
4 
3 
The student response demonstrates a good understanding of the Statistics and Probability concepts involved in representing data on two quantitative variables on a scatterplot and describing how the variables are related. 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 representing data on two quantitative variables on a scatterplot and describing how the variables are related. 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 representing data on two quantitative variables on a scatterplot and describing how the variables are related. 
0 
The student response contains insufficient evidence of an understanding of the Statistics and Probability concepts involved in representing data on two quantitative variables on a scatterplot and describing how the variables are related to merit any points. 
Note: There are 2 sample student responses for Score Point 4.
Grade 10 Mathematics
 Question 17: Geometry
 Question 20: Number and Quantity
 Question 21: Statistics and Probability
 Question 36: Algebra and Functions
 Question 41: Geometry
 Question 42: Algebra and Functions
Return to the MCAS 2017 Student Work Directory
Last Updated: March 20, 2018


