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Massachusetts Comprehensive Assessment System

2013, Grade 8 Mathematics

  Question 11: Open-Response no calculator allowed
Tony collected data on the years of employment and the annual salaries of the salespeople at Company Z. He made a scatterplot and drew a trend line that approximated the line of best fit for the data, as shown below.
A scatterplot is shown titled 'Salaries of Salespeople at Company Z.' The x-axis is titled 'Years of Employment' and ranges from 0 to 10 in increments of 1. The y-axis is titled 'Salary' and starts at 0, shows an axis break, and then ranges from $30,000 to $70,000 in increments of $10,000. The scatterplot contains point 2, 37500; point 3, 40000; point 3, 43000; point 4, 37500; point 4, 39000; point 7, 50000; point 8, 51000; point 8, 52000; point 9, 54000; point 9, 55000; and point 10, 60000.  The trend line goes through point 3, 40000; point 7, 50000 and point 9, 55000.
  1. Based on the trend line drawn for the data, what is the salary a salesperson with 3 years of employment at Company Z can expect to earn? Show or explain how you got your answer.
  2. What is the slope of the trend line that Tony drew? Show or explain how you got your answer.
  3. What does the slope mean in this situation?
Tony expects his salary to be about $70,000 after he has been employed as a salesperson at Company Z for 15 years.
  1. Use the trend line and your answer from part (b) to explain why Tony’s salary expectation is reasonable.

Scoring Guide and Sample Student Work
Select 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 using the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. The student determines and analyzes the slope of a trend line drawn for a scatterplot and makes predictions based on the trend line.
4
3
The student response demonstrates a good understanding of the Statistics and Probability concepts involved in using the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. 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 using the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. 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 only minimal understanding of the Statistics and Probability concepts involved in using the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept.
0
The student response contains insufficient evidence of an understanding of the Statistics and Probability concepts involved in using the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept, to merit any points.

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

Grade 8 Mathematics

Question 11: Statistics and Probability
Question 20: Functions

Return to the MCAS 2013 Student Work Directory



Last Updated: Jul 11, 2016
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