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Massachusetts Comprehensive Assessment System

2013, Grade 10 Mathematics

  Question 17: Open-Response no calculator allowed
The scatterplot below shows the number of pounds of newspaper that a recycling club recycled per month for 10 months.
A scatterplot titled Number of Pounds of Newspaper Recycled. The label for the x axis is Month. The x axis goes from 0 to 12 in increments of 1 month. The label for the y axis is Number of Pounds. The y axis goes from 0 to 1000 in increments of 50 pounds. There are  points plotted at 1, 300; 2, 200; 3, 600; 4, 700; 5, 800; 6, 400; 7, 600; 8, 700; 9, 450; 10, 350
  1. What is the total number of months for which more than 500 pounds of newspaper was recycled per month?
  2. What is the range of the numbers of pounds of newspaper recycled per month for the 10 months? Show or explain how you got your answer.
  3. What is the median number of pounds of newspaper recycled per month for the 10 months? Show or explain how you got your answer.
During months 11 and 12, the club recycled a combined total of 600 pounds of newspaper. The range of the numbers of pounds of newspaper recycled per month for the 12 months is the same as the range for the 10 months.
  1. What is the median number of pounds of newspaper recycled per month for the 12 months? 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.

ScoreDescription
4 The student response demonstrates an exemplary understanding of the Statistics and Probability concepts involved in using statistics appropriate to the shape of the data distribution to compare center and spread of two or more different data sets. The student calculates the range and median of a set of data and determines how the median changes with the addition of new data points.
4
3 The student response demonstrates a good understanding of the Statistics and Probability concepts involved in using statistics appropriate to the shape of the data distribution to compare center and spread of two or more different data sets. 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 statistics appropriate to the shape of the data distribution to compare center and spread of two or more different data sets. 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 statistics appropriate to the shape of the data distribution to compare center and spread of two or more different data sets.
0 The student response contains insufficient evidence of an understanding of the Statistics and Probability concepts involved in using statistics appropriate to the shape of the data distribution to compare center and spread of two or more different data sets to merit any points.

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

Grade 10 Mathematics

Question 17: Statistics and Probability
Question 20: Number and Quantity
Question 21: Algebra and Functions
Question 31: Algebra and Functions
Question 41: Geometry
Question 42: Geometry

Return to the MCAS 2013 Student Work Directory



Last Updated: May 1, 2001
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