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# Massachusetts Comprehensive Assessment System

## 2013, Grade 10 Mathematics

 Question 17: Open-Response Reporting Category: Statistics and ProbabilityStandard: 10.D.1 - Select, create, and interpret an appropriate graphical representation (e.g., scatterplot, table, stem-and-leaf plots, box-and-whisker 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.1.02 - Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.* The scatterplot below shows the number of pounds of newspaper that a recycling club recycled per month for 10 months.What is the total number of months for which more than 500 pounds of newspaper was recycled per month?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.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.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 WorkSelect 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:
Question 20:
Question 21:
Question 31:
Question 41:
Question 42:

Return to the MCAS 2013 Student Work Directory

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