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Massachusetts Comprehensive Assessment System

2016, Grade 7 Mathematics

  Question 10: Open-Response no calculator allowed
A snow day occurs when school is canceled for the day because of bad winter weather. The box below shows the number of snow days at Andrew's school during each of the past six winters.
2,  5,  5,  3,  4,  5
  1. For the past six winters, what was the median number of snow days per winter at Andrew's school? Show or explain how you got your answer. 
  2. For the past six winters, what was the mean number of snow days per winter at Andrew's school? Show or explain how you got your answer. 
  3. For the past six winters, what was the mean absolute deviation of the number of snow days per winter at Andrew's school? Show or explain how you got your answer.
Maria lives in another state. The box below shows the number of snow days at Maria's school during each of the past six winters.
0,  2,  9,  3,  1,  3
  1. At which school, Andrew's or Maria's, is the number of snow days per winter more predictable? Explain your reasoning. Use specific data from both schools in your explanation.

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 measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. The student finds the median, mean, and mean absolute deviation of two sets of data and then compares them.
4
3 The student response demonstrates a good understanding of the Statistics and Probability concepts involved in using measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. 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 measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. 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 using measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.
0 The student response contains insufficient evidence of the Statistics and Probability concepts involved in using measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations to merit any points.

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

Grade 7 Mathematics

Question 10: Statistics and Probability
Question 21: Expressions and Equations

Return to the MCAS 2016 Student Work Directory



Last Updated: September 25, 2017
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