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# Massachusetts Comprehensive Assessment System

 Question 20: Open-Response Reporting Category: Data Analysis, Statistics, and ProbabilityStandard: 7.D.2 - Find, describe, and interpret appropriate measures of central tendency (mean, median, and mode) and spread (range) that represent a set of data. Use these notions to compare different sets of data. This standard is intentionally the same as standard 8.D.3. For this question, you will create sets of numbers that satisfy the requirements given in parts (a) through (d). You will create a different set of numbers for each part. Write a data set of any 5 numbers that has a median equal to 7. Explain your reasoning.Write a data set of any 5 numbers that has a mean equal to 9. Explain your reasoning.Write a data set of any 5 numbers that has both of the characteristics given below. Explain your reasoning.range equal to 8 mode equal to 6 Write a data set of any 5 numbers that has all of the characteristics given below. Explain your reasoning. mode equal to 6 median equal to 7 mean equal to 9

### 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 data analysis, statistics, and probability concepts involved in finding measures of central tendency and spread (range). The student creates data sets that have specific measures of central tendency and spread.
4
3 The student response demonstrates a good understanding of the data analysis, statistics, and probability concepts involved in finding measures of central tendency and spread (range). 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 data analysis, statistics, and probability concepts involved in finding measures of central tendency and spread (range). 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 contains a minimal understanding of the data analysis, statistics, and probability concepts involved in finding measures of central tendency and spread (range).
0 The student response contains insufficient evidence of an understanding of the data analysis, statistics, and probability concepts involved in finding measures of central tendency and spread (range) to merit any points.

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