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Massachusetts Comprehensive Assessment System

Question 11: Open-Response
A salesperson records the number of miles she travels each week. The table below shows the number of miles the salesperson traveled each week for 5 weeks.
 Week 1 2 3 4 5 Number ofMiles Traveled 216 210 250 225 209
1. What is the median number of miles traveled by the salesperson? Show or explain how you got your answer.
2. What is the mean number of miles traveled by the salesperson? Show or explain how you got your answer.
The salesperson plans to travel 402 miles in week 6.
1. Which measure, median or mean, will change more when the number of miles for week 6 is included in the data? 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 summarizing numerical data sets in relation to their context, such as by giving quantitative measures of center and variability, as well as describing any overall pattern and any striking deviations from the overall pattern in reference to the context in which the data were gathered. The student finds the median and the mean for a set of data and determines which measure changes more when a new data value is added.
4
3
The student response demonstrates a good understanding of the Statistics and Probability concepts involved in summarizing numerical data sets in relation to their context, such as by giving quantitative measures of center and variability, as well as describing any overall pattern and any striking deviations from the overall pattern in reference to the context in which the data were gathered. 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 summarizing numerical data sets in relation to their context, such as by giving quantitative measures of center and variability, as well as describing any overall pattern and any striking deviations from the overall pattern in reference to the context in which the data were gathered. 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 summarizing numerical data sets in relation to their context, such as by giving quantitative measures of center and variability, as well as describing any overall pattern and any striking deviations from the overall pattern in reference to the context in which the data were gathered.
0
The student response contains insufficient evidence of an understanding of the Statistics and Probability concepts involved in summarizing numerical data sets in relation to their context, such as by giving quantitative measures of center and variability, as well as describing any overall pattern and any striking deviations from the overall pattern in reference to the context in which the data were gathered to merit any points.

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