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Massachusetts Comprehensive Assessment System

2012, Grade 10 Mathematics

  Question 20: Open-Response no calculator allowed
The line plot below shows the number of hits made by each of 10 players on a baseball team during batting practice.
A line plot titled Number of Hits Made by Players numbered three to fourteen. Zero players had three hits, zero players had four hits, two players had five hits, zero players had six hits, one player had seven hits, zero players had eight hits, zero players had nine hits, two players had ten hits, one player had eleven hits, three players had twelve hits, one player had thirteen hits, zero players had fourteen hits.
  1. What was the mode of the numbers of hits made by the players? Show or explain how you got your answer.
  2. What was the median number of hits made by the players? Show or explain how you got your answer.
  3. What was the mean number of hits made by the players? Show or explain how you got your answer.
Two additional players arrived at practice. The number of hits made by each additional player was included in the line plot with the following results:
  • The median number of hits increased.
  • The mode of the numbers of hits remained the same.
  1. What could be the number of hits made by each of the two additional players? 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 Data Analysis, Statistics, and Probability concepts involved in interpreting an appropriate graphical representation for a set of data and using appropriate statistics to communicate information about the data. The student interprets a line plot to calculate the mode, median, and mean of a data set and determines how the mode and median change when additional data is added to the set.
4
3 The student response demonstrates a good understanding of the Data Analysis, Statistics, and Probability concepts involved in interpreting an appropriate graphical representation for a set of data and using appropriate statistics to communicate information about the data. 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 fair understanding of the Data Analysis, Statistics, and Probability concepts involved in interpreting an appropriate graphical representation for a set of data and using appropriate statistics to communicate information about the data. 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 Data Analysis, Statistics, and Probability concepts involved in interpreting an appropriate graphical representation for a set of data and using appropriate statistics to communicate information about the data.
0 The student response contains insufficient evidence of an understanding of the Data Analysis, Statistics, and Probability concepts involved in interpreting an appropriate graphical representation for a set of data and using appropriate statistics to communicate information about the data to merit any points.

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

Grade 10 Mathematics

Question 17: Patterns, Relations, and Algebra
Question 20: Data Analysis, Statistics, and Probability
Question 21: Number Sense and Operations
Question 31: Data Analysis, Statistics, and Probability
Question 41: Patterns, Relations, and Algebra
Question 42: Measurement

Return to the MCAS 2012 Student Work Directory



Last Updated: November 5, 2014
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