School Improvement in Maryland
Public Release Item Scoring Information Return

Goal 3 Data Analysis And Probability

Expectation 3.1 The student will collect, organize, analyze, and present data.

Indicator 3.1.2 The student will use the measures of central tendency and/or variability to make informed conclusions.

Assessment Limits:

  • Measures of central tendency include mean, median, and mode.
  • Measures of variability include range, interquartile range, and quartiles.
  • Data may be displayed in a variety of representations which may include: frequency tables, box and whisker plots, and other displays.

Brief Constructed Response (BCR) Item - Released in 2006

The student government wants to determine if students get better grades in morning or afternoon classes. They randomly surveyed 20 students that take math class in the morning and 20 students that take math class in the afternoon. The survey results are shown in the stem-and-leaf plots below.

Complete the following in the Answer Book:

  • What are the mean, median, and mode for each class?
  • Based on the data, do students get better grades in the morning classes? Use measures of central tendency to justify your answer.

The following 8 Anchor Papers represent a range of score points and are used in conjunction with the rubrics to assess student responses.

Anchor Paper #1

image of student response

Score for Anchor Paper #1: Rubric Score 1

Annotation: This response indicates little attempt to apply a reasonable strategy. The means for both the morning and afternoon classes are correct. The medians are incorrect because two answers are given for each median instead of one averaged answer (81 and 83; 76 and 79). The modes are incorrect (45; 35). The student indicates that the morning classes get better grades, but the justification using a measure of central tendency is missing (This is not clinicly proven; I would guess that they do better in the morning). The response demonstrates a minimal understanding and analysis of the problem.


Anchor Paper #2

image of student response

Score for Anchor Paper #2: Rubric Score 1

Annotation: This response indicates little attempt to apply a reasonable strategy. The modes for both the morning and afternoon classes are correct. However, the means and medians are all incorrect. The justification for students in the morning classes getting better grades is missing. The response demonstrates a minimal understanding and analysis of the problem.


Anchor Paper #3

image of student response

Score for Anchor Paper #3: Rubric Score 2

Annotation: This response indicates an incomplete application of a reasonable strategy. The median and mode are correct for the morning classes but the mean is incorrect. For the afternoon classes, the mode is correct but the mean and median are incorrect. The justification (according to the mean (81.2) and median (82) of the first class, they ranked higher than the second class (72.15 and 79)) supports the solution that the morning classes get better grades. Although some of the values used in the justification are incorrect, the relationship between the values still supports the solution. The response demonstrates a conceptual understanding and analysis of the problem.


Anchor Paper #4

image of student response

Score for Anchor Paper #4: Rubric Score 2

Annotation: This response indicates an incomplete application of a reasonable strategy. All the values given for the means, medians, and modes are correct. The justification for students getting better grades in the morning classes is missing. The response demonstrates a conceptual understanding and analysis of the problem.


Anchor Paper #5

image of student response

Score for Anchor Paper #5: Rubric Score 2

Annotation: This response indicates an incomplete application of a reasonable strategy. With the exception of the morning median, all the values given are correct. The justification (the average was higher in the morning classes) supports the solution that students get better grades in the morning. The response demonstrates a conceptual understanding and analysis of the problem.


Anchor Paper #6

image of student response

Score for Anchor Paper #6: Rubric Score 3

Annotation: This response indicates application of a reasonable strategy that leads to a correct solution in the context of the problem. All the values given for the means, medians and modes are correct. The justification (the morning class mean was 85 and the median was 82 while the afternoon class mean was 77.5 and median was 79) is fully developed and supports the solution that the morning classes get better grades. In addition, the student also justifies why the mode being higher in the afternoon classes does not mean that the afternoon classes get better grades. The response demonstrates a complete understanding and analysis of the problem.


Anchor Paper #7

image of student response

Score for Anchor Paper #7: Rubric Score 3

Annotation: This response indicates application of a reasonable strategy that leads to a correct solution in the context of the problem. All the values given for the means, medians and modes are correct. The justification (the mean for the morning class is 9.55 better than the afternoon classes; the median is 4.5 better) is fully developed and supports the solution that the morning classes get better grades. The response demonstrates a complete understanding and analysis of the problem.


Anchor Paper #8

image of student response

Score for Anchor Paper #8: Rubric Score 3

Annotation: This response indicates application of a reasonable strategy that leads to a correct solution in the context of the problem. All the values given for the means, medians and modes are correct. The justification (the mean and median are higher but the mode is lower) is fully developed and supports the solution that the morning classes get better grades. The response demonstrates a complete understanding and analysis of the problem.


Brief Constructed Response (BCR) Rubric

Print: Scoring Rubric (pdf)
Score 3

The response indicates application of a reasonable strategy that leads to a correct solution in the context of the problem. The representations are essentially correct. The explanation and/or justification is logically sound, clearly presented, fully developed, supports the solution, and does not contain significant mathematical errors. The response demonstrates a complete understanding and analysis of the problem.

Score 2

The response indicates application of a reasonable strategy that may be incomplete or undeveloped. It may or may not lead to a correct solution. The representations are fundamentally correct. The explanation and/or justification supports the solution and is plausible, although it may not be well developed or complete. The response demonstrates a conceptual understanding and analysis of the problem.

Score 1

The response indicates little or no attempt to apply a reasonable strategy or applies an inappropriate strategy. It may or may not have the correct answer. The representations are incomplete or missing. The explanation and/or justification reveals serious flaws in reasoning. The explanation and/or justification may be incomplete or missing. The response demonstrates a minimal understanding and analysis of the problem.

Score 0

The response is completely incorrect or irrelevant. There may be no response, or the response may state, “I don't know.”

Explanation refers to the student using the language of mathematics to communicate how the student arrived at the solution.

Justification refers to the student using mathematical principles to support the reasoning used to solve the problem or to demonstrate that the solution is correct. This could include the appropriate definitions, postulates and theorems.

Essentially correct representations may contain a few minor errors such as missing labels, reversed axes, or scales that are not uniform.

Fundamentally correct representations may contain several minor errors such as missing labels, reversed axes, or scales that are not uniform.

Last Revised 8/16/00

/share/clg/xml/public_release/mathematics/2006_312_alg28.xml
Resources for 3.1.2:
Skill Statements | PUBLIC RELEASE ITEMS | Lesson Plans |