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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 2004

Matt caught 6 fish and recorded each of their weights as shown in the table below.

Complete the following in the Answer Book:

  • Find the mean and the median of the data.
  • Which measure of central tendency, mean or median, should Matt use to best represent the typical weight of the fish he caught? Use mathematics to justify your answer.

The following 3 Sample Student Responses represent a range of score points.

Sample Student Response #1

image of student response

Score for Sample Student Response #1: Rubric Score 1

Annotation: This response indicates little application of a reasonable strategy. Both the mean (8) and the median (3.5) are correct. Although the student defines the mean (the average) and the median (the middle number), the choice of mean to represent the fishes' typical weight demonstrates an incorrect application of this knowledge. The justification (the median only shows the middle number in the data, which doesn't really prove anything about a typical fish weight) shows a flaw in reasoning. The effect of the outlier on the mean is not considered. This response demonstrates a minimal understanding and analysis of the problem. Compare to Anchor Paper #2.
Sample Student Response #2

image of student response

Score for Sample Student Response #2: Rubric Score 3

Annotation: This response indicates application of a reasonable strategy that leads to a correct solution in the context of the problem. Both the mean (8) and the median (3.5) are correct. The student correctly selects the median to represent the fishes' typical weight and provides a logically sound justification. (He only had one fish over 8 pounds. The median is a closer weight to the majority of the fish he caught.) This response demonstrates a complete understanding and analysis of the problem. Compare to Anchor Paper #7.
Sample Student Response #3

image of student response

Score for Sample Student Response #3: Rubric Score 2

Annotation: This response indicates incomplete application of a reasonable strategy. While the mean (8) is correct, the median (3) is incorrect. The median is correctly chosen to represent the fishes' typical weight. Clearly presented justification is given (because the mean is too high because of the one 32 pound fish). This response demonstrates a conceptual understanding and analysis of the problem. Compare to Anchor Paper #5.

Additional Resources

Anchor Papers used in scoring

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
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Resources for 3.1.2:
Skill Statements | PUBLIC RELEASE ITEMS | Lesson Plans |