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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 7 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 application of a reasonable strategy. The mean (8) is correct, but the median (3) is incorrect. The student incorrectly chooses the mean to represent the fishes' typical weight. Although the student correctly defines the mean (the average weight of the fish), the justification contains a flaw in reasoning (the average allows people to see what the majority of fish weigh). The effect of the outlier on the mean is not considered. This 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 application of a reasonable strategy. Both the mean (8) and the median (3.5) are correct. The student defines the mean (the amount in the middle, average weight) and the median (the middle of the data), which indicates that the student does not have a clear understanding of the mean and median. The student incorrectly chooses the mean to represent the fishes' typical weight. The effect of the outlier on the mean is not considered. This response demonstrates a minimal understanding and analysis of the problem.


Anchor Paper #3

image of student response

Score for Anchor Paper #3: Rubric Score 1

Annotation: This response indicates little application of a reasonable strategy. The mean (8) and the median (3.5) are correct. The student correctly chooses the median to represent the fishes' typical weight; however, no justification is given. This response demonstrates a minimal 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 incomplete application of a reasonable strategy. While the mean (8) is correct, the median (4) is incorrect. The student correctly selects the median to represent the fishes' typical weight. Complete justification is provided. (He caught one fish that was much heavier than the rest. It was 32 pounds and was an outlier. This weight brought the mean up to a higher number. Most of the fish he caught were 2, 3, 4, and 5 pounds) This 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 incomplete application of a reasonable strategy. The mean (8) is correct, but the median (4) is incorrect. The student correctly chooses the median to represent the fishes' typical weight. The justification (because there is an outlier of 32. This makes the mean greater than what it should be) supports the solution. This 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. Both the mean (8) and the median (3.5) are correct. The student correctly selects the median to represent the fishes' typical weight. A clearly presented justification that supports the solution is given. (The median was not affected by the outlier, which was 32 pounds. The mean, on the other hand, was affected by the outlier and as a result brought the average weight up.) This 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. The mean (8) and the median (3.5) are correct. The median is chosen to represent the fishes' typical weight. The justification (because 5 out of the 6 fish are 2-5 pounds. The 32-pound fish throws off the mean because it is so much higher) is logically sound and supports the solution. This 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/2004_312_alg05.xml
Resources for 3.1.2:
Skill Statements | PUBLIC RELEASE ITEMS | Lesson Plans |