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 2008

Nineteen families live in a small town. The income for each family is listed in the table below.

Complete the following in the Answer Book:

• What are the median and mean family incomes for this small town?
• Should the mean or median be used to describe the typical family income in this small town? Use mathematics to justify your answer.
• If each family’s income increases by \$1,000, Alison believes the mean family income will increase more than the median family income. Do you agree with Alison? Use mathematics to justify your answer.

The following 6 Anchor Papers represent a range of score points and are used in conjunction with the rubrics to assess student responses.

Anchor Paper #1

Score for Anchor Paper #1: Rubric Score 1

Annotation: This response indicates little attempt to apply a reasonable strategy. The mean and the median are both incorrect. The student correctly selects the median to describe the typical family income in the town and gives justification (there is a large income that will throu off the mean by alot). No correct justification is given for disagreeing with Alison’s belief that the mean will increase more than the median if each family’s income increases by \$1000. The response demonstrates a minimal understanding and analysis of the problem.

Anchor Paper #2

Score for Anchor Paper #2: Rubric Score 1

Annotation: This response indicates little attempt to apply a reasonable strategy. The mean and the median are both correct. The student incorrectly selects the mean to describe the typical family income in the town and no correct justification is given. The student incorrectly states that Alison is correct in her belief that the mean will increase more than the median if each family’s income increases by \$1000. No valid justification is given. The response demonstrates a minimal understanding and analysis of the problem.

Anchor Paper #3

Score for Anchor Paper #3: Rubric Score 2

Annotation: This response indicates an incomplete application of a reasonable strategy. The mean and the median are both correct. The student correctly selects the median to describe the typical family income in the town and gives justification (\$320,000 is only made by one of the nineteen families and \$320,000 is an outlier). Although the student correctly disagrees with Alison’s belief that the mean will change more than the median if each family’s income increases by \$1000, no correct justification is given. The response demonstrates a conceptual understanding and analysis of the problem.

Anchor Paper #4

Score for Anchor Paper #4: Rubric Score 2

Annotation: This response indicates an incomplete application of a reasonable strategy. The mean and the median are both correct. The student incorrectly selects the mean to describe the typical family income in the town and no correct justification is given. The student correctly disagrees with Alison’s belief that the mean will change more than the median if each family’s income increases by \$1000 and gives justification (the mean income would be \$57,578.94737 and the median would be \$41,000 both the mean and the median would increase by the same amount). The response demonstrates a conceptual understanding and analysis of the problem.

Anchor Paper #5

Score for Anchor Paper #5: 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 and the median are both correct. The student correctly selects the median to describe the typical family income in the town and gives justification (more than half (50%) of the families are making around \$40,000. If we were to use the mean only one family would be able to say that they make \$56,579 as an income). The student correctly disagrees with Alison’s belief that the mean will change more than the median if each family’s income increases by \$1000 and gives justification (The mean and the median both changed by \$1000. For example, the mean before: \$56,579, mean now: \$57,579. The median before: \$40,000, the median now: \$41,000). The response demonstrates a complete understanding and analysis of the problem.

Anchor Paper #6

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. The mean and the median are both correct. The student correctly selects the median to describe the typical family income in the town and gives justification (its centrally located in the data. The mean can’t be used because it’s affected by the outlier 320,000. The outlier mades it higher than most of the data in the table). The student correctly disagrees with Alison’s belief that the mean will change more than the median if each family’s income increases by \$1000 and gives justification (the new mean would be \$57579 and the new median would be \$41000. The mean family income increase by \$1000 and the median family income increase by \$1000. They increase by the same amount). The response demonstrates a complete understanding and analysis of the problem.

### Brief Constructed Response (BCR) Rubric

Print: Scoring Rubric (pdf)
 Score 3The 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 2The 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 1The 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 0The 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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