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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 2001

The table below shows the salaries of the teachers at Polk High School.

Complete the following in the Answer Book:

  • What are the median and mean of this salary data? Use mathematics to explain how you determined your answers. Use words, symbols, or both in your explanation.
  • A journalist who believes that teachers earn too much money is going to write an article based on this data. Which measure of central tendency (mean or median) should the journalist use to convince the public to agree with her opinion? 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

image of student response

Score for Anchor Paper #1: Rubric Score 1

Annotation: This response indicates little application of a reasonable strategy. The student uses an inappropriate strategy to calculate the mean and median of the annual teacher salaries: $37,533.3 and $37,250 result when the entries in the salary column are not weighted by the frequency. An explanation is not provided. An analysis of which measure of central tendency the journalist should use, along with justification, is missing from this response. The student 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. The student uses an inappropriate strategy to calculate the mean and median: $37,533 and $37,250 result when the entries in the salary column are not weighted by the frequency. The explanation is plausible but incomplete: "adding them all together, then dividing by 6" and "finding the number that's in the exact middle." The student correctly applies the incorrect values for the mean and median to provide a logical justification for which measure of central tendency the journalist should use: "A journalist should use the mean...the bigger of them both." This response, lacking the concept of weighting by frequency, demonstrates only 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 application of a reasonable strategy that leads to a correct solution. The correct values for both the mean and the median have been provided; however, the explanations are incomplete. The student's explanation for the mean is fully developed ("...adding up all of the salaries + dividing them by the total # of salaries added up."), but an explanation for the median is not provided. The student correctly justifies the mean as the measure the journalist should use ("...because it is higher."). This 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: In this response, the student applies a reasonable strategy that leads to a correct solution. The student correctly calculates the mean and median. No explanation is provided. The student correctly justifies the mean as the measure of central tendency the journalist should use: "it is the bigger number." 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 3

Annotation: This response indicates application of a reasonable strategy that leads to a correct solution in the context of the problem. The correct values for both the mean and median have been provided. The omission of the unit label (dollars) is not a significant mathematical error. The explanations are fully developed, logically sound, and clearly presented ("...adding up all of the salaries and then by 51 [total # of teachers]..." and "...put the salaries in order and selected the middle #..."). The choice of the mean to show that the teacher's salaries are too high is fully justified ("...it comes up with a higher salary range with the mean."). This response demonstrates a complete understanding and analysis of the problem.


Anchor Paper #6

image of student response

Score for Anchor Paper #6: Rubric Score 3

Annotation: In this response, the student applies a reasonable strategy that leads to a correct solution within the context of the problem. The correct values for both mean and median have been provided. The explanations are fully developed, clearly presented, and support the solution: "To get the median I found the one in the middle of the salaries, with the same amount of salaries lower than it and higher than it. Then for the mean I added all the salaries together and divided them by the number of teachers." The justification of the mean for the measure of central tendency the journalist should use is logically sound and supports the solution: "...he/she is trying to convince the public that the teacher's salary is too high! And the mean brings the teacher's salary average higher." 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
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Resources for 3.1.2:
Skill Statements | PUBLIC RELEASE ITEMS | Lesson Plans |