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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 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. The student uses an inappropriate strategy to calculate the mean and median of the annual teacher salaries; $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 up all the salaries, and then dividing by 6." and "...I added the middle two numbers and then divided by 2"). The student correctly applies the salaries to provide a logical justification for the mean as the measure the journalist should use ("...it has the highest salary number, $37,533 is higher then $37,250."). Because this response lacks the concept of weighting by frequency, it demonstrates only 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: 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 the mean and the median have been provided. The explanations are clearly presented, logically sound, and support the solution: "by adding all the salaries together and dividing them by 51...looking at the middle # which was for teachers with 4-6 years of experience." The justification of the mean for the measure of central tendency the journalist should use is clearly presented and logically sound: "it is higher and would be more convincing for her side of the story." This response demonstrates a complete understanding and analysis of the problem.


Sample Student Response #3

image of student response

Score for Sample Student Response #3: Rubric Score 2

Annotation: This response indicates an incomplete application of a reasonable strategy. The student's mean is incorrect: $4,415 results when the entries in the salary column are not weighted by frequency. The explanation is plausible and supports the solution: "I added all of the annual salaries and divided by the number of teachers which is 51." The student gives the correct value for the median and provides a fully developed explanation: "the first 25 salaries ranges from $28,200 to $35,100 and the last 25 range from $35,100 to $48,400. The only number left is the teacher that makes $35,100." The student then chooses the higher of the two numbers and justifies the median as being more than some professions make: "She could write that one teacher make $35,100 a year which is more than any regular citizen." However, this is not a mathematical justification. This response demonstrates a conceptual understanding and analysis of the problem.


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 |