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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 2002

The table below shows the number of medals won by 24 countries during the 1998 Winter Olympic Games.

Complete the following in the Answer Book:

  • Use the data from the table to create a box-and-whisker plot on the grid provided in the Answer Book.
  • What was the least number of medals won by a country in the top 25% of the final medal standings? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.

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 an incomplete application of a reasonable strategy. The representation is missing. There is no attempt to create a box and whisker plot. However, the student correctly gives 13 as the answer for the least number of medals won by a country in the top 25% of the final medal standings. In addition, the explanation is fully developed and supports the solution. 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 attempt to apply a reasonable strategy. The representation is partially correct. In the box and whisker plot, the minimum (1), lower quartile (1.5), and maximum (29) are correct. The median and the upper quartile are incorrect. The student correctly gives 13 as the least number of medals won by a country in the top 25% of the final medal standings, but the explanation is missing. 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 2

Annotation: This response indicates an incomplete application of a reasonable strategy. The representation is correct. All the values in the box and whisker plot are correct and plotted correctly, and the scale is uniform; however, the student chooses the least number of medals won — not the least number won by a country in the top 25% of the final medal standings. 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: This response indicates an incomplete application of a reasonable strategy. The representation is fundamentally correct. In the box and whisker plot all the values are correct except for the lower quartile which is plotted as "2" instead of "1.5." The student correctly gives 13 as the least number of medals won by a country in the top 25% of the final medal standings. The explanation is logically sound and supports the solution ("The upper quartile starts at 12.5, you can't have a medal so the least is 13"). 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 representation is correct. All the values in the box and whisker are correct and correctly plotted, and the scale is uniform. The student correctly gives 13 as the least number of medals won by a country in the top 25% of the final medal standings. The explanation is fully developed and supports the solution ("I looked at Q3 and it's 12.5 and you can't win 12 medals so you would have to win 13"). 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: This response indicates application of a reasonable strategy that leads to a correct solution in the context of the problem. The representation is correct. All the values in the box and whisker plot are correct and correctly plotted, and the scale is uniform. The student correctly gives 13 as the least number of medals won by a country in the top 25% of the final medal standings. The explanation is clearly presented and supports the solution. 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 representation is correct. All the values in the box and whisker plot are correct and correctly plotted, and the scale is uniform. The student correctly gives 13 as the least number of medals won by a country in the top 25% of the final medal standings. The explanation is clearly presented and supports the solution ("25% of 24=6. So the top 6 were 29, 25, 18, 17, 15, and 13. That makes 13 the lowest"). 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/2002_312_alg31.xml
Resources for 3.1.2:
Skill Statements | PUBLIC RELEASE ITEMS | Lesson Plans |