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Goal 3 Data Analysis And Probability

Expectation 3.2 The student will apply the basic concepts of statistics and probability to predict possible outcomes of real-world situations.

Indicator 3.2.2 The student will interpret data and/or make predictions by finding and using a line of best fit and by using a given curve of best fit.

Assessment Limits:

  • Items should include a definition of the data and what it represents.
  • Data will be given when a line of best fit is required.
  • Equation or graph will be given when a curve of best fit is required.

Brief Constructed Response (BCR) Item - Released in 2002

The table below shows the sales for a greeting card company for the years 1990 through 1998.

Complete the following in the Answer Book:

  • Write an equation for the line of best fit for this data. Let x represent the years since 1900 and y represent the sales, in thousands of dollars. (If you choose to draw a graph, use the grid provided in the answer book.)
  • According to your equation, what were the sales in 1999? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.

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 attempt to apply a reasonable strategy. The representation is missing. No equation is given for the line of best fit. The value given for the sales in 1999 indicates that the student recognized a pattern from the table and used that to determine an answer, showing relevant interaction with the data. The explanation is missing. On the graph, the student plotted the points from the table but did not draw in a line of best fit. This response demonstrates a minimal understanding and analysis of the problem.


Sample Student Response #2

image of student response

Score for Sample Student Response #2: Rubric Score 2

Annotation: This response indicates an incomplete application of a reasonable strategy. The representation is correct. An appropriate equation is given for the line of best fit based on "x" representing the years since zero. (Instead of letting "x" represent the years since 1900, the student lets "x" represent the years since zero.) The answer given to the sales in 1999 is correct (although not expressed in thousands of dollars). The explanation is incomplete. This response demonstrates a conceptual understanding and analysis of the problem.


Sample Student Response #3

image of student response

Score for Sample Student Response #3: 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. An appropriate equation is given for the line of best fit based on "x" representing the years since zero. The answer given to the sales in 1999 is correct. The explanation is clearly presented and supports the solution ("substituting 1999 for 'x' and then I solved the equation"). This response demonstrates a complete 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 3.2.2:
Skill Statements | PUBLIC RELEASE ITEMS |