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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 2001

The table below shows the distances, in miles, and the lowest-priced airfares, in dollars, of flights from Baltimore to various destinations.

The data from the table is graphed on the scatter plot below.

Complete the following in the Answer Book:

  • Write an equation for a line of best fit that can represent the relationship between the distance (d) traveled and the lowest-priced airfare (f).
  • Graph the equation for your line of best fit on a scatter plot.
  • According to your equation, what is the cost of a plane ticket to Orlando, which is 790 miles from Baltimore? Use mathematics to justify your answer.

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 little application of a reasonable strategy. The representations are incomplete. The student has made a reasonable attempt at graphing a line of best fit; however, the slope and y-intercept are not within an acceptable range for the data given and are not expressed in the required form of an equation. The solution of $180.00 for the cost of an airplane ticket from Baltimore to Orlando, though feasible, is an estimate from the student's own line rather than a calculation using an equation. There is no justification. The 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 application of a reasonable strategy. The line of best fit is not graphed within an acceptable range for the data given; the y-intercept is close to zero. The student then chooses points from that line in order to derive an equation. However, by inverting the slope formula, the student actually arrives at the reciprocal of the slope. The student applies a reasonable strategy to solve for the y-intercept but the error in the slope leads to an incorrect y-intercept. The estimate for the cost of the airplane ticket is feasible; however, the student's equation is not used to arrive at the solution. There is no justification. The 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 representations are correct; both the equation for the line of best fit and the graph of the equation are within an acceptable range for the data given. The solution of $118.88 for the cost of the airplane ticket, however, reveals an incorrect application of the student's equation, and there is no justification. 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 representations are correct; both the equation for a line of best fit and the graph of the equation are within an acceptable range for the data given. The solution for the cost of the airplane ticket represents a correct application of the student's equation. However, the student provides an explanation for the solution rather than a justification: "by using the calculator's table after graphing and finding the line of best fit." 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 2

Annotation: This response indicates an incomplete application of a reasonable strategy. The representations are correct; both the equation for the line of best fit and the graph of the equation are within an acceptable range for the data given. The solution for the cost of the airplane ticket, $179.00, represents a correct application of the student's equation. There is no justification. This response demonstrates a conceptual 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 student determines an equation for the line of best fit that is within an acceptable range for the data given, graphs it accurately, and uses the equation to arrive at a solution of $176.48. The justification is logically sound and supports the solution: "I looked at my line of best fit and it showed $176.00 too." 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 student determines an equation for the line of best fit that is within an acceptable range for the data given, graphs it accurately, and uses the equation to arrive at a solution of $179.00. The justification is fully developed, logically sound, and supports the solution: "Also, the line of best fit seems to show the same correlation." 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 3.2.2:
Skill Statements | PUBLIC RELEASE ITEMS |