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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 2003

Mike wants to know how many calories he can burn while jogging. The number of calories burned depends on the length of time Mike jogs. The table below shows the number of calories Mike burns while jogging.

Complete the following in the Answer Book:

  • Write an equation for a line of best fit. (If you choose to draw a graph, use the grid provided in the Answer Book.)
  • What is the slope of your line of best fit? What does the slope mean in the context of this problem?
  • Mike jogged for 60 minutes. According to your line of best fit, how many calories did he burn? 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 2

Annotation: This response indicates an incomplete application of a reasonable strategy. Although the variables are not defined, an appropriate equation is given for the line of best fit. The slope is correct; however, the meaning of slope is not ("for every 10 minutes it will go up 9.811 in calories burned"). The correct context for slope would be that for every 1 minute 9.811 calories are burned. A correct answer ("588.708") for the number of calories burned and a clearly presented explanation (substitutes 60 for x in the equation) are given. This response demonstrates a conceptual understanding and analysis of the problem.


Sample Student Response #2

image of student response

Score for Sample Student Response #2: 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 variables are defined, and an appropriate equation for the line of best fit is provided. The slope and the meaning of slope ("means that Mike burns 9.81 calories per minute of jogging") are correct. A correct answer ("589") for the number of calories burned is given. The student substitutes 60 for x in the equation, providing a clearly presented and fully developed explanation. 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 1

Annotation: This response indicates little attempt to apply a reasonable strategy. An appropriate equation for the line of best fit, a numerical answer for the slope, and the meaning of slope are not given. The student correctly answers ("587") for how many calories are burned, demonstrating some meaningful interaction, but no explanation is provided. Although a graph of the line of best fit is not required, the student plots the points from the table and connects the dots. This is not, however, a line of best fit. This response demonstrates a minimal 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 |