Mathematics 9 -
Statistics and Probability (Data Analysis)

This sub-organizer contains the following sections:
Prescribed Learning Outcomes
Suggested Extentions
Suggested Instructional Strategies
Suggested Assessment Strategies
Recommended Learning Resources

In order to prepare students to collect and analyse experimental results expressed in two variables, using technology as required, it is expected that students will:

• design, conduct, and report on an experiment to investigate a relationship between two variables
• create scatter plots
• interpret a scatter plot to determine if there is an apparent linear relationship
• determine the lines of best fit from a scatter plot for an apparent linear relationship by:
  • inspection
  • using technology (equations are not expected)
• draw and justify conclusions from the line of best fit
  

SUGGESTED EXTENSIONS

To extend students' understanding of data analysis, they could:

• assess the strengths, weaknesses, and biases of samples and data-collection methods
• critique ways in which statistical information and conclusions are presented by the media and other sources

SUGGESTED INSTRUCTIONAL STRATEGIES

Collecting, displaying, and interpreting data can help students see the relevance of statistical analysis. Statistical analysis allows us to make sense of the data in the world around us, which is an essential part of being an informed citizen.

• Have students design, conduct, and report on an investigation into a selected relationship, using a scatter plot to investigate that relationship. Ask students to estimate and draw the lines that best fit their scatter plot and then discuss the following questions with a partner:
  • Is it appropriate to connect the dots (e.g., is the relationship linear)?
  • Can the line be used to make predictions?
  • Would any point that lies on the line have meaning with respect to the two variables?

  Why or why not?

• Give each student a scatter plot based on a linear relationship, and have them:
  • determine the line of best fit manually
  • determine the line of best fit using technology
  • identify conclusions that can be drawn from the data
  • describe the relationship
• Ask students to collect and report on data comparing the relationship between two seemingly unrelated variables (e.g., height versus performance in mathematics class, head circumference versus grade in English). Discuss as a class:
  • Is there a direct relationship between the two factors, or are there associated factors (e.g., relationships between race and crime rates)?
  • How may this type of information be used or misused in society (e.g., statistics correlating performance to race or gender)?
  • Do statistics provide the answers to all questions?
• Use population or immigration statistics over time to initiate a discussion about the applications of data analysis. For example, looking at population statistics of Aboriginal peoples over the last two centuries raises questions about why and when the population declined. A good source of data is E-stat (http://www.statcon.ca)

SUGGESTED ASSESSMENT STRATEGIES

Research projects can provide students with meaningful experiences in collecting, analysing, and displaying information, as well as using scatter plots to draw and justify conclusions derived from the research.

Collect

• Help students design individual experiments to investigate relationships between two variables. Have them gather data, create scatter plots, and determine lines of best fit. Ask them to analyse their findings and draw conclusions. Then have students describe their experiments and data-collection methods to the class, present their findings, and justify their conclusions. A prepared list of questions may be used to help students organize their thoughts when doing evaluations of each other's work. Evaluate presentations using criteria such as:
  • relevancy of the experiment
  • appropriateness of data-collection methods
  • validity of conclusions and student's ability to justify conclusions
  • organization and clarity of the presentation
  • accuracy of development of scatter plot and identification of line of best fit
• Provide articles from the media that present statistical information and conclusions. Ask students to write simple evaluations, analysing the way the data were gathered and presented and the conclusions that were drawn. Review students' evaluations and provide feedback. Evaluations should address questions such as:
  • How were the samples selected? Why were they selected in this manner? Are they biassed?
  • Were the data-collection methods appropriate for the data and the issues?
  • Is the data presented clearly and honestly?
  • Do conclusions follow logically from the data?
  • What questions were left unanswered? Was this done on purpose?

Self-Assessment

• Ask students to compare lines of best fit they create through inspection to those they create using technology. Are they relatively close?
  

RECOMMENDED LEARNING RESOURCES

Print Materials

• Interactions (Level 9)
• MATHPOWER 9, Western Edition
• Triple 'A' Mathematics Program:
  Data Management & Probability
  

Multimedia

• Hot Dog Stand: The Works
• The Learning Equation Mathematics 9 (TLE)
• Math Tools
• Mathematics 9 (Distance Education Package)
• Minds on Math 9, Revised Edition
• Statistics Workshop
  

© Copyright 2001. All Rights Reserved. BC MOE Standards Department.
Maintained by: Mathematics Coordinator
Revised: September 1, 2001

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