Principles of Mathematics 10 -
Statistics and Probability (Data Analysis)

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

PRESCRIBED LEARNING OUTCOMES

It is expected that students will implement and analyse sampling procedures, and draw appropriate inferences from the data collected.

It is expected that students will:

• choose, justify and apply sampling techniques that will result in an appropriate, unbiased sample from a given population
• defend or oppose inferences and generalizations about populations, based on data from samples

SUGGESTED INSTRUCTIONAL STRATEGIES

Most data collection involves the use of samples rather than populations. Understanding the uses, advantages, and disadvantages of sampling is critical to interpreting statistical information.

• Ask students to identify ways of using sampling to deliberately skew survey results (e.g., survey of probable Stanley Cup winners by polling only fans of one team, survey of favourite musical groups by polling people from only one age group). Have students identify examples of biased or invalid samples on data reported in the media. Ask them to work in groups to analyse the data and determine what the sample population might have been. Discuss as a class.
• Have students suggest real-world applications for using distributions (e.g., knowing the size distribution, how many of each shoe size a shoe store should stock).
• Invite a pollster to speak to the class about polling as a sampling technique. Discuss various types of polls (e.g., random selection, target market, phone-in polls). Ask students: Are each of these sampling techniques unbiased? If they are biased, how? (e.g., a telephone sample would not include people who do not speak English well enough to answer the questions)
• Students could design a survey, drawing their sample from the school or community at large. Have students justify their survey content and sampling method. Ask students to draw valid non-trivial conclusions from their data.
• Give students a series of case studies involving survey information and have them critique the studies and support or reject conclusions in the case studies. Alternatively, limit the case study to the survey setup and data and then have students develop their own conclusions.

SUGGESTED ASSESSMENT STRATEGIES

Projects of both long and short duration provide a basis for ongoing assessment and summative evaluation. Assessment in this area should give students a chance to demonstrate their skills and knowledge while completing projects they find meaningful.

Collect

• Have students design and conduct research projects requiring them to choose and apply sampling techniques. As students work on their projects, ask questions such as:
  • How did you choose your sampling technique?
  • Can you justify your choice?
  • Can you identify possible sources of bias or error in your sample?
  • When might someone want to bias a sample and how might they do it?
  • What makes the graphical representations you are using appropriate for your data?
  • How are your conclusions affected by your sample?
• Work with students to develop criteria they can use to assess their projects. Students use the criteria to assess their own work, then describe how their projects could be changed to correct identified problems. Criteria might include:
  • a clear description of sampling procedures
  • justification for the sampling technique
  • accurate identification of possible reasons for bias or error
  • effective graphical representations of data summaries
  • appropriate references, clearly linked to the data, about the population from which the sample was taken

Self-/Peer Assessment

• Provide students with materials necessary to develop study cards describing terms and concepts related to data analysis. Have students quiz one another using the cards. Small groups of students can use the cards to compose tests for other groups to take. Give students basic test requirements such as length and type of items. Students should be able to answer their own questions.

RECOMMENDED LEARNING RESOURCES

Print Materials

• Exploring Statistics with the TI-82 Graphics Calculator
• Graphing Calculator Activities for Enriching Middle School Mathematics
• An Introduction to the TI-82 Graphing Calculator
• Modeling Motion: High School Math Activities with the CBR
• Pure Mathematics 10 (Distance Learning Package)
• What If ...?: The Straight Line: Investigations with the TI-82 Graphics Calculator

Multi-Media

• The Learning Equation: Mathematics 10 Lessons 43 & 44
• Mathematics 10, Western Canadian Edition
  Ch. 9 (Sections 9.1 - 9.4)
• MATHPOWER 10, Western Edition
  Ch. 8 (Sections 8.1 - 8.4)

Software

• Secondary Math Lab Toolkit

© 2000 Copyright. All Rights Reserved. Curriculum Branch.
Maintained by: Mathematics Coordinator
Revised: November 22, 2000

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