Applications 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
• determine the equation of a line of best fit, using:
  • estimate of slope and one point
  • least squares method with technology
• use technological devices to determine the correlation coefficient r
• interpret the correlation coefficient r and its limitations for varying problem situations, using relevant scatterplots

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).
• 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.
• Have students plot anonymous class scores from a math test to develop a median-median best fit line, then find its equation. Have them use a graphing calculator or graphing software to find the least squares best fit line then calculate its equation. Ask students to compare and contrast the two and comment on which one is the best representation. Ask them to analyse the point-slope method for accuracy and ease of use.
• Produce six scatterplots with correlation coefficients approximately equal to -1, -0.5, 0, 0.25, 0.75, and 1. Have students calculate the correlations for each graph (perhaps as a small group exercise) using graphing calculators and have them define the difference between strong, weak, and zero coefficients as well as positive and negative coefficients.
• Present students with a series of business- or school-based case studies involving either raw data, scatterplots or pre-calculated correlation coefficients. Have students use the data to make decisions within the context of the case study.

SUGGESTED ASSESSMENT STRATEGIES

While many students are able to collect experimental data, their ability to make meaning of it mathematically will help their understanding of science, social sciences, and technology.

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

Question

• Where student collected data contains obvious anomalies (or outliers) ask students if these should be included or excluded and have them explain why.

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.

RECOMMENDED LEARNING RESOURCES

Print Materials

• Applied Mathematics 10, Western Canadian Edition
  Ch.4 (Sections 4.1 - 4.5)
  Ch.6 (Sections 6.6 - 6.9
  Projects: Student Choice Awards, Ecosystem Study, The News, Hair products, Anthropology
• 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
• Using the TI-81 Graphics Calculator to Explore Statistics
• What If...?: The Straight Line: Investigations with the TI-82 Graphics Calculator

© 2000 Copyright. All Rights Reserved. Curriculum Branch.
Maintained by: Mathematics Coordinator
Revised: November 29, 2000

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