Mathematics 8 -
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 develop and implement a plan for the collection, display and analysis of data, using technology as required and to evaluate and use measures of central tendency and variability, it is expected that students will:

• formulate questions for investigation, using existing data
• select, defend, and use appropriate methods of collecting data:
  • designing and using surveys
  • research, using electronic media
• display data by hand or by computer in a variety of ways
• determine and use the most appropriate measure of central tendency in a given context
  

SUGGESTED EXTENSIONS

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

• describe the variability of data sets, using such techniques as range and box-and-whisker plots
• construct sets of data given measures of central tendency and variability
• determine the effect on the mean, median, and/or mode when:
  • a constant is added or subtracted from each value
  • each value is multiplied or divided by the same constant
  • a significantly different value is included

SUGGESTED INSTRUCTIONAL STRATEGIES

The science of statistics is a powerful tool to help convey information. It can also misrepresent the truth. As consumers, students must develop an understanding of data analysis if they are to make informed decisions.

• Assign a survey project requiring each student to:
  • formulate a question
  • decide on a suitable sample
  • record data
  • display the results (using available technology)
  • calculate the mean, median, and mode where appropriate
  • make and justify conclusions based on the survey results
  
  
  Encourage students to design projects based on learning in another subject area (e.g., career goals, cultures of origin, musical preferences).
• Ask students to select survey or research projects reported in the media and evaluate them in terms of methods of display and conclusions made. They could then write letters to the editor reporting any questions or problems they have with the data or its representation. Where possible, students could design and conduct their own surveys on the same issue.
• Discuss with the class the use of mode, median, and mean with different sets of data and for different purposes (e.g., ice cream flavours, grades on a test, bowling scores, population density).
• Ask students to select sets of data and intentionally bias the information by manipulating the way they display it. Have them present their displays to other students, who attempt to identify the bias in each case.
• Present students with a box-and-whisker plot. Have them record in their own words what information is being presented and share their responses with partners.
  

SUGGESTED ASSESSMENT STRATEGIES

Students can demonstrate a broad range of data-analysis skills by planning, implementing, and analysing their own research projects.

Observe

• Have students describe possible sources of bias in a collection and display of data, and explain or demonstrate how bias can be avoided.
• As students work with box-and-whisker plots, note whether they can identify the components. Do they correctly determine the extremes, quartiles, and median?

Collect

• Ask students to bring in articles from the media that present statistical information. Then have them analyse the data and graphs and draw their own conclusions. Compare conclusions drawn by students to those drawn by the media. Discuss differences. Are students' conclusions similar to those of the media? If not, can students defend their conclusions?

Self-/Peer Assessment

• Work with students to develop criteria for evaluating their research projects. For example:
  • appropriateness of research questions
  • effectiveness of data-collection methods
  • adequacy of survey design
  • effectiveness of the method used to record data
  • appropriateness of the graph scale and type
  • accurate calculation of mode, range, median, and mean
  • validity of conclusions
  • organization and clarity of presentation
  • students' ability to justify their conclusions
  Ask students to identify strengths and weaknesses in their work and briefly summarize how identified problems might be corrected in future projects.
• Have students determine the mode, median, and mean for different sets of data. Students should identify the best methods for describing different kinds of data and provide a rationale to support their choices. Check the accuracy of students' calculations and provide feedback regarding the validity of their conclusions.

RECOMMENDED LEARNING RESOURCES

Print Materials

• Interactions (Level 8)
• MATHPOWER 8, Western Edition
• Triple 'A' Mathematics Program:
  Data Management & Probability
  

Multimedia

• Hot Dog Stand: The Works
• The Learning Equation Mathematics 8 (TLE)
• Math Tools
• Mathematics 8 (Distance Education Package)
• Minds on Math 8, Revised Edition
• Statistics Workshop
  

CD-ROM

• Mathville VIP

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

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