Applications of Mathematics 11 -
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 analyse graphs or charts of given situations to derive specific information.

It is expected that students will:

• extract information from given graphs of discrete or continuous data, using:
  • time series
  • continuous data
  • contour lines
• draw and validate inferences, including interpolations and extrapolations, from graphical and tabular data
• design different ways of presenting data and analyzing results, by focusing on the truthful display of data and the clarity of presentation
• collect experimental data and use best-fit exponential and quadratic functions, to make predictions and solve problems

SUGGESTED INSTRUCTIONAL STRATEGIES

Creating and interpreting graphs and charts are important real-life skills. Students will encounter many day-to-day situations in which they will be required to interpret and analyse graphs and make reasonable inferences about the data.

• Have students use previously learned sampling skills to collect bivariate data such as:
  • the number of absences from class and corresponding course grade
  • age of the school bus and cost of upkeep of the bus the previous month
  • points scored by a professional sport team at home compared to the attendance at the game and attendance at the next game
• Use the calculator based laboratory (CBL) to :
  • generate data and scatter plots (e.g., motion data, data from science labs
  • plot data for populations from various age groups to confirm or disprove the occurrence of a baby boom
• Present data from spreadsheets in different forms (e.g., pie chart, histogram, broken line) and determine the appropriate use of differing forms of data presentation. Note: Translating from data functions is a good way to relate tangible problems to theoretical mathematical manipulations.
• With collected data, have students create a scatter plot and then determine the line of best fit. They compare the resulting plots and determine the linear correlation coefficient of the data. Finally, they draw conclusions based on the lines of best fit, keeping in mind the limitations associated with the correlation coefficient.
• Have students research examples that exhibit misuse of statistics such as:
  • assumed cause and effect based on calculated correlation
  • linear projections made beyond the relevant range of the data
  • use of inappropriate data (e.g., outliers) to calculate the correlation coefficient
• Provide samples that may be misleading from sources such as political pamphlets or advertisements, and encourage students to question conclusions drawn from the data.

SUGGESTED ASSESSMENT STRATEGIES

Statistics is the science of collecting, organizing, and interpreting data. In assessing student progress in data analysis, look for evidence that students can determine the curve of best fit for the data.

Observe

• In assessing student performance in analysing data, look for evidence that they can:
  • differentiate between discrete and continuous data
  • determine the equation of the curve of best fit
  • use functions to extrapolate and interpolate trends
  • use reasoning to choose the appropriate regression curves based on trend of data and the context from which the problem is based
• As students work with graphing calculators and tables of data obtained from experiments, circulate, asking questions and observing how effectively they are able to:
  • enter the data into their calculators
  • sketch, on graph paper, an accurate representation of the calculator’s resulting graph
  • determine the regression equation that best models the date
  • use the regression equation to solve applied problems

Collect

• Have students investigate real-life situations to determine possible relationships among the data (e.g., education and income, deaths and car speed). For each data set, ask them to construct the scatter plot, determine the curve of best fit, and calculate the correlation coefficient. Assess their work for the extent to which they accurately determine the line of best fit.

Self/Peer Assessment

• Students can discuss and debate the validity of other student’s analyses of data. Look for reasons why they choose particular regression lines, displayed data in particular way, and how they reached a conclusion based on data.

RECOMMENDED LEARNING RESOURCES

Print Materials

• Applied Mathematics 11, Western Canadian Edition
• Exploring Statistics with the TI-82 Graphics Calculator
• 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 22, 2000

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