Unit Outline for Core Learning Goal 3:
Data Analysis and Probability

The following Unit Outline is offered as a first attempt to identify good sources of activities and background information for teachers who are preparing students to pass the Maryland State High School Assessment 1 (HSA 1) on Algebra and Data Analysis. The sources emphasize active student participation and the use of real data. A complete list of the references cited is given following the tables.

The student will demonstrate the ability to apply probability and statistical methods for representing and interpreting and communicating results, using technology when needed.

I. Measures of Central Tendency and Variability
The student uses measures of central tendency and variability to solve problems and make informed decisions. (CLG 3.1.2)
Central Tendencies
  Mean
  Median
  Mode
  • Exploring Data: A8, A9
  • Contemporary Mathematics in Context, Course 1, Part A, Unit 1: Lesson 2 Shapes and Centers
  • Mathematics in a World of Data: Lesson 6
  • Exploring Centers: Lessons 2, 3, 4
Variability
  Range
  Interquartile range
  Quartile
Solving Problems

Making informed decisions
  • Exploring Data: A10, A11, A12, A13, A17
  • Contemporary Mathematics in Context, Course 1, Part A, Unit 1: Lesson 3 Variability
  • Mathematics in a World of Data: Lessons 12, 13

II. Proper and Improper Use of Statistics
Given a set of data or statistics, the student will analyze and identify both proper and improper use of statistics. (CLG 3.2.3)
Communicating the use and misuse of statistics
  Misuse of scaling
  Inappropriate measure of central tendency
  Misuse of 3-D figures
  Data bias
  Predicting outside the domain
  • The Visual Display of Quantitative Information: Chapter 2, Graphical Integrity
  • The Visual Display of Quantitative Information: Chapter 3, Sources of Graphical Integrity and Sophistication
  • Chance Website: Chance News
  • How to Lie with Statistics

III. Probability and Simulations
Using data, the student determines the experimental or theoretical probability of an event. (CLG 3.1.3)
Theoretical Probability
  • Exploring Probability: A14, A15, A16, A17, A18, A19, A23, A, 24, A25, A26, A30, A31, A32, A33
  • Mathematics in a World of Data: Lesson 11
Using simulations
  • The Art and Technique of Simulation: A1, A2, A3, A4, A5, A6, A7, A8, A9, A10, A11, A12, A13, A14, A15, A16, A17
  • Contemporary Mathematics in Context, Course 1, Part B: Unit 7, Lesson 1 Simulating Chance Situations; Unit 7, Lesson 2 Estimating Expected Values and Probabilities; Unit 7, Lesson 3 Simulation and the Law of Large Numbers
  • Probability Through Data: Lessons 3 and 4
Using statistical inference
  • The Art and Technique of Simulation: A12, A13
Estimating probability
  • The Art and Technique of Simulation: A6, A7, A8, A9, A10, A11
Given data from simulation or research, the student makes informed decisions and predictions. (CLG 3.2.1)
Based on data from simulations or research
  Make informed decisions
  Make predictions
  • Exploring Surveys and Information from Samples: A27, A28, A19, A2, A3, A4, A5, A6
  • Mathematics in a World of Data: Lesson 9

IV. Experimental Design
The students will describe how they would do an investigation, select an investigation and defend their choice. Students will consider simple random sampling (SRS) techniques that may include sampling size, bias representation, and randomness.(CLG 3.1.1)
Simple random sample
  Sample size
  Bias representation

Describe how to do an investigation

Select an investigation

Defend the selection

Analyze data
  • Exploring Surveys and Information from Samples: A17, A18, A19, A20
  • Activity-Based Statistics: "Random Rectangles"
  • Mathematics in a World of Data: Lesson 5
  • Probability through Data: Lesson 5

V. Line of Best Fit
The students will demonstrate his or her understanding of the process by finding a line of best fit and by using it to make predictions and/or interpret data (slope and intercepts) or by using a curve of best fit to make a prediction. (CLG 3.2.2)
Line of best fit
  Interpreting data
  Making predictions

Given curve of best fit
  Interpreting data
  Making predictions
Interpolate/extrapolate
  • Exploring Data: A20, A 21, A22, A23, A24, A25, A26, A27, A28, , A29, A30, A31, A32, A33, A34,
  • Exploring Regression: Lessons 1 through 6
  • Contemporary Mathematics in Context, Course 2, Part A, Unit 3: Patterns of Association


References

Books:

Burrill, Gail, et. al., Data Driven Mathematics: Exploring Regression, Palo Alto, California: Dale Seymour Publications, 1999

Burrill, Gail, et. al., Data Driven Mathematics: Mathematics in a World of Data, Palo Alto, California: Dale Seymour Publications, 1999

Coxford, Arthur, et al., Contemporary Mathematics in Context, A Unified Approach Course 1, Parts A and B, Chicago: Everyday Learning, 1997

Coxford, Arthur, et al., Contemporary Mathematics in Context, A Unified Approach Course 2, Part A, Chicago: Everyday Learning, 1998

Gnanadesikan, Mrudulla, et al., The Art and Techniques of Simulation. Palo Alto, California: Dale Seymour Publications, 1987

Hopfensberger, P., et al., Data Driven Mathematics: Probability through Data, Palo Alto, California: Dale Seymour Publications, 1999

Huff, Darrell, How to Lie with Statistics, Norton, W.W., New York, New York, 1993

Kranendonk, H., et al., Data Driven Mathematics: Exploring Centers, Palo Alto, California: Dale Seymour Publications, 1999

Landwehr, James M, et al., Exploring Surveys and Information from Samples. Palo Alto, California: Dale Seymour Publications, 1987

Landwehr, James M. and Anne Watkins, Exploring Data. Palo Alto, California: Dale Seymour Publications, 1986

Newman, Claire M, et al, Exploring Probability. Palo Alto, California: Dale Seymour Publications, 1987

Paulos, John Allen, A Mathematician Reads the Newspaper. New York: Basic Books, A Division of HarperCollins Publishers, Inc., 1995

Scheaffer, Richard L. et al, Activity-Based Statistics, New York: Springer, 1996

Tufte, Edward Rolf, Envisioning Information, Cheshire, Connecticut: Graphics Press, 1990

Tufte, Edward Rolf, The Visual Display of Quantitative Information, Cheshire, Connecticut: Graphics Press, 1983

Tufte, Edward Rolf, Visual Explanations, Cheshire, Connecticut: Graphics Press, 1997

Internet Resources:

Chance Website

http://www.dartmouth.edu/~chance

Contains statistics newsletters, activities, real examples of misuse of statistics.

Information Please Website

http://www.infoplease.com

Contains online dictionary, encyclopedia, almanac, and references containing current data sorted by category.

WWW Resources for Teaching Statistics

http://it.stlawu.edu/~rlock/tise98/onepage.html

Contains links to online resources for teaching statistics sorted by type.