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Statistics and Probability
Because of the importance of statistics and probability in everyday
life, virtually every set of standards and recommendations for the secondary
school curriculum includes a strand in statistics and probability. The
National Council of Teachers of Mathematics in the Principles and
Standards for School Mathematics (PSSM) recommends an increased
emphasis on data analysis and probability from kindergarten through grade 12.
Instructional programs should enable all students to
- formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them
- select and use appropriate statistical methods to analyze data
- develop and evaluate inferences and predictions that are based on data
- understand and apply basic concepts of probability." (PSSM, p.324)
Each course in the Core-Plus Mathematics curriculum includes one unit on statistics and one on probability, which are described briefly below.
Course 1
Unit 1 - Patterns in Data
Using appropriate graphs to display data; summarizing data using measures
of center such as the mean, median, and mode and measures of spread;
scatterplots and association; plots over time and trends
Unit 7 - Simulation Models
Simulating probabilistic situations; frequency tables; random-digit tables
and random-number generators; independent trials; the Law of Large
Numbers
Course 2
Unit 3 - Patterns of Association
Computing and interpreting correlation; regression lines and their use
in prediction; making cause and effect statements
Unit 7 - Patterns in Chance
Probability distributions and their graphs; multiplication rule for independent
events; the waiting time (geometric) distribution; expected value;
rare events; summation notation
Course 3
Unit 2 - Modeling Public Opinion
Surveys and polls; the purpose of sampling; types of samples; relationship
between a sample and a population; confidence intervals; margin of
error in polls; critical analysis of elections and surveys
Unit 5 - Patterns in Variation
Standard deviation and its properties; the normal distribution; statistical
process control including the use of control charts; mutually exclusive
events and the addition rule of probability
Course 4
Unit 3 - Logarithmic Functions and Data Models
Fitting functions when the data aren't linear including the use of log
transformations
Unit 5 - Binomial Distributions and Statistical Inference
Computing probability in success/failure (binomial) situations; binomial
distributions; normal approximation to a binomial distribution; meaning
of statistical significance; test of a proportion; design of an experiment;
randomization test; test for the statistical significance of the difference
of two proportions