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)
Why not wait for college to teach statistics and probability? Because most students are 18 years old before they even begin college. At that age they can vote, buy cigarettes and lottery tickets, join the army, get married, and make independent medical decisions. They can't afford to delay learning how to evaluate probabilistic situations and how to use data to make intelligent decisions.

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

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