Handouts from a Summer Master's Course on Probability and Statistics for Teachers

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This page will contain links to handouts  (with brief comments on their contents) from a  master's course on probabiity and statistics for secondary teachers that I taught for several years, the last time in 2010.

I will be adding to this page from time to time and will try to remember to mention when it is complete.

Added September 10, 2015:

Normal Random Variables and The Central Limit Theorem Discussion, exercises, and applications of the Central Limit Theorem, plus exercises involving normal random variables.

Added March 12, 2015:

Models and Measures Brief introduction to models and measure, using measuring poverty as a case study.

Measures, Word, Rates, Ratios and Proportions A follow-up to the preceding handout.
    Part I: Problems involving choice of measure (exercises in thinking about the
different measures that might be used to answer a question, and the consequences of
choosing one measure over another)
    Part II: Words and Operations (exercises in figuring out from context what
operation to do to what numbers where; exercises in  practicing using possibly unfamiliar definitions; and execises to become familiar with concepts that will come up later in more complex contexts later)

Uncertainty Discusses different types of uncertainty.

What is Probability? Different conceptions of probability.

Random Variables The idea of a random variable; a variety of examples (pointing out useful distinctions); probability distributions, pdf's, empirical distribution, density histogram; normal distribution -- with lots of examples and exercises.

Cumulative Distribution Functions    Definition and 11 exercises.

What Do You Mean By Average
Average of speeds vs average speed; corporate average fuel economy; a Car Talk Puzzler.

Weighted Means and Means as Weighted Sums
Builds on the preceding handout to discuss weighted means, the mean of a random variable, harmonic means, and root mean square.

Logarithms and Means
    I. Approaches logarithms via pH. (Several students said they planned to change their teaching of logs to use an approach like this one, rather than the one in their textbooks.)
    II. Introduces the geometric mean and its connection to the arithmetic mean via logs; exercises on the geometric, arithmetic, and harmonic means.

Lognormal Distributions 1
Definition of lognormal distribution; "multiplicative central limit theorem"; examples; a couple of problems.

Lognormal 2 The geometric standard deviation and its connection with lognormal distributions.

Added January 27, 2015:

Basic Probability Basics of probability(including Bayes Theorem), plus exercises and problems, including a number of medical applications

More Probability Problems
 More medical applications: introduces sensitivity, specificity and prevalence rate, then problems using these concepts.  dDpends on the preceding handout)

More on Diagnosing Disorders
 Builds on the preceding handout to study the tradeoff between being able to detect when a disorder is present and being able to detect when it is not present.

Last updated 
September 10, 2015