Handouts from a Summer Master's Course on Probability and
Statistics for Teachers
My Home Page (contains contact information)
This page will contain links to handouts (with brief
their contents) from a master's course on probabiity and
for secondary teachers that I taught for several years, the last time
I will be adding to this page from time to time and will try
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
Added March 12, 2015:
Models and Measures Brief
introduction to models and measure, using measuring poverty as a case
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
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