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- Introduction
- Reasoning based on probability and statistics gives modern
societies the ability to cope with uncertainty. It has astonishing power to
improve decision-making accuracy and test new ideas. Within probability and
statistics there are certain amazing applications which stand out for their
profound or unexpected results. This page is aimed especially at AP
Statistics students and explores many of these
amazing applications.
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- The Probability of
Penalizing the Innocent Due to Bad Test Results
- Tests used for detecting things like drug abuse,
intoxication, disease, genetic and birth defects, etc. often lead to life changing
situations including job termination,
incarceration, surgery, and abortion. We like to think these
tests are accurate, yet, horror stories seem to abound.
This article explores why a good test can give bad results.
- (AP Statistics Topics: probability)
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- How to Set Up Small Groups for Decision Making
- Everyone believes in teamwork. Yet, anyone who has attended a
meeting probably feels that a camel is indeed a horse designed by a
committee. Probability and statistics can shed a great deal of light on
how to set up decision making groups with real horsepower.
- (AP Statistics Topics: probability, combinations or
binomial coefficient)
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- Simpsons's Paradox - When
Big Data Sets Go Bad
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It's a well accepted rule of thumb that the larger the data
set, the more reliable the conclusions. Simpson' paradox, however,
slams a hammer on the rule and the result is a good deal worse than a
sore thumb.
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(AP Statistics Topics: data analysis)
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- Benford's Law Part 1 - How to Spot Fraud
- Everyone knows that our number system uses the digits 1 through 9 and that the
odds of randomly obtaining any one of them as the first digit in a number is
1/9. These odds work well for data faked by embezzlers but with real data
the odds are considerably different.
- (AP Statistics Topics: random numbers)
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- Benford's Law Part 2
- The 80/20 Rule or Pareto Principle
- Is the large wealth difference between rich and poor a
result of capitalistic greed or could it be a naturally occurring process as
suggested in 1906 by the Italian economist Vilfredo Pareto. Benford's law can
be extended to this and other questions about ranked data.
- (AP Statistics Topics: explains why income
distributions tend to be skewed to the high side or skewed right)
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- The Awesome Power of Twenty
Questions
- It's a common classroom game for gradeschoolers and yet
contains a profoundly powerful problem solving strategy which can be used to
de-bug software, troubleshoot equipment and solve problems in business and
industry.
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- The
Central Limit Theorem – How to Tame Wild Populations
- The American justice system is remarkably similar to a
hypothesis test in statistics.
- (AP Statistics Topics: Central limit theorem, law of
large numbers, parameters, statistics, standard error;
Applet Included)
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- Type I and Type II Errors -
Making Mistakes in the Justice System
- Data tends to be wildly variable but thanks to the central
limit theorem we can tame it.
- (AP Statistics Topics: hypothesis testing, type I
and type II errors, power of the test;
Applet Included)
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Perfecting Simulations – The Quest for a Perfect Random Number
Generator
- Monte Carlo simulations consume huge quantities of
random but good random numbers are hard to find. are hard to find. (AP Statistics Topics:
hypothesis testing, random numbers, time plots;
Applet Included)
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- Pseudo-Random Numbers and
Wireless Signals – Why Cell Phone Are hard to Tap
- Cell phone companies help maintaining privacy by
deliberately adding noise generated by pseudo-random number generators. (AP Statistics Topics:
random numbers;
Applet Included)
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