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Amazing Applications of Probability and Statistics
by Tom Rogers, Twitter Link
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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.
 
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)
 
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)
 
Simpsons's Paradox - When Big Data Sets Go Bad
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. 
(AP Statistics Topics: data analysis)
 
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)
 
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)
 
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.
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)
 
 
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)
 
 
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)
 
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)

Acknowledgements

Parts of this project were supported by a National Science Foundation Research Experience for Teachers grant as part of Clemson University's Summer Undergraduate Research Experience in Wireless Communications

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