How to use and misuse mathematical statistics (1/3)

People like statistics. In newspaper articles we regularly meet references to the law of big numbers, the central limit theorem, normal distributions, or even Markov chains. The notions of probability, random variable, and (in)dependence became so common that their wide use and misuse does not attract anyone's attention any more.

We are going to discuss very informally, how to achieve different results starting from a fixed set of data. The first example is a widely used notion of the average salary. Ironically, there is no verifiable and widely accessible detailed data in Internet on the distribution of salaries in Germany, so I had to take the U.S. as an example. Can we really prove—without lying or manipulating the data, and based on a solid mathematical ground—that it is almost zero? Another interesting example are social polls and ratings derived from them. Everybody knows, the TV never lies. Assuming this, if we hear in the news that the rating of our favorite politician dropped by 1% since last week, should we be really worried about it? The last topic will choosing distributions for real life phenomena. Namely, why are some distributions used more often than the others? Is the normal distribution really normal? Are the others abnormal?

The format will be a series of informal interactive discussions with non-mathematically looking examples and a handful of brainteasers. The goal is to share some knowledge on catchy examples and get fun of it. No technical proofs on the blackboard or deep analysis are expected. The series is loosely based on the great book by Gregory Kimble "How to Use (and Misuse) Statistics", the lectures on probabilistic models and mathematical statistics at the Moscow State University in 2002–2003, and my personal experience.

#1. Title: "The average salary in America"
#2. Title: "Is the normal distribution really normal?"
#3. Title: "Applied statistics is an art"