Next month, I am scheduled to give a talk on Zoom about statistics. I studied statistics in graduate school and taught the subject in person, online and on tapes. Statistics is a subject of the modern age. As with anything else, the subject can mislead. When I think of good advice about statistics, I think of the book "How to Lie with Statistics" by Darrell Huff.
I don't remember a single equation in the Huff book. I do remember many visual and numerical tricks that are listed and explained. For instance, if the meanings of the scales or axes on a graph are manipulated, just about any sort of resulting line can represent the data. Like this:
A picture of my house:
It is my house from far, far away.
I think I can say that the subject I am thinking of tries to answer the question: What is there? But it tries to answer such a question when the "there" is complex and complicated.
So, often the first step is to try to find one number from a large set of numbers that can stand for all the numbers in the set. We get a list of all the ball players and their scores. Maybe the points they scored, the number of fouls they committed, their salaries. We expect different values and we get them. Let's put them in order - not alphabetical but in size, largest first and on down. We could add all the figures and divide by the number of figures for the "mean". We could find a value above half of the set and below half for the "median". We could find a value that is the score for more players than any other value for the "mode".
Truthfully, it may be that nobody is average, in any of the senses listed. There are many different values. We can feel that xxx is a typical number but it helps to remember that most of the players don't have that score. If some do, we could put their names on a plaque in the "Typical" wing of the hall of fame. If some player has a typical score season after season, we could celebrate that person as "outstandingly average."
