Statistics and Probability: Part I - What they don't tell you about Statistics and Probability.
Someone once said that statistics and probability is the branch of mathematics that that tells you some important stuff without telling you the most important stuff.
Take for example: It can tell you what the chances are that you will win the lottery, but it can’t tell you if you will win the lottery or not. People across the world buy lottery tickets (ignoring what statistics and probability tell us), because they are sure that they are more likely to win than everybody else – but they have no evidence to back up that claim.
Suppose you attend a school with 1000 students. Suppose on half of the students (500) are boys, and that each of those boys has two testicles (a total of 2 x 500 or 1000 testicles). Suppose the other half of the students (500) are girls, and that each of those girls have two ovaries (a total of 2 x 500 or 1000 ovaries). Statistics will tell you that the average student at that school has one testicle and one ovary. In fact we already know that no student has one testicle and one ovary – so there are no average students in this school.
If you are shopping for a house statistics can tell you what the average price, or what the median price of a home in the neighborhood that you want to live in is. But statistics cannot tell you the price of the home that you want to buy.
Statistics tells me that it is not very likely for a plane to crash while I am a passenger on that plane. But it cannot tell me if it will or will not crash.
I have been pretty lucky in each of these areas. I married a girl that I went to school with. Neither of us were “average”, and it worked out well. I bought a house that was exactly what we wanted, and possibly a little more than what we needed, but paid less than the price of the “average house” in our area. And I have taken off in an airplane two times more that I have landed in an airplane. (Once I parachuted from the plane, on purpose, and every worked like it was planned. And once it crashed, but nobody died or was injured.)
I recommend that statistics and probability are important areas of mathematics, and that you should study them. But I always recommend that you think things through before you rely heavily on what statistics and probability tell you. What is more important are the things that statistics and probability does not tell you.
What does statistics and probability tell me about playing the lottery. It tells me that if I don’t play I can’t win – but I probably won’t anyway, but if I don’t play I can’t lose. It also tells me that if I play a billion times (supposing I had the money to play a billion times), that I will most likely win some money – but I will likely win far less than what I spent to buy the tickets. But people don’t believe that and still like up to buy as many lottery tickets as they can afford this week (even though statistics tell us that most people who do win the lottery are broke within three to five years of winning).
Statistics and probability tell us that if people do just four things they are likely not to be poor. First, graduate high school. Second, don’t commit crimes and stay out of prison. Third, get a job, and do what you can to keep that job until you get promoted to or are offered a better job. And fourth, don’t have children out of wedlock.