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.

David

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