The webpages in this section contain the text of a book I am writing about Probability and Statistics.
The intended audience is both teachers and students — at A level, and non-specialists at undergraduate level.
And the intention of the book itself is to supplement rather than to replace other books and teaching. There will be no exercises to do, nor any formal proofs, though there will be links to these where they are important, relevant and high quality. Being old fashioned, I’ll also point you to the few really excellent actual physical books that I’ve read that are really worth your time.
My goal is to deepen understanding of the subject and, as much as possible, make it intuitive. I will aim to demonstrate why it matters and show how it is used.
I don’t know why but I loved Statistics at school. Maybe it was because I was in an A level class of four students for two years. With a really outstanding teacher.
That’s pretty rare. In every respect. Statistics is typically taught by people who wish they didn’t have to teach it. They likely didn’t study the subject at university level — the cool kids taking maths degrees rarely opt for modules in Statistics — and so they tend to have neither a feel nor an enthusiasm for the subject. They pass on their sense that Statistics is boring and stupid to their students who, when they become teachers, do the same.
The focus of Statistics teaching is typically exams, and the writers of A level specifications and exam papers have a lot to answer for. They have done an outstanding job of making the subject seem tedious and irrelevant.
Many undergraduate courses at university include a module or two in Statistics. Students generally don’t take it seriously because that’s not what they’re there to study. The teaching may well not come from a subject specialist and so, once again, the subject is garbled and mis-sold.
This is a great pity because Statistics is a genuinely important subject. It has a distinguished history, with many of the biggest names in mathematics contributing to it. And research — of all kinds and at all levels — is meaningless and worthless unless it is grounded in a solid statistical foundation.
Public understanding of probability and statistics is notoriously poor. But — oh! — that this ignorance were limited merely to the public. Politicians and leaders frequently display a horrifyingly weak grasp of the subject. And these are the people who are making the Big Decisions.
Large corporations, on the other hand, often do appreciate the significance of mastering an understanding of data. That is how many of them have managed to achieve the enormous financial successes that they have. And increasingly in historically very short periods of time.
So if you worry about decisions made by government, and distrust the workings of big businesses — like Google and Facebook — an understanding of Statistics is part of being a well-informed citizen.
That great Monument to Probability — Las Vegas — is testament to the truth and power of the underlying theory of this subject. If you want to build a new casino, you won’t get much change from a couple of billion dollars. No-one invests that much money without being pretty confident of a healthy return. I know. I’ve lost plenty of money on the craps and blackjack tables there. When it comes to gambling, I’m just as dumb as everyone else.