How to learn statistics from scratch

Oscar Nieves
5 min readJul 22, 2021

And understand it properly.

Statistics is a huge field of study. Most people only come across some statistics in school, and perhaps at university. Unless you have done a dedicated degree in data science, mathematics/statistics, quantitative finance or actuarial science; chances are you probably know very little. In fact, so little that you don’t know how to make use of the knowledge you have, which kind of defeats the purpose of knowing any statistics at all.

But it’s not people’s fault. I mean, I have qualifications in physics and even then my knowledge of statistics is extremely limited. I have had to teach myself at least 95% of what I currently know (primarily because my PhD research has required me to do so), and it has certainly not been an easy journey. What I have learned though is that statistics need not be a boring subject like they teach it in most courses, there’s actually quite a lot of interesting mathematics in it if you look in the right places. In this story I will tell you what steps you should take if you have zero knowledge of statistics, but want to learn enough so that you can apply it to build your own mathematical models, perform decent data analysis, and even design appropriate experiments to suit your needs. Here are some tips to make your learning more efficient and fruitful.

1) Learn the core mathematics first, then the statistics

Statistics is a whole field of study in itself, so if you think you can learn enough in one sitting then you are gravely mistaken, I am afraid. However, you don’t need to be a trained mathematician to understand some pretty sophisticated statistical tools and method. The key mathematics you should be familiar with are mainly linear algebra (vectors, matrices, matrix operations, eigenvalues, eigenvectors, diagonalization, simultaneous equations, etc.) and calculus (this includes derivatives, definite integrals, integrals with infinite limits, sums and sequences, and so on). You will also need to know some multivariable calculus, namely partial derivatives and multiple integrals (double, triple, integrals in non-Cartesian coordinate systems). Also, knowing basic set theory will be advantageous.

Oscar Nieves

I write stories about applied math, physics and engineering.