18 January 2016

The normal distribution – three tricky bits

There are several tricky things about teaching and understanding the normal distribution, and in this post I’m going to talk about three of them. They are the idea of a model, the limitations of the normal distribution, and the idea of the probability being the area under the graph. It’s a model! When people hear the term distribution, they tend to think of the normal distribution. It is an appealing idea, and remarkably versatile. The normal distribution is an appropriate model for the outcome of many natural, manufacturing and human endeavours. However, it is only a model, not a rule. […]
18 August 2014

Teaching random variables and distributions

Why do we teach about random variables, and why is it so difficult to understand? Probability and statistics go together pretty well and basic probability is included in most introductory statistics courses. Often maths teachers prefer the probability section as it is more mathematical than inference or exploratory data analysis. Both probability and statistics deal with the idea of uncertainty and chance, statistics mostly being about what has happened, and probability about what might happen. Probability can be, and often is, reduced to fun little algebraic puzzles, with little link to reality. But a sound understanding of the concept of […]
29 July 2013

Let’s hear it for the Triangular Distribution!

Telly monster is my favourite character on Sesame Street, and a few years ago I was lucky enough to actually meet him. This morning I was delighted to find out from my resident Sesame Street expert that Telly monster is a triangle lover. I too am becoming a triangle lover. I have learned recently about the triangular distribution. For some reason it is in the New Zealand curriculum and I wondered why, never having used it or seen it in any statistics textbook. I still don’t know the official motivation for including it, but it is a really good idea. […]
26 June 2012

All models are wrong

In my title I quote George Box, who wrote,  “Essentially, all models are wrong, but some are useful“. I wish economists would remember this more often. Statistics and Operations Research (and many other sciences) are based on the concept of a mathematical model. Aspects of a “real world” problem are quantified, analysed, explored, experimented with, sometimes even optimised, and the results are linked back to the original problem. This idea of a model is one we have tried to teach our students. It is a surprisingly difficult idea, and one that needs frequent revisiting. The following diagram is more complex […]