Parameters of a Normal Distribution

Two numbers that define it all

Yesterday we talked about the Normal Distribution in non-technical terms.

If you understand the general concept, this next part should be pretty easy. If you don’t get it, either reread the last post or shout at me in the comments and I’ll try and clarify some things.

So what is a parameter then? You can think of it as settings on a TV such as brightness or volume. They’re both expressed as numbers and each combination of parameters can re-define the whole viewing experience.

Imagine two televisions, TV-A and TV-B. If TV-A has its (Brightness, Volume) settings tuned to (30, 30) and TV-B has them set to (40, 20), then TV-B is brighter than TV-A, but TV-A is louder than TV-B. You’re still watching TV in each case, but the experience is meaningfully different.

With the Normal Distribution then, there are two parameters that define the shape of the distribution. We have the mean value and the variance.

The mean value is written with the Greek letter μ (written as “mu” and pronounced as “mew”) and the variance is written as σ², or “sigma squared”.

The illustration below* shows how the shape of the bell curve changes with different values of μ and σ². You will see that the position of the peak of each curve is defined by the value μ and that the ‘spread’ or ‘width’ of each bell curve is defined by the σ² value.

If you’d rather see this in action, play about with this interactive Normal Distribution for a bit and see if you can convince yourself of how it works. There won’t be a test, so just have fun with it!

*Image credit: Wikipedia entry for ‘Normal Distribution’