Question

Essay Question: The Normal Distribution is arguably the most important concept in statistics. Why? (include the central limit theorem, standardized scores, etc.)

Answer 1

The normal distribution is important because it makes statistics a lot easier, and more feasible.

I know that may be tough to believe, because statistics is tough as it is. But it would be a lot harder without the normal distribution (and its three close relations).

The problem with collecting data is that you do not generally know what distribution the data follows. So you have a sample, but no distribution to help figure it out. The true distribution is generally not knowable, but you could often find something workable if you tried (which is why Stats I texts start with the binomial, which shows up a lot). The thing is, there are a ton of distributions (which is why many students start to get lost in Stats I as additional distributions are introduced). And quite possibly your sample might match up with none of them, and then you’d need to dream up a new one.

Then along comes the central limit theorem. It implies under fairly easy to satisfy conditions that some of the summary statistics you’d calculate from your sample do have a known distribution even if you do not know the distribution of your sample.