Tuesday, July 17, 2012

Statistics and being "Normal".

Normal. It's a word that we all seem to have a love/hate relationship with. Everyone wishes they were more normal, while also wanting to be unique.

I've been meaning to post this for a while, because it's one of my more abstract thoughts. That, and it involves statistics.

I think most people recognize this:

This is the normal distribution curve. The theory goes that this is the natural distribution of probability of observations made in nature. The average, or the norm, is right in the middle and typically has the highest chance of occurring. As you move away from the normal on either side, the probability goes down sharply. 

See those little numbers on the bottom? Those represent standard deviations. The standard deviation shows how much variation or"dispersion" exists from the average value. The normal standard deviation represents ~68% of the total values in the total sample size.

So, let's apply this theory to people. Look at the above curve and say we apply it to how attractive a person is on a scale of 1-10. So the norm would be a 5, the far right side would be a 10, and the far left would be a 1. If you picked 100 people at random, on average they would rate a 5 for attractiveness and 68% of the people would rate between a 2.6 and a 7.4. So if you were a normal person, you would be a 5.

Now, let's look at this graph in two dimensions:

So, here we are grouping observations in two dimensions. Let's take our attractiveness observation (x) from earlier and add a new independent dimension, intelligence (y). Just by looking at the graph, that most people are middle of the road attractive and intelligent. Compared to entire graph, people that are super smart and super hot (-4,-4) would be in the extreme minority, while most people would fall into the standard deviation range.

From here we can extrapolate and add as many independent dimensions as we want to measure people by: ethnicity, age, favorite color, whatever...

You end up with a hypergraph measuring all these things at the same time and defining the truly normal person: middle of the road in every imaginable aspect. This person is normally attractive, intelligent, average interests, average everything. This "normal" person isn't really remarkable in any way, and that's my point. They don't stand out, they aren't unique even in the slightest way. Why do we compare ourselves, and in some cases aspire to be this normal person? What does this measurement provide?

As far as I can understand, the normal yardstick is great so that we can measure ourselves against something. We imagine normal people but this person isn't average, they are usually better than average. If normal is 5, we envision someone maybe 7 or 8 to be the normal. Not perfect, but not a dirt-bag either. This may be a way to encourage ourselves to be better than average, to aspire not to perfection, but to be the 7 or 8 that feels like a great compromise between average and perfect.

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