Normal Distribution

This is a normal distribution graph. It may seem familiar to you (it should be), and this mountain-like graph turns out to represent a lot of, if not all, aspects of our everyday life. From the size of amoebas and the daily food consumption of a human to the components of cosmic things in the universe—they all follow the normal distribution rule.

Before going any deeper, let's get to know some key variables that are attached to the normal distribution graph.

First things first, there is the mean (μ). Basically, the mean is the same as the average. If you draw a verticla line in the middle of the normal distribution graph, the peak is the value of the mean. You can also get the value of mean by using the ordinary average formula which is adding up all the value and divide by the total amount of data.

Second is the standard deviation (σ). This tells us how spread out the values of the distribution are. A small standard deviation means the data are tightly clustered, with the curve being tall and narrow. A large standard deviation means the value are more spread out, the curve are lower and wider.

After understanding the key variables, let's jump into some real world examples:

The graph above shows the normal distribution of Indonesian male height. 166 is the average height—while the range of 158.2 to 173.8 represents the most common heights. Anything below 158.2 or over 173.8 is considered outside the typical range, but is still not an outlier. An outlier is identified when the data is outside (lower or higher than) 3σ—which includes only about 0.27% of the data.

For a comparison, let's take a look at the graph below—which shows the normal distribution of global male height. I don't want you to care about the numbers, just get the idea that a normal distribution is not attached to a number because the range of data between these two cases is definitely different but still distributed the same way. It is also not attached to a geographical location or any other attribute such as gender, age, or anything—because any of those attributes has its own normal distribution and you can also aggregate it to a higher level.

Imagine you are a male Indonesian living in one of the Nordic countries. In terms of normal distribution, you can be grouped in the 'world' context, 'Nordic', 'Denmark' (if that is the Nordic country), 'Indonesian male in Denmark', and any other hundred or even thousand contexts. Not to mention that you can also add attributes in each of those contexts and make an endless combination, e.g., height, wealth, age, skin color, etc

Our creator really did a great job by making anything comply under this normal distribution rule. Anyway, one of the reason in the making of this writing is to make us understand better about context.

I often throw out some statements such as 'bad government in Indonesia' or 'good schools determine your success,' and some people be countering that statement with 'not all people in government are bad' or 'I have a friend who came from a bad school or even did not attend any school but is successful now.

Of course, there would be cases where the statement becomes false. But by understanding the normal distribution rule,  we realize that these are simply outliers—special cases that fall beyond the 3σ

So next time you hear someone wanna drop out of college because Mark Zuckeberg did that and became a billionaire, just remember that he falls under this 0,27% or maybe less—a too good to be true number with poor risk-reward ratio.