There are some mathematical concepts that everyone should just understand. The bell curve is one such concept. It is everywhere. Here's what it looks like:
The way you read this diagram is that you have some sort of attribute on the x-axis, for instance height, or IQ scores, people's guesses for how many jellybeans in a jar... The y-axis is the number of instances of the attribute; taller means more people or instances of that particular value of attribute. For instance, IQ is defined with an average of 100, and a lot of people will have this average IQ. As you look at people with higher or lower IQ, you'll notice there's fewer and fewer of them the more you deviate from the average. Super smart and super dumb people are pretty rare, they are at the tail ends.
Generally, a bell curve is when a series of independent random choices can contribute to an outcome. For instance, your height is determined by a series of random genetic markers and nutritional health. If you sample enough people from a population, most people, about 68%, will be clustered near the average. Then some people will be really tall and some will be really short. The SD in the diagram stands for standard deviation, which is just a specific value for what we are measuring that describes how much people can be different to the average. For instance, in IQ measurement, one SD is about 15 IQ points. This means that about 68% of people are between 85-115 IQ points. Only 2% of people have a 130+ IQ!
The bell curve describes a lot of naturally occurring measurements and phenomena in life and is useful towards explaining or understanding how things work. The other really important maths distribution to understand is the Pareto distribution and the power law, which I'll cover in a later blog. For instance, wealth follows the power law where 80% of wealth is controlled by 20% of people.
One thing it teaches you is the basics of statistics, which is, take lots of samples! If you were an alien visiting Earth and you talked to Gauss, you would assume everyone was just as smart as Gauss, when in fact he's in the 0.0001% of all humans! Taking lots of samples is critical to seeing the bigger picture and bigger pattern underlying a lot of the daily observations we see in life. You've almost certainly noticed that some people are taller and some people are shorter, but it turns out if you measure enough of them, they form this weird hump when graphed out. That's kind of cool right?
Your own performance and ability also follows a bell curve! You'll have good days and bad days as a huge number of random variables affect your performance in a given moment. This is just natural. Professional athletes as such account for their variance in performance by lifting the average of the entire curve up, and reducing the standard deviation value so they perform more consistently! For me personally, I've always struggled with consistent performance under pressure so I really need to get that SD value down.
The bell curve also describes a lot of natural phenomena that affect your life such as your level of talent in different skills. You land randomly somewhere on the curve for all your skills and this