Initial Thoughts on Bell Curves.
Bell curves show the distribution of any specific attribute across a sample.
For instance, there can be the distribution of height across the population of a country.
The reason why bell curves are called bell curves is because when we measure the distribution of many attributes, they tend to take a bell curves shape. Crazy, huh?
There are all sorts of bell curves. Some are very symmetrical, while others can be quite skewed.
The height example I gave earlier would likely be a fairly symmetrical bell curve since most people are of average height.
However, if we were to measure the distribution of wealth across a population, that would likely be a very skewed bell curve, with a small number of people having most of the wealth.
Bell curves can be useful when trying to understand how common or rare something is.
For instance, if we want to know what percentage of people in a population are taller than 6 feet, we can look at the bell curve for height and find out.
Similarly, if we want to know what percentage of people in a population are wealthy, we can look at the bell curve for wealth and find out.
There are all sorts of applications for bell curves, and they can be a useful tool for understanding data.
However, it’s important to remember that bell curves are just one way of looking at data, and they don’t necessarily tell the whole story.
For instance, a bell curve might show that most people in a population are of average height, but it doesn’t tell us anything about how those people feel about their height.
So while bell curves can be helpful, we should always be careful not to put too much emphasis on them as a standalone tool.
What is interesting is that not everything that we measure fits into a bell curve shape, but sometimes if we take things far enough, it turns out that some things do.
One example of this is with IQ scores.
While the distribution of IQ scores doesn’t always look like a bell curve, if we take enough people, it eventually does.
This is because IQ is actually a pretty normal distribution.
So while not everything fits into a bell curve, many things do, and it’s something that’s worth keeping in mind.
Let me give you quite an interesting example.
I had a perplexing question in one of my interviews for the entrance exam at a prestigious London school. I was asked how many grains of sand it takes to create a mountain and at what point a pile of grains of sand becomes a mountain.
I didn’t have an answer, but still managed to get a scholarship 😉
Twenty years later, I think I may have finally got it.
But, let’s take a step back and get a few definitions.
Oxford dictionary defines a mountain as:
A large natural elevation of the earth’s surface rising abruptly from the surrounding level; a large steep hill.
National Geographic goes further:
Mountains usually have steep, sloping sides and sharp or rounded ridges, and a high point, called a peak or summit. Most geologists classify a mountain as a landform that rises at least 1,000 feet (300 meters) or more above its surrounding area.
My insight with this question, and how it relates to bell curves, is that people’s opinions of how many grains of sand it takes to create a mountain also fall into a distribution curve.
On an initial overview, we may actually think this is not a bell curve but a graph that goes up very quickly and then eventually flattens out as at a large enough pile of sand, almost everyone will believe that the pile is mountain-sized.
So, at the start, with just a few grains of sand, essentially no one will claim that this is a mountain, with the exception of people who are mentally ill or purposefully lying, so it won’t be quite zero.
Then, as we keep adding grains of sand, eventually, we will get to a point where 10% of people look at the pile and call that a mountain. At some point, we get closer and closer to 100% (again, with those few exceptions). For simplicity’s sake, we will ignore the shape of the pile of grains, we can assume that we are always piling them up in a mountain-shaped form.
And so, we can probably say that the point in the curve where more than 80% or 90% of people think that the pile of grains of sand makes a mountain is, in fact, what makes a mountain.
But, things don’t end here.
What happens if we keep piling up sand?
If we get to this stage, most people would probably claim that this pile of sand is not a mountain but actually something else, like a desert or even a small planet. And if we were to grow this number a thousandfold, then this would for sure be the case.
So actually, the distribution of opinion on how many grains of sand it takes to create a mountain is a bell curve, but in our initial example, we were just not scaling things up enough.
