Welcome to Normal Distribution for Dummies
Our blog aims to make the concept of normal distribution accessible to all, providing easy-to-understand explanations and practical examples.
What is Normal Distribution Exactly?
When talking about “Normal Distribution”, you may think it is a complex statistical concept that is studied by statisticians everyday. However, it is much simpler than what you may expect it to be. Here we are going to reveal its myth, introducing its discovery, mechanism, and how it affects our everyday life. We will start by discovering how mathematicians discovered this interesting distribution=).
History Time!
In the 18th century, a French mathematician named Abraham de Moivre was studying a gambling problem. In a single experiment, he tossed a coin for 2, 4, 12 times, and repeated the experiments many times. In the end, he found out the number of faces in each experiment are mainly 1, 2, 6 times, and the distribution will look like a bell. Moivre realized he could simulate the probability of the number of faces when tossing a coin for 100 times, without actually tossing a coin 100 times. (7.2: History of the Normal Distribution - Statistics LibreTexts).
Normal? Gaussian!
Later in the 19th century, a German mathematician Carl Friedrich Gauss, known as the “prince of mathematics”, worked out the equation of this distribution and used it to analyze astronomical data. (978-0-387-46409-1_7.pdf)Due to Gauss's significant contribution to Normal Distribution, the distribution is also named as the Gaussian Distribution. Meanwhile, French mathematician Pierre-Simon Laplace discovered the Central Limit Theorem, which furtherly proves why the most data is concentrated at the mean.(Central limit theorem | Probability, Distribution & Statistics | Britannica).
Image:Carl Friedrich Gauss | Biography, Discoveries, & Facts | Britannica
How About Some Examples?
An Example of HUMAN IQ
This is the distribution of HUMAN IQ in the whole population. You can see that the data is centred at around 75 to 125, and reaches its peak at 100. This sketch is a uniform bell-shaped graph, as you may have discovered. Indeed, this is a standard illustration of a Normal Distribution.
Image:
The central idea of Normal Distribution is that it assumes the probability of a natural event is most likely to occur at its mean, and the probability will decrease when the event tends to the highest extreme and the lowest extreme. You may find it fascinating as it perfectly explains why the distribution of human IQ looks like that. As human IQ is randomly distributed in nature, its distribution will be normal. This clearly shows that the majority of the people have IQ of the interval of 75 to 125. Frequency gets less when the IQ tends to the lower end or the higher end. Since it takes extraordinary talent to achieve an IQ above 125, this also explains why geniuses are uncommon.
A Counter Example of Income
In 1976, a British statistician named George Box wrote the famous line, “All models are wrong, some are useful.”
That means Normal Distribution cannot explain everything in this world. For instance, if you look at the curve of income distribution, the median is not located in the middle of the horizontal axis, and the majority is concentrated at the left side of the graph. Since the income is not a natural event, it is unlikely to be normally distributed.
Normal Distribution is All Over the Place
Other than these serious topics, there are some fun facts related to Normal Distribution. If you have ever played with the Galton Board, you will find out it demonstrates how random events cumulate to form the Normal Distribution.
Also, if you ever have a chance to see the distribution of one of your test results in your class, you may notice that most students are distributed around the class average, and there are a few students with very high or very low marks. The same distribution applies for human heights, stock market, insurance expectation and so on.
To Conclude:
It seems surprising that all these random and varied events share the same property, but nothing is indeed a coincidence.
With mathematics, we reveal the core of nature, and discover the beauty of the world. Thank you for reading.
About us
Normal Distribution for Dummies is a platform dedicated to simplifying statistics concepts for beginners and enthusiasts alike. Our team of experts is committed to breaking down complex topics into digestible pieces, helping our readers gain a solid understanding of the subject.
--Ellison & Rock
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