The Bell-Shaped Curve: A Common Pattern in Nature…
Following is Maxwell’s Distribution of Velocity Curve, in Kinetic Theory of Gases.
Following is the Wein’s Displacement Law, in Thermal Radiations.
Following is the Distribution of Kinetic Energy of Beta Particles in Radioactive Decays.
Following is the distribution of Intelligence among people in general.
Following is the distribution of Salaries in various countries among people.
Do you notice a pattern here?
All of them are Bell-Shaped curves. All the graphs shown above come from completely different fields of studies and still, they share a similar distribution pattern. Isn’t it strange and amazing? Doesn’t that point to some hidden mysteries of nature?
The bell-shaped curve is a common feature of nature and psychology. In statistics it is called a “Normal Distribution” and it is given a lot of importance in statistics and probabilistic distributions.
What is a Normal Distribution in Statistics?
A normal distribution has a bell-shaped curve and is symmetrical around its center, so the right side of the center is a mirror image of the left side.
Most of the continuous data values in a normal distribution tend to cluster around the mean, and the further a value is from the mean, the less likely it is to occur. The tails are asymptotic, which means that they approach but never quite meet the horizon (i.e. x-axis).
For a perfectly normal distribution the mean, median and mode will be the same value, visually represented by the peak of the curve.
The normal distribution is often called the bell curve because the graph of its probability density looks like a bell. It is also known as called Gaussian distribution, after the German mathematician Carl Gauss who first described it.
Why is the normal distribution important?
The bell-shaped curve is a common feature of nature and psychology
The normal distribution is the most important probability distribution in statistics because many continuous data in nature and psychology displays this bell-shaped curve when compiled and graphed.
For example, if we randomly sampled 100 individuals we would expect to see a normal distribution frequency curve for many continuous variables, such as IQ, height, weight and blood pressure.
Parametric significance tests require a normal distribution of the samples’ data points. The most powerful (parametric) statistical tests used by psychologists require data to be normally distributed. If the data does not resemble a bell curve researchers may have to use a less powerful type of statistical test, called non-parametric statistics.
The normal distribution is so important in statistics that statisticians have written down books and have developed several theorems on just this single idea! One of the epitome of such theorems is Central Limit Theorem, which summarizes the idea discussed so far.
Later, I posted the same question on Physics Stack Exchange too, to receive more knowledge on the subject and yes it resulted positively. Following is the conversation.
Further Readings and explorations.
1. The Normal Distribution: Crash Course Statistics #19
2. What is a Normal Distribution in Statistics?
3. Why is Normal Distribution Bell Shaped?
4. The Normal Distribution and the 68–95–99.7 Rule (5.2)
5. Why do airlines sell too many tickets? — Nina Klietsch
