Normal Distributions (AKA Gaussian Distribution)

#Mathematics #Normal Distributions

The Normal Distribution is one of the many powerful concepts I’ve learned in Mathematics. Plenty of things in real life are modelled by a Normal Distribution. Let’s take income distribution as an example.

The majority of middle income lies within the shaded blue region (1 standard deviation away from the mean, the statistical shaded region is approx 68%) , whereas a smaller percentage of the rich and poor lies in the unshaded region. A normal distribution can also model many other things in life, for instance — the height of the population, IQ of the population, etc.

What makes Normal Distribution an even more powerful concept is due to Central Limit Theorem (CLT) — In probability theory, CLT states that the distribution of sample means approximates a normal distribution as the sample size gets larger, regardless of the population's distribution. CLT is a powerful concept that works well together with the Normal Distribution concept. CLT is used in many fields such as finance when analyzing a large collection of securities to estimate portfolio distributions and traits for returns, risk, and correlation.

The key takeaway is to learn how to use concepts and theories you learned and apply them in reality to solve more complex real-life problems.

True mastery is when you can apply things you learned to different fields in life and solve more complex problems.