# Central Limit Theorem

January 20th, 2024 (9 months ago) • 2 minutes

Normal Distribution Curve

The distribution of sample means approximates a normal distribution as the sample size gets larger, regardless of the population's distribution.

In plain words, it says that if we take a sample from a population (any population) and calculate the mean of that sample, we will get a normal distribution (also called a bell curve). And if we take a larger sample, then the curve will approximately more closely.

This idea is important because it explain why a lot of life phenomenon is normally distributed. For example, the height of people, the weight of people, the IQ of people, the income of people, etc.

It's highly unlikely that some random event happening will be close to either extreme. For example, you are more likely to row any number in the middle rather than 2 or 12 in a dice roll because there are just more combination of them. Similarly, you are more likely to be of average height than extremely tall or short because there are just more people of average height.

I rereading this concept as I am preparing for USF's grad school interview. Fingers crossed 🤞.