But what is the Central Limit Theorem?

Summary by Krater

An introduction to the central limit theorem using Galton boards, dice rolls, and probability distributions to explain why sums of random variables tend toward a normal distribution.

From the video

Answers: What is the central limit theorem and why do normal distributions appear everywhere?

• Central limit theorem
• Normal distribution
• Galton board
• Probability distributions
• Convolutions of probability distributions
• Mean and standard deviation
• 68-95-99.7 rule

What it concludes

• The central limit theorem explains why the normal distribution is so common by showing that the sum of multiple independent random variables tends toward a normal distribution as the number of samples increases.
• For the sum of multiple independent and identically distributed random variables, the mean of the sum is the sum of the individual means, and the standard deviation scales with the square root of the number of samples.
• The underlying assumptions of the central limit theorem are that the variables are independent, drawn from the same distribution, and have a finite variance.
• The 68-95-99.7 rule states that approximately 68%, 95%, and 99.7% of values in a normal distribution fall within one, two, and three standard deviations of the mean respectively.