Demonstration of Central Limit Theorem and Law of Large Numbers: Simulated rolls of a die
Excel file (12MB): CLT_die_roll_simulation.xlsx
In this demonstration I use simulated data from rolls of a six-sided die to show that the relative frequency distribution of individual die rolls in a sample of rolls becomes more similar to the probability distribution of individual rolls as the sample size gets larger. I also show that the distribution of sample means is a normal distribution centered on the true mean of the probability distribution and that the distribution of sample means gets narrower as the sample size gets larger.
For another helpful demonstration of the Central Limit Theorem, see Daniel Kunin's website: https://students.brown.edu/seeing-theory/probability-distributions/index.html#section3