• PhD Candidate
  • Department of Political Science
  • Social & Behavioral Science Building, 7th floor
  • Stony Brook University
  • Stony Brook NY 11794-4392
  • james.cragun [[ at ]] stonybrook . edu

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 rolls in a sample becomes more similar to the probability distribution of individual rolls as the sample size gets larger (Sheet 1). I also show that the distribution of sample means approximates 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 (Sheet 2).

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