Curiosities · Foundation · 9 min
The central limit theorem
Averages of independent observations concentrate and become approximately bell-shaped under the Central Limit Theorem.
WHAT HAPPENS IF…If n is quadrupled, what happens to standard error?
Loading the mathematical model…
Here each observation is Bernoulli(p), so n times the mean has an exact binomial distribution. The blue bars remain discrete at finite n. For independent identically distributed variables with finite positive variance, standardized means converge in distribution to normal. Approximation quality depends on n and p, not one universal sample-size cutoff.
A detail that matters
n is observations in each average, not the number of repeated averages in a simulation.
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