Using R to illustrate the Central Limit Theorem

Interesting thread. The graphics are great, the only thing that might be
worth doing for teaching purposes would be to illustrate the original
distribution that is being averaged 1000 times.

Below is one option based on Bill Venables code.  Note that to do this I
had to start with a k of 2.

N <- 10000
for(k in 2:20) {
   graphics.off()
   par(mfrow = c(2,2), pty = "s")
   hist(((runif(k))-0.5)*sqrt(12*k),main="Example Distribution 1")
   hist(((runif(k))-0.5)*sqrt(12*k),main="Example Distribution 2")
   m <- replicate(N, (mean(runif(k))-0.5)*sqrt(12*k))
   hist(m, breaks = "FD", xlim = c(-4,4), main = k,
           prob = TRUE, ylim = c(0,0.5), col = "lemonchiffon")
   pu <- par("usr")[1:2]
   x <- seq(pu[1], pu[2], len = 500)
   lines(x, dnorm(x), col = "red")
   qqnorm(m, ylim = c(-4,4), xlim = c(-4,4), pch = ".", col = "blue")
   abline(0, 1, col = "red")
   Sys.sleep(3)
 }

By the way, I should probably know this but what is the logic of the
"sqrt(12*k)" part of the example?  Obviously as k increases the mean
will approach .5 in a uniform distribution, so runif(k)-.5 will be close
to zero, and sqrt(12*k) increases as k increases.  Why 12, though?

PB