Why is the average of the highest value from 100 draws from a normal distribution different from the 98% percentile of the normal distribution? It seems that by definition that they should be the same. But... Code in R: NSIM <- 10000 x <- rep(NA,NSIM) for (i in 1:NSIM) { x[i] <- max(rnorm(100)) } qnorm(.98) qnorm(.99) mean(x) median(x) hist(x) I imagine that I'm misunderstanding something about what the maximum of a 100 draws from the normal distribution should be. As is demonstrated by an unexpectedly asymetrical distribution of maximum values.