# Is there a relation between sample size and variable range?

I have done simulations with different sample sizes of a normal distribution (mean=0, sd=10) and plotted the number of samples against statistical parameters. I understand that the relation of sample size and mean, sd and the relative frequency of samples ouside of 2*sd is due to the law of great numbers. (Variance reduces with sample size). I do not understand the relation of sample size and variable range. Is there an intuitive explanation for this relation?

• By "range", do you literally mean the maximum value in your sample - the min? Also, it may be of interest to some readers if you posted your code. – gung Aug 17 '16 at 15:41
• See some of the discussion here, including a plot showing the asymptotic growth in mean range like $\sqrt{\log n}$ – Glen_b Aug 18 '16 at 3:51