Distributions of mean and sum

This diagram can be used to show the theoretical distributions of the mean and sum of a random sample of n values from a normal distribution. It also performs a simulation to demonstrate the formulae for the means and standard deviations.

Firstly drag the slider to show how the theoretical distributions are affected by the sample size. In particular, explain why the three distns are identical if n = 1 and make the point that:

Click Accumulate then take several samples to perform a simulation and state that the empirical distributions conform to the theory.