The sampling distributions for the sample mean and the sample standard deviation are explored for a finite population as well as several infinite populations normal uniform Laplace gamma All distributions are chosen to have the same mean and standard deviation as the finite population The finite population consists of the marks of 256 students on a midterm test The population distribution is shown in the top plot The bottom plot shows normal approximation to the sampling distribution exact for the sample mean if the population is also normal and its empirical estimate using the histogram These histograms are available sample sizes and for 1000 5000 and 10000 samples at a time From the central limit theorem the sampling distribution of the sample mean is approximated by for infinite populations In the finite population case the standard deviation is reduced slightly due to the finitesample correction factor see the Details section The sampling distribution for the sample standard deviation is more complicated but as increases it is also approximated by a normal distribution However in this case we need to use simulation to estimate the parameters in the approximating normal sampling distribution In all cases as increases the sampling distribution becomes more concentrated about the true parameter and the normal distribution approximation improves It is interesting that in the case of the mean all sampling distributions converge to the same distribution as expected by the central limit theorem But the sampling distribution for the standard deviation is very complex analytically for nonnormal populations Our computer experiments illustrate that it is approximately normal Notice these distributions although all approximately normal depend on the population distribution The sensitivity of the results to random variation may be explored by varying the random seed