Let’s start small and draw 6 samples randomly from the uniform population presented on the previous page. Each sample has only 5 subjects (N=5). The central limit theorem requires that all samples must have the same sample size. The distribution of scores in each of these samples is presented below.  

Once we have drawn each of these samples, we will calculate the mean of each set of scores. The red blocks on the distributions represent the raw data; the blue blocks on the distribution of sample scores indicate the means of the samples.  Finally, we will plot the distribution of the sample means calculated on each sample drawn from the population.

What does this demonstration show us about the values of sample means (blue squares) and the shape of the sampling distribution?

As we increase the number of samples taken from the population, the distribution of sample means should become "smoother" and should more closely resemble a normal distribution.