The central limit theorem gives a fundamental result for sampling - that large samples, or any samples from a Normally distributed population, are Normally distributed. Test this result to see that it really works. For this you can:
· use a spreadsheet to generate a population of random numbers
· draw a frequency distribution of the numbers and confirm that they follow a uniform distribution (where each number has the same probability)
· take large samples from this population of numbers and calculate the mean of each sample
· draw a frequency distribution of these means (i.e. the sampling distribution of the mean)
· confirm that the result is Normally distributed.
Now repeat this process for different sample sizes and initial distributions of values to see what effect this has.