Susanne Tak

Sampling distribution simulation

In statistics, you often need to estimate parameters of the population based on statistics of the sample. But are these sample statistics good estimators of the population parameters? For example, if you find that you sample mean is 50, can you conclude that your population mean is 50 as well?

Using the simulation on this page, you can examine this question. In particular, you examine the case where you know the population mean and standard deviation, and explore what values you can expect to find for the mean and the standard deviation of a sample from this population. If the population mean is 100, would you expect the mean of sample to always be (exactly) 100 as well? If not, how far off from the population mean can you expect to be?

First, let's define some variables for our simulation: the population mean is 100, and the population standard deviation is 30. For now, let's keep the distribution set to 'normal'. The sample size is 10. In the charts below, the population is shown in the top left chart.
Open the simulation in a new window if the charts below don't fit on your screen.
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Click the 'take sample' button to take a sample from the population. You can see the sample in the top right chart, including the mean and standard deviation of the sample. Is the sample mean equal to the population mean? And what about the standard deviation?

Note that what you have done now is what would typically be the case 'in real life': you take a sample only once and have to use this sample to estimate the population parameters. However, as this is a simulation you can take another sample (click the 'take sample' button again) and see another possible outcome of the sampling. The bottom two charts will now track all the samples' means and standard deviations. The top right chart will show the information about the last sample. Take a sample a couple more times, or use the 'take 100 samples' button if you're bored with clicking a button very often.