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From Population Distribution to Sampling Distribution (Simulation)

Sampling distribution is an important concept in statistics. We rely on sampling distributions (e.g., sample mean and sample proportion) to make decisions about whether to accept or to reject the hypotheses about the population properties.

Students usually have tough time understanding the concept due to its highly theoretical nature. The attached Excel spreadsheet can help visualize the process of obtaining a sampling distribution of population mean. Specifically, it allows you to specify a sample size n and the number of sample groups of k. Thus, you will have k number of sample averages can be used to construct a distribution. This Excel applet allows the process of obtaining the sampling distribution more visible.

Note:

  • Original file has a population of 10,000 observations that follow a normal distribution with mu = 500 and sigma = 50. If you wish to demonstrate the law of large numbers, you can replace the population data with your own.
  • When you specify a very big k, for example 400, Excel will freeze for a moment to process the request. Please monitor your CPU usage.
  • My website does not allow me to upload Macro enabled Excel file as/is. That is reason why you are seeing a zip file.
  • When use in Windows 10, please enable Macro, Data Analysis ToolPak, and Data Analysis ToolPak – VBA. Otherwise, it will report a run time error.
  • For Mac, please see this link. Essentially you need to enable the developer ribbon.

(Note: Written in Excel VBA)

I have another similar worked example in R here.

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