Sampling Distribution of a Positively Skewed Population

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This Demonstration is meant to help students understand how, based on the central limit theorem, the sampling distribution of a skewed population distribution will become normally distributed.

Contributed by: Scott R. Colwell (June 2011)
Open content licensed under CC BY-NC-SA


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A population of the size that is positively skewed is randomly generated when you click the "population" button. You can then change the "sample size", . This sets the size of a single sample that will be drawn from the population. You can then change the number of samples, . This sets the number of samples that will be drawn (of size ) from the population. For example, setting to 10 and to 50 means that you are drawing a sample of 10, 50 times. The mean for each sample is then calculated (e.g. 50 means) and plotted on the histogram, which represents the sampling distribution of the means. As per central limit theorem, as the sample size (the number of means, i.e. the number of samples) increases, the sampling distribution of the means will become more normally distributed even though the population distribution is skewed.



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