 # Sampling Distribution

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Definition

The distribution of a sample statistic obtained by taking a large number of Random Samples of the same size from the specified population. It lists all possible values of the statistic and their corresponding probabilities for a given sample size.

Examples 1000 samples of size 25 are drawn from a process and the sample means calculated. The histogram alongside shows the population distribution of the individual values. The histogram below shows the frequency distribution of the means from the 1000 samples. This is the sampling distribution of the sample means. Because they’re means, they ‘average out’ the values across all the samples, which results in a smaller variance overall. The standard error (standard deviation) of the sample means is given by the standard deviation of the individual values divided by the square-root of the sample size.

Application

According to the Central Limit Theorem, as the sample size increases, the sampling distribution of the sample mean is closely approximated by the normal distribution irrespective of the shape of the original population from which the samples were drawn.