When the repeated random samples of the given size ‘n’ has been taken from the population of values for the quantitative kind of variable, wherein the population mean is μ (mu) and the standard deviation of the population is σ (sigma), in such scenario, the mean of the sample means (x-bars) is population mean μ (mu).
Furthermore, the sampling distribution helps in representing distribution of points that helps in estimation based on the samples of the fixed size from certain kind of population. It is the most useful aspect as the sampling distribution of the mean is the mean of the entire population from which the different items are being sampled. When the population distribution is normal, in such scenarios, the sampling distribution of the mean is likely to be normal for the samples of the different sizes.
The main properties of the sampling distribution of the mean includes the following aspect which is shown as follows:
The mean is equal to the population mean and it can be showed with the help of the following instance- drawing all the possible samples of size 2 without any kind of replacement from population consisting of 3,6,9,12 and 15.
From the instance, it can be identified that as the sample size increases, the variability of each of the sampling distribution decreases and in such scenarios, the range of the sampling distribution is smaller in nature than the actual range of the original population.
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