Answer and Step-by-step explanation:
Sampling distribution of an average is described as follows.
The student takes the sample of 100 units and observes the average to be 4.80.
But if another sample of 100 units is now taken then the average may not be 4.80.
Yet again if another sample of 100 units be taken the again average might be something else than previous obtained sample averages.
This way we can say that sample average is also varying for different samples. Thus Sample average can also be regarded as a random variable. The distribution of such is called sampling distribution of an average.
Mathematically, let total no of units in the population be N.
a sample of size n can be taken out in NCn ways. Then distribution of averages of all NCn samples give rise to sampling distributuion of average.
It can be shown further that the mean of the sample averages is equal to the population mean and the Variance of the sample averages is equal to the Population variance divided by the sample size.