# Consider a population consisting of five values - 1, 2, 2, 4, and 8. Find the population mean and variation. Calculate the sampling distribution of the mean of a sample of size 2 by generating all possible such samples. From them, find the mean and variance of the sampling distribution. How is the variance of the sampling distribution different from that of the population variation?

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Consider a population consisting of five values - 1, 2, 2, 4, and 8. Find the population mean and variation. Calculate the sampling distribution of the mean of a sample of size 2 by generating all possible such samples. From them, find the mean and variance of the sampling distribution. How is the variance of the sampling distribution different from that of the population variation?

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Step 1

Assume that the population size as 5 with the values of 1, 2, 2, 4, 8.

Population mean: X-bar=∑Xi/N where i= 1, 2, …5.

Population variance: σ2=∑(X-X-bar)2/N.

The population mean is:

Step 2

The population variance is,

Step 3

The different sample of size 2 is given below:

Here, the required sample size is n=2. Therefore, 5C2 = 10 samples are possible and are listed as follows:

(1,2), (1,2), (1,4), (1,8), (2,2), (2,4), (2,8),...

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