Question

Consider all samples of size 4 from this population: 6, 8, 10, 12 ,13. What is the mean and standard deviation of the Sampling Distribution?

Answer 1

Now, let us first create the samples of size 4 from the given population and compute the their respective means as

As we know, the formula for computing the mean and standard deviation of a probability distribution is given as

$mean = \mu = \sum \bar{x}P(\bar{x})$

Standard deviation

$\sigma = \sqrt{\sum \bar{x^2}P(\bar{x}) - \mu^2}$

Now, using the above information, we can create the sampling distribution of the sample mean and the compute its mean and standard deviation as

Therefore, the mean and standard deviation can be computed as

$\mu = 9.8 \\ \sigma = \sqrt{96.45 -(9.8)^2} \\ = \sqrt{0.41} \\ = 0.64$

Thus, the mean and standard deviation of the sampling distribution is

$\mu = 9.8 \\ \sigma= 0.64$