Discuss why the sampling distribution will be less variable than the population distribution.

Discuss why the sampling distribution will be less variable than the population distribution. Give a short example to illustrate your answer.

Sampling distribution is less variable than population distribution, and I will show this using an example. If we have a population (2,4,6,8) its mean will be 5.

The sampling distribution is 2.38.

All samples (2,2),(2,4),(2,6),(2,8),(4,2),(4,4),(4,6),(4,8),(6,2),(6,4),(6,6),(6,8),(8,2),(8,4),(8,6),(8,8)

Sample means (2,3,4,5,3,4,5,6,4,5,6,7,5,6,7,8) and their mean is 5.

The sample distribution is 1.63, so we see that the sample distribution is less than population distribution.