Discuss why the sampling distribution will be less variable

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

The sampling distribution will be less variable than the population distribution.

Extreme scores occur less frequently in the sampling distribution of the mean, therefore it is less variable than the population.

Example:

Let us consider the Population = (2,4,6,8)

Population mean =20/4=5

Population sd =2.3848

List of 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)

Mean of sample means =5

SD of sample means =1.63

We found that 1.63 < 2.38

There fore the sampling distribution will be less variable than the population distribution.