Question

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

Answer 1

The sampling distribution will be less variable than the population distribution because of the following reason:

Consider the Sampling Distribution of Sample Means. For calculating variance of Sampling Distribution of Sample Means, deviations of the sample means will taken from the Population mean. For calculating the variance of the population, deviations of the individual values will be taken from the population. The Sample means do not vary as the values of the population because each sample mean in the average of all the values in the sample whereas population consists of all data values which can take a wide range of values.

Consider population Standard Deviation = = 20

Sample Size = n = 100

SE = Standard Deviation of the Sampling Distribution of Sample Means = /

                                                                                                     = 20/

                                                                                                       = 2

Thus, we note that the sampling distribution is less variable (SE = 2) than the population distribution ( = 20)