The variance of a distribution of means is smaller than the original population variance because
A)it is based on fewer individuals than is the original population.
B)it is an estimate of the sample parameters rather than of the original population.
C)extreme scores are less likely to affect a distribution of means.
D)the mean of a distribution of means is so different than the population mean.

Question

Quizplus · Accepted Answer

When we take samples from a population, extreme scores are less likely to occur, which means that extreme values (whether very high or very low scores) will not be over-represented in the sample data. Consequently, the distribution of sample means will be less variable (or have a smaller variance) than the original population. Therefore, option C is correct. Option A is incorrect because the variance of a distribution of means is actually based on more individuals than is the original population. Option B is incorrect because a distribution of means is an estimate of the population parameters, not of the sample parameters. Option D is incorrect because the difference between the mean of the distribution of means and the population mean does not determine the variance of the distribution of means.

The Variance of a Distribution of Means Is Smaller Than