Question

We know that the standard deviation of a sampling distribution is smaller than that of its parent population. Explain in the space below whythis occurs (do not say it is because the standard deviation is divided by the square root of the sample size – I’m not asking for the formula, but why this formula works).

Answer 1

The Standard Deviation of the Sampling Distribution of means is smaller than the Standard Deviation of the distribution of the population because when the scores are averaged, there are less sample scores to choose in comparison to all the single un-averaged scores, which allows for more variation in the un-averaged scores. The sample means do not vary as much as the individual scores in the population. Population consists of individual outcomes that can take a wide range of values