Which term describes the standard deviation of the sampling distribution of the mean?

Which term describes the standard deviation of the sampling distribution of the mean?

• A. Standard Error of the Mean
• B. Standard Deviation of the Population
• C. Margin of Error
• D. Standard Deviation of the Sample

Answer: (A)

The idea here is that the spread of the sampling distribution of the mean is captured by the standard error of the mean. When we take many samples of size n from a population, the means of those samples form their own distribution, and the standard deviation of that distribution tells us how much those sample means tend to vary from one another. That quantity is the standard error of the mean. It is calculated as SE = σ/√n (or s/√n as an estimate when the population standard deviation is unknown). This value shrinks as the sample size grows, reflecting increasing precision in our estimate of the population mean. For contrast, the standard deviation of the population measures how spread out individual observations are, not how much sample means vary across samples; the margin of error uses the standard error to describe the range around a sample mean in a confidence interval; and the standard deviation of the sample describes variability within a single sample.

The idea here is that the spread of the sampling distribution of the mean is captured by the standard error of the mean. When we take many samples of size n from a population, the means of those samples form their own distribution, and the standard deviation of that distribution tells us how much those sample means tend to vary from one another. That quantity is the standard error of the mean. It is calculated as SE = σ/√n (or s/√n as an estimate when the population standard deviation is unknown). This value shrinks as the sample size grows, reflecting increasing precision in our estimate of the population mean. For contrast, the standard deviation of the population measures how spread out individual observations are, not how much sample means vary across samples; the margin of error uses the standard error to describe the range around a sample mean in a confidence interval; and the standard deviation of the sample describes variability within a single sample.