What is the measure of variability for a distribution of sample means?

• A. Margin of error
• B. Standard deviation
• C. Standard error
• D. Variance

Answer: (C)

When you examine how much the means from different samples vary from one another, you’re looking at the spread of the sampling distribution of the mean. That dispersion is captured by the standard error of the mean. The standard error is the standard deviation of the sampling distribution of the mean; it equals the population standard deviation divided by the square root of the sample size (or the sample standard deviation divided by sqrt(n) as an estimate). As sample size increases, the standard error decreases, so the sample means cluster more tightly around the true population mean. Margin of error is tied to confidence intervals and is derived from the standard error, but it is not itself the dispersion of the sampling distribution. The standard deviation (and its square, variance) describe variability of individual observations within a single sample, not the variability of sample means across samples.