Which measure describes the precision of a statistic by describing the spread of its sampling distribution?

Which measure describes the precision of a statistic by describing the spread of its sampling distribution?

• A. Standard error
• B. Standard deviation
• C. Confidence interval
• D. Margin of error

Answer: (A)

The key idea is how much an estimator would vary if you repeated the study many times. The standard error measures that variation—the standard deviation of the sampling distribution of a statistic (like the mean). It tells you how precise your estimate is: a smaller standard error means the statistic is expected to be closer to the true population value across repeated samples. The standard deviation describes how spread out the individual observed data are within a single sample, not how the estimator would vary across samples. A confidence interval uses the standard error to define a range of plausible values for the population parameter, and the margin of error is the half-width of that interval. So the measure that directly describes the spread of the sampling distribution and thus the precision of the estimator is the standard error.

The key idea is how much an estimator would vary if you repeated the study many times. The standard error measures that variation—the standard deviation of the sampling distribution of a statistic (like the mean). It tells you how precise your estimate is: a smaller standard error means the statistic is expected to be closer to the true population value across repeated samples. The standard deviation describes how spread out the individual observed data are within a single sample, not how the estimator would vary across samples. A confidence interval uses the standard error to define a range of plausible values for the population parameter, and the margin of error is the half-width of that interval. So the measure that directly describes the spread of the sampling distribution and thus the precision of the estimator is the standard error.