An estimate of the typical difference between the sample mean and the population mean

An estimate of the typical difference between the sample mean and the population mean

• A. Standard deviation
• B. Standard error
• C. Variance
• D. Mean

Answer: (B)

The standard error of the mean is the measure that captures how close the sample mean is likely to be to the population mean across repeated samples. It represents the typical distance between the sample mean and the true population mean because it reflects the precision of the mean as an estimator. The standard error is the standard deviation of the sampling distribution of the mean (often estimated by the sample standard deviation divided by the square root of the sample size). As sample size grows, the standard error shrinks, meaning the sample mean becomes a more precise estimate of the population mean. The standard deviation describes how spread out individual observations are within a single sample, not how far the sample mean sits from the population mean. The variance is just the square of the standard deviation, giving a similar idea of spread but in squared units. The mean is the central value itself, not a measure of how variable an estimate is across samples.

The standard error of the mean is the measure that captures how close the sample mean is likely to be to the population mean across repeated samples. It represents the typical distance between the sample mean and the true population mean because it reflects the precision of the mean as an estimator. The standard error is the standard deviation of the sampling distribution of the mean (often estimated by the sample standard deviation divided by the square root of the sample size). As sample size grows, the standard error shrinks, meaning the sample mean becomes a more precise estimate of the population mean.

The standard deviation describes how spread out individual observations are within a single sample, not how far the sample mean sits from the population mean. The variance is just the square of the standard deviation, giving a similar idea of spread but in squared units. The mean is the central value itself, not a measure of how variable an estimate is across samples.