Which term describes the spread of the sample means around the population mean?

Which term describes the spread of the sample means around the population mean?

• A. Standard error of the mean
• B. Standard error of the proportion
• C. Standard deviation of the population
• D. Variance of the sampling distribution

Answer: (A)

The spread of the sample means around the population mean is described by the standard error of the mean. This quantity shows how much the mean you get from a sample would vary if you repeated the study many times. It equals the population standard deviation divided by the square root of the sample size (SE = σ/√n). If σ isn’t known, you estimate it with the sample standard deviation (SE ≈ s/√n). This is different from the standard deviation of the population, which measures how individual data points vary around the population mean, and from the standard error of the proportion, which applies to proportions rather than means. The variance of the sampling distribution is the square of the standard error.

The spread of the sample means around the population mean is described by the standard error of the mean. This quantity shows how much the mean you get from a sample would vary if you repeated the study many times. It equals the population standard deviation divided by the square root of the sample size (SE = σ/√n). If σ isn’t known, you estimate it with the sample standard deviation (SE ≈ s/√n). This is different from the standard deviation of the population, which measures how individual data points vary around the population mean, and from the standard error of the proportion, which applies to proportions rather than means. The variance of the sampling distribution is the square of the standard error.