What is the standard error of the mean?

What is the standard error of the mean?

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

Answer: (A)

This is about how precisely a sample mean estimates the population mean. The standard error of the mean is the standard deviation of the sampling distribution of the mean—the typical amount the sample mean would vary from one random sample to another. If the population standard deviation is known, it’s sigma divided by the square root of the sample size; if sigma is unknown, you estimate it with the sample standard deviation and still divide by the square root of n. This measure reflects sampling variability, not the spread of individual values within the population. It’s also different from the standard error of the proportion, which applies to categorical outcomes. The variance of the sampling distribution is the square of this quantity, so the standard error is the square root of that variance.

This is about how precisely a sample mean estimates the population mean. The standard error of the mean is the standard deviation of the sampling distribution of the mean—the typical amount the sample mean would vary from one random sample to another. If the population standard deviation is known, it’s sigma divided by the square root of the sample size; if sigma is unknown, you estimate it with the sample standard deviation and still divide by the square root of n. This measure reflects sampling variability, not the spread of individual values within the population. It’s also different from the standard error of the proportion, which applies to categorical outcomes. The variance of the sampling distribution is the square of this quantity, so the standard error is the square root of that variance.