What is the standard deviation of the sampling distribution of the sample mean called?

What is the standard deviation of the sampling distribution of the sample mean called?

• A. Standard Deviation
• B. Mean Absolute Deviation
• C. Standard Error of the Mean
• D. Variance

Answer: (C)

The standard deviation of the sampling distribution of the sample mean is called the standard error of the mean. This quantity shows how much the sample mean would fluctuate if you repeated the sampling many times from the same population. If the population standard deviation is known, the standard error equals sigma divided by the square root of the sample size (sigma / sqrt(n)); if sigma is unknown, you estimate it with the sample standard deviation and use s / sqrt(n). This measures how precisely the sample mean estimates the population mean—the bigger the sample, the smaller the standard error, and the more exact the estimate. It’s different from the standard deviation of individual observations (which describes spread within one sample) and from variance (which is the square of a standard deviation).

The standard deviation of the sampling distribution of the sample mean is called the standard error of the mean. This quantity shows how much the sample mean would fluctuate if you repeated the sampling many times from the same population. If the population standard deviation is known, the standard error equals sigma divided by the square root of the sample size (sigma / sqrt(n)); if sigma is unknown, you estimate it with the sample standard deviation and use s / sqrt(n). This measures how precisely the sample mean estimates the population mean—the bigger the sample, the smaller the standard error, and the more exact the estimate. It’s different from the standard deviation of individual observations (which describes spread within one sample) and from variance (which is the square of a standard deviation).