The standard error of the mean is given by which formula?

• A. SE = s
• B. SE = s^2
• C. SE = s / sqrt(n)
• D. SE = sqrt(n) / s

Answer: (C)

The standard error of the mean shows how precisely a sample mean estimates the population mean. It is found by taking the variability of individual scores (the sample standard deviation) and dividing it by the square root of the sample size: SE = s / sqrt(n). As the sample size grows, this value shrinks, meaning the sample mean becomes a more reliable estimate of the population mean.

Why this form fits: s alone describes spread of single observations, not of the distribution of means. s^2 is the variance, not the standard error. sqrt(n)/s would imply a relationship that isn’t correct for the standard error and would increase with n, which is opposite of how SE behaves.