Which statement correctly distinguishes standard deviation and the standard error of the mean?

• A. SD measures variability of population data.
• B. SEM measures variability of the individual observations.
• C. SD measures variability of individual observations in a sample; SEM estimates variability of the sample mean across samples.
• D. SD and SEM measure the same thing.

Answer: (C)

The main idea is understanding what each statistic describes about variability. Standard deviation reflects how spread out the individual observations are around the mean—the typical distance a single data point is from the center of the distribution.

The standard error of the mean, on the other hand, reflects how precisely the sample mean estimates the population mean. It is the standard deviation of the sampling distribution of the mean—how much the mean would vary across many repeated samples of the same size. Because it depends on how many observations you have, it gets smaller as the sample size grows (roughly SEM = SD divided by the square root of n).

So, standard deviation measures variability of individual observations; the standard error of the mean estimates how variable the sample mean would be across different samples. That’s why the statement correctly links SD to the spread of individual data and SEM to the variability of the sample mean across samples.