Which statement about standard deviation is true?

• A. It measures how spread out observations are from the median
• B. It measures how spread out observations are from the mean
• C. It is the same as the range
• D. It indicates the precision of a measurement

Answer: (B)

The key idea here is how standard deviation describes data spread. Standard deviation measures how far each observation tends to lie from the average value, the mean. It quantifies dispersion specifically around the mean, not around the median. If the data cluster tightly around the mean, the standard deviation is small; if they’re spread out, it’s larger. It’s not the same as the range, which only looks at the biggest and smallest values, nor is it simply a direct measure of measurement “precision.” While a smaller standard deviation can indicate more consistent measurements, standard deviation itself is a measure of variability about the mean. Because of that, the statement that standard deviation measures how spread out observations are from the mean is the correct one.