Which statistic describes the variability of data around the mean?

• A. Mean
• B. Median
• C. Standard deviation
• D. Mode

Answer: (C)

Understanding how spread or variability of data around the average is quantified is the key idea here. The standard deviation measures that spread, telling you, on average, how far observations are from the mean. It’s in the same units as the data, which makes it intuitive to interpret: a small standard deviation means the data sit close to the mean, while a large one indicates they're more spread out. In many distributions, you’ll see the rule that about 68% of values fall within one standard deviation of the mean, about 95% within two, illustrating how the spread relates to the center.

The other measures describe central tendency rather than spread. The mean is the average value, the median is the middle value when data are ordered, and the mode is the most frequent value. While these tell you where the data tend to lie, they don’t describe how variable or dispersed the data are around that center. That’s why standard deviation is the best descriptor of variability around the mean.