Which statistic is used to describe the variability of the data around the mean?

Which statistic is used to describe the variability of the data around the mean?

• A. Mean
• B. Median
• C. Mode
• D. Variance

Answer: (D)

Describing how spread the data are around the average is captured by variance. Variance measures the average squared distance of each value from the mean, so it grows as data points move further from the center. This use of squared deviations ensures all differences contribute positively and highlights larger gaps in the data. While standard deviation serves a similar purpose and is easier to interpret because it’s in the same units as the data, it is the square root of variance. The mean, median, and mode describe where the data tend to cluster, not how spread out they are, so they describe central tendency rather than variability.

Describing how spread the data are around the average is captured by variance. Variance measures the average squared distance of each value from the mean, so it grows as data points move further from the center. This use of squared deviations ensures all differences contribute positively and highlights larger gaps in the data. While standard deviation serves a similar purpose and is easier to interpret because it’s in the same units as the data, it is the square root of variance. The mean, median, and mode describe where the data tend to cluster, not how spread out they are, so they describe central tendency rather than variability.