Which statistic describes the typical dispersion of data around the mean?

Which statistic describes the typical dispersion of data around the mean?

• A. Population variance
• B. Sample value
• C. Property value
• D. Standard deviation

Answer: (D)

Describing how data spread around the mean is about a measure of dispersion. The standard deviation is the statistic that captures the typical distance of data points from the mean, and it does so in the same units as the data, making it easy to interpret. It’s calculated as the square root of the average squared deviations from the mean, which directly ties to how far values tend to deviate on average. Variance also measures spread, but because it uses squared units, it’s less intuitive when you want a “typical” deviation in the original scale. The other options aren’t standard ways to describe dispersion around the mean. In a normal distribution, about 68% of values lie within one standard deviation of the mean, illustrating why this measure is so practical for describing typical dispersion.

Describing how data spread around the mean is about a measure of dispersion. The standard deviation is the statistic that captures the typical distance of data points from the mean, and it does so in the same units as the data, making it easy to interpret. It’s calculated as the square root of the average squared deviations from the mean, which directly ties to how far values tend to deviate on average. Variance also measures spread, but because it uses squared units, it’s less intuitive when you want a “typical” deviation in the original scale. The other options aren’t standard ways to describe dispersion around the mean. In a normal distribution, about 68% of values lie within one standard deviation of the mean, illustrating why this measure is so practical for describing typical dispersion.