Which statistic describes the average distance of data values from the mean?

Which statistic describes the average distance of data values from the mean?

• A. Standard Deviation
• B. Variance
• C. Range
• D. Skewness

Answer: (A)

The concept being tested is how we measure how spread out data are around the average value. The standard deviation is the best descriptor of the average distance of data values from the mean because it quantifies how far observations typically lie from the mean in the same units as the data. It does this by taking each deviation from the mean, squaring them to avoid cancellation, averaging those squared deviations, and then taking the square root to return to the original units. The result is a single number that reflects the typical or average distance from the mean: larger values mean more spread, smaller values mean tighter clustering around the mean. Variance also uses deviations from the mean but is in squared units, so it’s harder to interpret in the original units. The range simply measures the gap between the highest and lowest values and tells you about span, not the typical distance from the mean. Skewness describes asymmetry of the distribution, not dispersion around the mean.

The concept being tested is how we measure how spread out data are around the average value. The standard deviation is the best descriptor of the average distance of data values from the mean because it quantifies how far observations typically lie from the mean in the same units as the data. It does this by taking each deviation from the mean, squaring them to avoid cancellation, averaging those squared deviations, and then taking the square root to return to the original units. The result is a single number that reflects the typical or average distance from the mean: larger values mean more spread, smaller values mean tighter clustering around the mean. Variance also uses deviations from the mean but is in squared units, so it’s harder to interpret in the original units. The range simply measures the gap between the highest and lowest values and tells you about span, not the typical distance from the mean. Skewness describes asymmetry of the distribution, not dispersion around the mean.