What is the square root of variance; the average distance from the mean?

What is the square root of variance; the average distance from the mean?

• A. Standard Deviation
• B. Range
• C. Variability
• D. Deviation

Answer: (A)

The square root of variance is standard deviation. Variance averages the squared deviations from the mean, which tells you how spread out the data are but in squared units. Taking the square root brings that measure back to the original data units, giving a sense of the typical distance from the mean. This standard deviation is a concise, widely used description of how spread out observations tend to be around the mean. The range, by contrast, doesn’t reflect an average distance from the mean—it’s just the difference between the largest and smallest values and can be unduly influenced by outliers. Deviation usually refers to a single observation’s difference from the mean, not the overall spread. Variability is a general term for how spread out the data are but doesn’t specify the exact relationship to variance and units.

The square root of variance is standard deviation. Variance averages the squared deviations from the mean, which tells you how spread out the data are but in squared units. Taking the square root brings that measure back to the original data units, giving a sense of the typical distance from the mean. This standard deviation is a concise, widely used description of how spread out observations tend to be around the mean.

The range, by contrast, doesn’t reflect an average distance from the mean—it’s just the difference between the largest and smallest values and can be unduly influenced by outliers. Deviation usually refers to a single observation’s difference from the mean, not the overall spread. Variability is a general term for how spread out the data are but doesn’t specify the exact relationship to variance and units.