Which statement defines standard deviation?

Which statement defines standard deviation?

• A. Range
• B. Median
• C. Sum of squared deviations
• D. Average distance from the mean

Answer: (D)

Standard deviation measures how spread out a data set is by averaging how far each data point lies from the mean. It’s found by taking the square root of the variance, and the variance itself is the mean of the squared deviations from the mean. That combination describes the typical distance from the mean in the same units as the data, which is why the statement “average distance from the mean” best captures what standard deviation represents. Other options describe different ideas: range only notes the overall spread as max minus min, not the average distance from the mean; median is just the middle value and says nothing about spread; sum of squared deviations is part of the calculation to get variance, but the standard deviation uses the average of those squared deviations and then takes the square root, not the sum alone.

Standard deviation measures how spread out a data set is by averaging how far each data point lies from the mean. It’s found by taking the square root of the variance, and the variance itself is the mean of the squared deviations from the mean. That combination describes the typical distance from the mean in the same units as the data, which is why the statement “average distance from the mean” best captures what standard deviation represents.

Other options describe different ideas: range only notes the overall spread as max minus min, not the average distance from the mean; median is just the middle value and says nothing about spread; sum of squared deviations is part of the calculation to get variance, but the standard deviation uses the average of those squared deviations and then takes the square root, not the sum alone.