The standard deviation is the square root of which measure?

The standard deviation is the square root of which measure?

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

Answer: (B)

The standard deviation measures how far data tend to be from the average, and it does this by taking the square root of the variance. The variance is the average of the squared deviations from the mean, so it’s in squared units and can be hard to interpret. By taking the square root, the standard deviation brings that spread back to the original units of the data, giving a directly interpretable sense of typical distance from the mean. Other measures mentioned don’t describe spread in the same way: the range is just the difference between the largest and smallest values, not tied to deviations from the mean; the median is a central value, not a spread; the mode is the most frequent value, also not a spread measure.

The standard deviation measures how far data tend to be from the average, and it does this by taking the square root of the variance. The variance is the average of the squared deviations from the mean, so it’s in squared units and can be hard to interpret. By taking the square root, the standard deviation brings that spread back to the original units of the data, giving a directly interpretable sense of typical distance from the mean.

Other measures mentioned don’t describe spread in the same way: the range is just the difference between the largest and smallest values, not tied to deviations from the mean; the median is a central value, not a spread; the mode is the most frequent value, also not a spread measure.