Which statistic is the square root of the variance?

Which statistic is the square root of the variance?

• A. Range
• B. Coefficient of Variation (CV)
• C. Standard Deviation (SD)
• D. Mean

Answer: (C)

The square root of the variance is the standard deviation, a primary way to describe how spread out the data are around the mean. Variance averages the squared deviations from the mean, which makes it hard to interpret directly because the units are squared. Taking the square root brings it back to the original units, giving a sense of, on average, how far observations lie from the mean. This makes standard deviation a natural and widely used measure of dispersion, including in quality control for setting rules like control limits. The other statistics describe different ideas: range is just max minus min and doesn’t reflect how data cluster around the mean; the coefficient of variation is the standard deviation divided by the mean, a relative measure of spread; and the mean is a measure of central tendency, not spread.

The square root of the variance is the standard deviation, a primary way to describe how spread out the data are around the mean. Variance averages the squared deviations from the mean, which makes it hard to interpret directly because the units are squared. Taking the square root brings it back to the original units, giving a sense of, on average, how far observations lie from the mean. This makes standard deviation a natural and widely used measure of dispersion, including in quality control for setting rules like control limits. The other statistics describe different ideas: range is just max minus min and doesn’t reflect how data cluster around the mean; the coefficient of variation is the standard deviation divided by the mean, a relative measure of spread; and the mean is a measure of central tendency, not spread.