The standard deviation is a more intuitive measure of spread because it is expressed in the _____ units as the random variable X, whereas the variance is expressed in ______ units.

The standard deviation is a more intuitive measure of spread because it is expressed in the _____ units as the random variable X, whereas the variance is expressed in ______ units.

• A. same, squared
• B. different, squared
• C. same, linear
• D. different, linear

Answer: (A)

Spread measures tied to the data scale: variance averages squared deviations, so its units are the original units squared. The standard deviation is the square root of the variance, returning to the original scale, so it shares the same units as the data. For instance, if X is measured in dollars, the standard deviation is in dollars, while the variance is in dollars squared. This makes the standard deviation easier to interpret as a typical deviation from the mean. The other options would imply the standard deviation has a different unit from the data or that the variance is in linear units, which doesn’t align with how variance is defined.

Spread measures tied to the data scale: variance averages squared deviations, so its units are the original units squared. The standard deviation is the square root of the variance, returning to the original scale, so it shares the same units as the data. For instance, if X is measured in dollars, the standard deviation is in dollars, while the variance is in dollars squared. This makes the standard deviation easier to interpret as a typical deviation from the mean. The other options would imply the standard deviation has a different unit from the data or that the variance is in linear units, which doesn’t align with how variance is defined.