What is the difference between the variance and the standard deviation?

What is the difference between the variance and the standard deviation?

• A. Standard deviation is expressed in the original units of measure.
• B. Variance is expressed in the original units of measure.
• C. They are the same quantity.
• D. Standard deviation equals variance.

Answer: (A)

The difference hinges on units and interpretation of spread. Variance is the average of squared deviations from the mean, so its units are the data units squared. Standard deviation is the square root of that variance, which brings the units back to the original data units, making it directly comparable to the data values. They are related by SD = sqrt(variance); they measure the same concept (spread) but in different forms. In practice, standard deviation is usually preferred for interpretation because it mirrors the scale of the data, while variance is often used in calculations and modeling.

The difference hinges on units and interpretation of spread. Variance is the average of squared deviations from the mean, so its units are the data units squared. Standard deviation is the square root of that variance, which brings the units back to the original data units, making it directly comparable to the data values. They are related by SD = sqrt(variance); they measure the same concept (spread) but in different forms. In practice, standard deviation is usually preferred for interpretation because it mirrors the scale of the data, while variance is often used in calculations and modeling.