How is variance related to standard deviation?

• A. Variance is the square root of standard deviation
• B. Standard deviation is the square of variance
• C. Variance is the average distance from the mean
• D. Standard deviation is the square root of the variance

Answer: (D)

Variance and standard deviation are closely related concepts in statistics that measure the spread of a set of data points around the mean. The correct answer states that standard deviation is the square root of the variance. This relationship holds because variance quantifies how much the individual data points deviate from the mean, and it does so by averaging the squared differences.

In more technical terms, variance is calculated by taking the mean of the squared deviations from the mean, which effectively gives greater weight to larger deviations. However, this can make variance difficult to interpret because its units are the square of the original data units. To express variability in the same units as the original data, standard deviation is used, which is derived by taking the square root of the variance. This operation effectively returns the measurement to the original scale of the data, enabling easier interpretation and comparison.

Thus, understanding that standard deviation is derived from the variance helps clarify how these two metrics function together in describing data dispersion.