American Institute of Certified Planners (AICP) Practice Exam

What does the standard deviation represent in relation to variance?

1. It is one half of the variance.

2. It is the square root of the variance.

3. It is the average of the variance.

4. It is unrelated to variance.

The correct answer is: It is the square root of the variance.

The standard deviation is a statistical measure that quantifies the amount of variation or dispersion in a set of values. Specifically, it is defined as the square root of the variance. Variance itself measures how far each number in a data set is from the mean and, consequently, from every other number in the set. By taking the square root of the variance, the standard deviation provides a measure of spread in the same units as the original data, making it more interpretable. For instance, if you have a variance expressed in square units, taking the square root gives you the standard deviation in the original unit of measurement. This relationship helps analysts and researchers easily understand the extent of variability in relation to the data's central tendency. Therefore, understanding that the standard deviation is the square root of the variance is essential when interpreting statistical data and making informed decisions based on that data.