Certified Advanced Alcohol and Drug Counselor (CAADC) Practice Exam

What distinguishes variance from standard deviation?

1. Variance is the mean minus squared standard deviation

2. Variance is the square root of the median

3. Variance is the sum of squares divided by N

4. Variance is the sum of the squares of itself

The correct answer is: Variance is the sum of squares divided by N

Variance is defined as the average of the squared deviations from the mean. More specifically, it is calculated by taking the sum of the squared differences between each data point and the mean, and then dividing that total by the number of data points (N) in the dataset. This process quantifies the degree to which data points differ from the mean, providing a measure of variability or dispersion within the dataset. Using this definition, the correct answer clearly highlights that variance is calculated as the sum of squares divided by N, which accurately describes how variance is derived mathematically in a population. The distinction between variance and standard deviation lies in their representation of variation: while variance provides a measure of how much data spreads around the mean through squared differences, standard deviation is the square root of variance, bringing the unit of measurement back to the same dimension as the original data. The other options do not accurately describe the computation or definition of variance, making them unsuitable. For example, the mean minus squared standard deviation does not align with how variance is defined, nor does taking the square root of the median as a measure of variability. Additionally, the sum of the squares of itself does not relate to either variance or standard deviation in any conventional statistical sense.