Ohio Assessments for Educators (OAE) Mathematics Practice Exam

What is the relationship between variance and standard deviation?

1. Variance is the cube of standard deviation

2. Variance is the square of standard deviation

3. Standard deviation is the variance of data

4. They are unrelated in statistical analysis

The correct answer is: Variance is the square of standard deviation

The correct answer highlights an important mathematical relationship between variance and standard deviation. Variance measures how much the data points in a set differ from the mean, which provides a sense of data spread or dispersion. Standard deviation, on the other hand, is a measure of the average distance of each data point from the mean and is expressed in the same unit as the original data. The key relationship is that the variance of a dataset is calculated as the average of the squared differences from the mean, while the standard deviation is derived from the variance by taking the square root. Thus, if you take the standard deviation and square it, you return to the variance. This is why variance is identified as the square of the standard deviation. Understanding this relationship is crucial for interpreting data and statistics correctly, as it allows one to move between these two measures of variability seamlessly.