In the context of probability and statistics, which of the following best describes what it means for two variables to be positively associated and negatively associated?

• A. Positively associated means that the variables are $\mathrm{independent}$; negatively associated means that the variables are $\mathrm{dependent}$.
• B. Positively associated means that the $\mathrm{sum}$ of the variables is always $+$; negatively associated means that the sum is always $-$.
• C. Positively associated means that both variables always have the $\mathrm{same}$ value; negatively associated means that both variables always have $\mathrm{opposite}$ values.
• D. Positively associated means that as one variable increases, the other variable tends to increase; negatively associated means that as one variable increases, the other variable tends to decrease.

Answer: (D)

Verified step by step guidance

1. Understand the concept of association between two variables: it describes how the variables change together.
2. Positive association means that when one variable increases, the other variable tends to increase as well. This indicates a direct relationship.
3. Negative association means that when one variable increases, the other variable tends to decrease. This indicates an inverse relationship.
4. Recognize that association is about the tendency or pattern of change, not about exact values or sums of the variables.
5. Therefore, the best description is: Positively associated means that as one variable increases, the other variable tends to increase; negatively associated means that as one variable increases, the other variable tends to decrease.