What does a correlation coefficient measure?

A correlation coefficient is a statistical measure that quantifies the strength and direction of a relationship between two variables. It typically ranges from -1 to +1, where a correlation of +1 indicates a perfect positive relationship, -1 a perfect negative relationship, and 0 indicates no correlation. This ability to capture both how closely two variables move in relation to one another and the nature of that movement (whether they increase together or one increases while the other decreases) is fundamental in fields such as data analysis, statistics, and research.

Understanding correlation helps analysts and researchers determine potential relationships and dependencies between variables, which can inform decisions, predictions, and further investigations. For instance, in a dataset where you are studying the relationship between hours studied and examination scores, a positive correlation coefficient would suggest that as hours increase, so do scores, guiding educational strategies.

The other options, while relevant to data analysis, do not capture the specific purpose of a correlation coefficient. The frequency of data points pertains more to counts and distribution, variability relates to how spread out the data is rather than the relationship between two distinct variables, and the average provides a central tendency without indicating any relationship.