What statistical tool can best describe the strength of the relationship between two variables?

The correlation coefficient is the most effective statistical tool for describing the strength and direction of the relationship between two variables. This coefficient ranges from -1 to +1, where values close to +1 indicate a strong positive correlation (as one variable increases, the other also tends to increase), values close to -1 indicate a strong negative correlation (as one variable increases, the other tends to decrease), and values around 0 suggest little to no correlation between the variables.

By quantifying the degree to which two variables are related, the correlation coefficient provides valuable insights that can be critical in various statistical analyses, such as regression. Its ability to convey not just the existence but also the strength and direction of the relationship makes it superior to the other options presented in this question.

The mean, standard deviation, and variance are measures of central tendency and dispersion, which describe single variables rather than the relationship between two variables. Thus, they are not suitable for assessing the strength of an association between pairs of data.