What aspect of a theory explains why crime varies in occurrence across different contexts?

The correct answer is rooted in the concept of explanatory power, which refers to a theory's ability to clarify and account for why certain phenomena occur. In the context of crime, a theory with strong explanatory power effectively identifies and articulates the underlying factors that contribute to variations in criminal behavior across different settings, such as geographical locations, social environments, or cultural contexts.

Explanatory power allows researchers and practitioners to understand the dynamics of crime, including how variables like socioeconomic status, community structure, legislation, and social norms can influence crime rates. By utilizing a theory with substantial explanatory power, one can formulate insights into the causal relationships that lead to crime, helping to inform policy-making, prevention strategies, and targeted interventions.

In contrast, other aspects like predictive power focus on a theory's capability to forecast future occurrences based on given data, while descriptive power simply summarizes observed phenomena without necessarily providing an understanding of their causes. Analytical power can denote the ability to break down complex issues into simpler components for better understanding but does not specifically address the causative elements of crime variations. Thus, explanatory power specifically highlights the importance of understanding the 'why' behind the changes in crime rates, making it the most appropriate choice.