In what type of study does the researcher collect detailed data about a variable or trend?

The correct choice is a case study because it involves an in-depth exploration and analysis of a particular instance, event, or individual that provides detailed information about a specific variable or trend. Case studies allow researchers to gather comprehensive qualitative data, which can lead to insights that statistical methods might not reveal. This approach is especially useful in fields where understanding context, motivations, and complexities is crucial, such as healthcare, psychology, or social sciences.

In a case study, the researcher often utilizes various data collection methods, including interviews, observations, and document analysis, to create a holistic view of the subject matter. This makes it particularly effective for examining unique or complex cases that do not lend themselves to more generalized quantitative approaches.

Other types of studies, like interviews or observational studies, while useful for obtaining information, do not inherently focus solely on detailed variable analysis in the same way a case study does. Quantitative studies primarily deal with numerical data and statistical analysis, which differs from the qualitative depth of a case study. Thus, the case study is the most suitable answer for the question regarding the collection of detailed data on a variable or trend.