Final answer:
A case-control study is the best study design for obtaining histories and other information from a group of known cases and a comparison group to determine the relative frequency of a characteristic under study.
Step-by-step explanation:
The study design that is best described by obtaining histories and other information from a group of known cases and a comparison group to determine the relative frequency of a characteristic under study is a case-control study. In this type of study, a group of subjects with the trait of interest (cases) are compared to a similar group without the trait (controls). It is a retrospective study where subjects report their past behaviors to find correlations with their current status.