Quantitative and qualitative research methods are used to define audiences in different ways. Quantitative research uses mathematical models and surveys to efficiently gather information about audience size, preferences, and opinions. Qualitative research provides a descriptive analysis of audiences through methods like focus groups to understand perspectives. Common uses of quantitative research include satisfaction studies, market research, and advertising assessments, while qualitative research helps uncover motivations and gather a range of ideas. Both approaches are useful depending on the type of insights needed.