Final answer:
Categorical data (qualitative data) represents characteristics that can be named or categorized, such as types of pets, favorite music genres, and brands of smartphones. It does not lend itself to traditional mathematical analysis like quantitative data does.
Step-by-step explanation:
Categorical data, also known as qualitative data, refers to data that represent characteristics or attributes that can be categorized or named but not quantitatively measured. This type of data is often described using words rather than numbers, and it includes anything that can be placed into distinct categories according to some attribute or characteristic.
For example, if we consider the types of pets people own, this is categorical because pets can be classified into groups such as dogs, cats, birds, etc., but these categories cannot be represented by a numerical value or an average. Another example is favorite genres of music among a group of friends, which could include rock, pop, classical, and jazz. Lastly, brands of smartphones used by students in a school is also a form of categorical data, where brands like Apple, Samsung, and Huawei serve to categorize the smartphones.
Unlike quantitative data, categorical data does not lend itself to traditional mathematical analysis, such as finding means or totals. Instead, researchers often use counts and percentages to describe and analyze this type of data.