Final answer:
The different favorite reality television shows identified by students make up a nominal scale of measurement, which is used to categorize data without implying any numeric value or order.
Step-by-step explanation:
The different television shows that students identify as their favorite reality television shows make up a nominal scale of measurement. In mathematics and statistics, a nominal scale refers to a classification that does not imply any sort of numeric representation; it merely categorizes or names a set of items without indicating any particular order or rank among them. This type of data is qualitative and can include things like categories, colors, names, labels, and in this case, personal preferences for television shows. As an example, whether a student's favorite show is 'Survivor,' 'Big Brother,' or 'The Bachelor,' these are just names of shows and do not have an inherent order or numeric value attached to them.