Question

classifying students by their music preference country jazz festival Rock alternative and rap is an example of what type of measurement scale

Answer 1

Nominal scale : When measuring using a nominal scale, one simply names or categorizes responses.
For example : Gender, favorite color, religion etc.
So nominal variable is not numerical , its just categorical variable , you can categorize that variable in different categories .

Ordinal scale : Data at this level can be ordered, but no differences between the data can be taken that are meaningful.
For example : Class ranks : distinction, first class , second class , pass class , fail.   
For ordinal scale we can rank the categories

For given problem students are classify by their music preferences :  country, jazz, festival, Rock, alternative and rap

So this is Nominal scale type of measurement.