Is a rating in a set range a categorical or numerical variable? For example, assume people were asked to rate a movie on a scale from 1 to 10, and their rating had to be a whole number in this range (so no decimals). 
Would this rating be classified as a numeric or categorical variable?
Also to take this a step further, say we asked them to rate 2 movies on the same scale, and then summed the result to produce a "result" variable. Would this be categorical or numeric?
I would be inclined to say numeric for both, but technically, there are only a set number of ratings they could give which would mean the "result" variable would have to be a number between 1 and 20 therefore, they could potentially be classified as categories?
What would you classify these variables in these scenarios as?
 A: Opinion variables on a 1 to 5 or 1 to 10 scale are usually considered
as ordinal categorical variables. On a 1-to-10 scale, suppose someone
rates one movie as 5 and and another as 10. Then it is difficult to
imagine what it would mean to say that they liked one movie 'twice as much' as the other. 
However, when you add two scores, you are automatically attributing
numerical characteristics to the scores. If one person gives scores
5 and 6 and another person gives the same two movies scores 1 and 10,
it is difficult to imagine the two people had exactly the same overall satisfaction
watching the two movies. The experience watching the movie rated 1 must
have been sufficiently dreadful (or tedious or offensive) to remember for a while.
The same difficulty arises with grade point averages. Grades in some
courses may be almost numerical, based on an average of test scores.
In other courses (perhaps an art course in making pottery) grades
may depend on an instructor's subjective opinion of the pots you made
during the term. It would make more sense to have 'grade point medians'
than grade point averages. The reason we have GPA's may be historical. More than 70 years ago, it would not have been possible for schools to compute grade point medians
for hundreds or thousands of students. Computationally, means are
easier than medians. 
For simple data such as 3, 1, 2, 7, 5 it may be easier to say the median is 3
than to say that the mean is 3.6. However, computation of medians requires
sorting, and sorting large numbers of scores takes more computing power
than adding them. Consider just the following 20 scores:
3  5  3  6  3  4  6  3  5  7  5  2  1  6  5  6 10  3  5  9

A $10 calculator can find the running total and get the mean 4.85. But
finding the median to be 5 requires sorting, which such a simple calculator
probably couldn't manage. 
Historically, statistics has been a bit slow
to adopt the use of truly appropriate procedures for ordinal data.
