The question is simply posed as " identity the variables as discrete or continuous. 1) Mark of a student in an examination. 2) Family income." What I think: 1) There must be a minimum gap between two possible consecutive marks that the examiner can assign. Eg. Suppose that there are N students and we are considering percentile scores. Then the scores can take values on N isolated points only, 100*1/N, 100*2/N,......, 100*N/N. Implying that scores are discrete. Again, if we assume that scores are sample observations from a merit distribution, and the distribution is continuous, then we will have a different answer. 2) Family income cannot be more accurate than the smallest currency, and hence discrete. My confusion is, my daughter's college professor in their introductory class of Statistics uniquely states both the variables as continuous.