Thank you. So in the sentence ,am I correct to assume that variety is being used as a singular noun hence the use of the indefinite article?
"Variety" is being used used as a singular noun in the same way that "number" is a singular noun in "a number of." As with the latter phrase, the reference with "a variety of" is to a plurality. If the phrase "a variety of students" functioned as the subject of a sentence, it would take plural verb agreement:
(a) A variety of students attend the school.
(b) *A variety of students attends the school.
Incidentally, to add a little to Gustavo's explanation above, "variety" is NEVER a noncount noun (it is ALWAYS a count noun) when it is followed by an "of"-phrase. We rarely use "variety" as a noncount noun. When we do, it has an abstract meaning, as it does in the proverb "Variety is the spice of life."