Is the blood pressure of a group of student the day before their final exam a discrete or continuous variable?

We have two different concepts mixed in one question.

First of all, independently of a group of students, we have a blood pressure of a person that can have, in theory, any real value within some reasonable boundaries. It can be higher or lower depending on a person and depending on the time of measurement. This blood pressure value is a continuous random variable; let's assign it a name, say, #xi#.

Secondly, we conducted an experiment of measuring the blood pressure of each person within a group of #N# students and received #N# discrete values of our random variable #xi#. The number of values equals to a number of students. Statistically, these values might serve as a basis to evaluate the distribution of probabilities of the continuous random variable #xi#

So, two concepts we deal with in this situation are:
(a) continuously distributed random variable (blood pressure);
(b) certain number of its discrete values that, with some statistical skills, might help to evaluate the distribution of probabilities function of a random variable mentioned in (a).

The first concept is a concept from the Theory of Probabilities. The second one is a task of Statistics. The former predicts behavior based on knowledge of the distribution of probabilities. The latter evaluates the distribution of probabilities based on behavior.

I recommend to go through lectures and exercises in theory of probabilities presented on Unizor under menu option "Probability".