Which term describes a “stepwise” variable?

Which term describes a "stepwise" variable? I.e. a variable that may only take sudden values (e.g. 0, 2/3 and 2), and has several observations at each of these values. The variable may indicate eg points in time.

The answer is not a discrete variable since these do not allow for decimal values. Nor is it a binned or grouped variable since there is no censoring.

Thank you.

• What is the basis for your assertion that discrete variables "do not allow for decimal values"? (by which I assume you mean values that are not integers) ... it's perfectly possible for a discrete random variable to take values like 0, 2/3 and 2. – Glen_b -Reinstate Monica Aug 31 '16 at 12:26

$$E(X) = \sum_{i=1}^k p_i x_i$$
for $k$ distinct outcomes $x_i$ occuring with probabilities $p_i$.