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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.

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    $\begingroup$ 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. $\endgroup$ – Glen_b -Reinstate Monica Aug 31 '16 at 12:26
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It is a categorical distribution. It is discrete since it can take a countable number of values. Discreteness is not about being integer, you can as well have your distinct values labeled by colors, names, letters, or anything you want. It's expected value is simply

$$ E(X) = \sum_{i=1}^k p_i x_i $$

for $k$ distinct outcomes $x_i$ occuring with probabilities $p_i$.

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