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Say I have a dataset of patient information, and some variable X representing labels for degree of a burn, with possible values of X = {1,2,3,4,5}:

1: First-Degree Burn

2: Second-Degree Burn

3: Third-Degree Burn

4: No Burn

5: Unknown

I'd be inclined to say X is ordinal (since you can "order" the degree of burns by severity or some other measure) but "unknown" as a possible value makes me unsure, since that really doesn't have a natural place on the "scale". Would this variable be considered nominal or ordinal, or both?

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I'd say that the variable is ordinal wrt "No burn", "first degree burn", "second degree burn" and "third degree burn", and I'd argue that "unknown" is not a valid value for the variable. Consider that in any instance with the label unknown, the true value of the variable is either 1,2,3, or 4. Thus, unknown is essentially the same as having no value at all. You then could move into methods for dealing with incomplete datasets with sparse or missing values.

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