Solved – Categorical or Quantitative

A colleague and I had a conversation about whether the following variables are categorical or quantitative.

1) Social security numbers

2) Phone numbers

3) Postal zip codes

We agreed that all three are in fact categorical, but couldn't agree on a good reason.

The definition of a categorical variable (at least here
In statistics, a categorical variable is a variable that can take on one of a limited, and usually fixed, number of possible values, thus assigning each individual to a particular group or "category."

However, it seems a somewhat weak case can also be made that the variables are discrete valued random variables. I need one good reason to convince students of why these variables are not quantitative. Any ideas?

Here's a simple test. If you 'add' two of the variables is that another 'value' of the variable. If we have income, the sum of any two incomes is another possible income. However what sense does (zipcode1) + (zipcode2) have. Ditto for ssn's and phone numbers. The bottom line is that one can make algebraic sense of numerical variables and that one can't make algebraic sense of categorical variables.

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