Should there be an discrete (integer) type for variables?

[evertrol]

One can configure variables to be categorial or continuous. For a variable that only takes integer values, either option is debatable.

Using discrete, integer values may change the representation in graphs (axes, for example).
It could also have the potential to change results of statistics such as average and stdandard deviation, by using integer division.
(I'm aware JavaScript/EcmaScript/TypeScript don't actually use integers, and even if there is a library doing this, it is, again, debatable whether this is wanted.)

The main reason for putting this here as a possible option, came out of playing with the Titanic dataset: it feels more natural to have age, and especially familiy size, as a discrete, integer type. (Perhaps also passenger class, which is presented as a floating point type, but should actually be a categorical type.)