A categorical variable (sometimes called a nominal variable) is ONE that has two or more categories, but there is no intrinsic ordering to the categories.  For example, gender is a categorical variable having LET’s say two categories (male and female) and there is no intrinsic ordering to the categories.  Hair colour is also a categorical variable having a number of categories (blonde, brown, BRUNETTE, red, etc.) and again, there is no agreed way to order these from highest to lowest.  A purely categorical variable is one that simply allows you to assign categories but you cannot clearly order the variables.  If the variable has a clear ordering, then that variable would be an ordinal variable, as described below. 

1. Ordinal Variable - An ordinal variable is similar to a categorical variable.  The difference between the two is that there is a clear ordering of the variables.
2. Interval Variable - An ordinal variable is similar to a categorical variable.  The difference between the two is that there is a clear ordering of the variables.

Why does it matter if a variable is categorical, ordinal or interval?

Statistical computations and analyses assume that the variables have specific levels of measurement.  For example, it would not make SENSE to compute an average hair colour.  An average of a categorical variable does not make much sense because there is no intrinsic ordering of the levels of the categories. Moreover, if you tried to compute the average of educational experience as defined in the ordinal section above, you would also obtain a nonsensical result. Because the SPACING between the four levels of educational experience is very uneven, the meaning of this average would be very questionable.  In short, an average requires a variable to be interval. Sometimes you have variables that are “in between” ordinal and interval, for example, a five-point Likert scale with values “strongly agree”, “agree”, “neutral”, “disagree” and “strongly disagree”.  If we cannot be sure that the intervals between each of these five values are the same, then we would not be able to say that this is an interval variable, but we would say that it is an ordinal variable.  However, in order to be able to use statistics that assume the variable is interval, we will assume that the intervals are equally spaced.