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(1), A continuous variable can take on any value in a range (subject to roundoff error). Examples are height, stock price, price, voltage, IQ, or paper thickness.
(2), A categorical variable (also called a nominal or discrete variable) is often not a number. A categorical variable can only take on a small number of discrete values. Examples of categorical variables are gender, employment status, dog breed, country of origin.
(3), An ordinal variable, which is a compromise between continuous and categorical. They can be ordered but are not continuous. For example, year in school (freshman, sophomore, junior, senior), military rank, letter grade for a course.
Reference: http://facweb.cs.depaul.edu/sjost/csc423/notes/0717.htm