t-Test for One-Variable Statistics

A discrete variable over a particular range of real values is one for which, for any value in the range that the variable is permitted to take on, there is a positive minimum distance to the nearest other permissible value. The number of permitted values is either finite or countably infinite. Common examples are variables that must be integers, non-negative integers, positive integers, or only the integers 0 and 1.

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." (The Practice of Statistics)

Discrete variables are NUMERIC variables that can only take on a finite number of values (NOT all values between its max and min value).

For example,

If a physical education teacher rates the performance 1-5 of each of her students (1, 2, 3, 4, or 5 and no decimal values allowed) the rating is a discrete variable.

Categorical variables are variables that can be put into different "categories". They have no order.

For example,

Colors is a categorical variable (red, blue, green, etc..) there is no order, but are still different categories.