A Discrete variable is a variable which takes only finite values like 1, 2, 3, 4, 5 etc. and can’t take any fractions like 1.5, 2.7 etc. Number of family members, number of floors in a building and number of buses, all represent discrete variables.
Variable maybe numerical or categorical. Discrete variable comes under numerical variable.
Discrete variables are also sometimes referred as qualitative variable as it is used for qualitative measures mostly. They can be classified into the following categories:
Nominal variables are used for qualitative classification which can be measured only in terms of items belonging to different categories. Nominal variables has no order and equal intervals, hence arithmetic and logical operations can’t be performed on them. E.g. Gender- Male, Female
Ordinal variable is a nominal variable, with the difference that they are ordered unlike nominal variables and hence logical operations may be carried on them.
E.g. We can say that tea with medium level sugar consists of sugar less than in the tea with higher level sugar but can’t differentiate by how much. Hence, Arithmetic operations are invalid for such variables.
Preference variables are the discrete variables, whose values are in an order (maybe increasing or decreasing).
E.g. A person taking marketing survey will ask sequential questions starting with name, details and ending with complaints, suggestions. Refer the below order where we can see that questions are in order but they are not having equal intervals as exact intervals can’t be defined.