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Variable or Variate.
A letter which can take values of all observations. e.g. If variable x represent marks of three students who have scored 40, 50 and 60 marks, then x1 = 40, x2 = 50, x3 = 60.

Categorical Variable.
A variable whose value ranges over categories, such as male, female. Some categorical variables are ordinal.

Continuous Variable.
A quantitative which can take all values in its range is called as continuous variable. Its set of possible values is infinite set. In practice, one can never measure a continuous variable to infinite precision, so continuous variables are sometimes approximated by discrete variables. A random variable X is also called continuous if its set of possible values is infinite set, and the chance that it takes any particular value is zero A random variable is continuous if and only if its cumulative probability distribution function is a continuous function (a function whose graph does not show any break).

Discrete Variable.
A quantitative which cannot take all values in its range is called as discrete variable. Its set of possible values is a finite set.. A discrete random variable is one whose set of possible values is countable. A random variable is discrete if and only if its cumulative probability distribution function has breaks in its graph.