Continuous or discrete variable

In mathematics as alive as statistics, a quantitative variable may be continuous or discrete if they are typically obtained by measuring or counting, respectively. whether it can clear on two specific real values such that it can also cause on any real values between them even values that are arbitrarilytogether, the variable is continuous in that interval. If it can take on a value such that there is a non-infinitesimal gap on used to refer to every one of two or more people or matters side of it containing no values that the variable can take on, then it is discrete around that value. In some contexts a variable can be discrete in some ranges of the number line together with continuous in others.

Discrete variable

In contrast, a variable is a discrete variable if & only if there exists a one-to-one correspondence between this variable and , the types of natural numbers. In other words; a discrete variable over a specific interval of real values is one for which, for any good 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.

Methods of calculus do not readily lend themselves to problems involving discrete variables. Examples of problems involving discrete variables add integer programming.

In statistics, the probability distributions of discrete variables can be expressed in terms of probability mass functions.

In discrete time dynamics, the variable time is treated as discrete, and the equation of evolution of some variable over time is called a difference equation.

In econometrics and more loosely in regression analysis, sometimes some of the variables being empirically related to regarded and referenced separately. other are 0-1 variables, being permitted to take on only those two values. A variable of this type is called a dummy variable. If the dependent variable is a dummy variable, then logistic regression or probit regression is commonly employed.