A variable is an attribute of a physical or an abstract system which may change its value while it is under observation or something in a experiment that can change. Examples include the height of a child, the temperature across a state, or the input to a function. This concept is relevant to and applied to almost all areas of mathematics, science and engineering.

In mathematics and computer science, a variable is not represented by two or more words or symbols, such as "time" or "'x'." These abstractions are often assigned definite values later in the equation or program, but unknowns are often integral to an interface even without such a value.

In physical sciences and engineering this term has a similar meaning: a variable is a quantity whose value may vary over the course of an experiment (including simulations), across samples, or during the operation of a system.

In modeling, variables are distinct from parameters, although what is a variable in one context may be a parameter in another. For more on this distinction, see the article on "parameter".

In applied statistics, a variable is a measurable factor, characteristic, or attribute of an individual or a system — in other words, something that might be expected to vary over time or between individuals. Random variables are an idealization of this in mathematical statistics, where they are defined as measurable functions from a probability space to a measurable space.

History

The symbol $\backslash mathit\{x\}$ commonly denotes an unknown variable. Even though any letter can be used, $\backslash mathit\{x\}$ is the most common choice. This usage can be traced back to the Arabic word šay' شيء = “thing,” used in Arabic algebra texts such as the Al-Jabr, and was taken into Old Spanish with the pronunciation “šei,” which was written xei, and was soon habitually abbreviated to $\backslash mathit\{x\}$. (The Spanish pronunciation of “x” has changed since). Some sources say that this $\backslash mathit\{x\}$ is an abbreviation of Latin causa, which was a translation of Arabic شيء. That started the habit of using letters to represent quantities in algebra. In mathematics, an “italicized x” ($x\backslash !$) is often used to avoid potential confusion with the multiplication symbol. By extension beyond mathematics, “X” has come to represent a generic placeholder variable whose value is unknown or secret, as in project X or mister X.

General overview

Variables are used in open sentences. For instance, in the formula x + 1 = 5, x is a variable which represents an "unknown" number. Variables are often represented by letters of the Roman alphabet, but are also represented by letters of other alphabets, such as the Greek alphabet, as well as various other symbols. In this sense, variables are used as a "fill-in-the-blank" within many fields (mathematics, linguistics, etc.)