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In psychology a variable is a symbol denoting a quantity or symbolic representation. Variables are often contrasted with constants, which are known and unchanging.

In statistics, variables refer to measurable attributes, as these typically vary over time or between individuals. Variables can be discrete (taking values from a finite or countable set), continuous (having a continuous distribution function), or neither. Temperature is a continuous variable, while the number of legs of an animal is a discrete variable. This concept of a variable is widely used in the natural, medical, and social sciences.

In causal models, a distinction is made between "independent variables" and "dependent variables", the latter being expected to vary in value in response to changes in the former. In other words, an independent variable is presumed to potentially affect a dependent one. In experiments, independent variables include factors that can be altered or chosen by the researcher independent of other factors.

So, in an experiment to test if the boiling point of water changes with altitude, the altitude is under direct control and is the independent variable, and the boiling point is presumed to depend upon it, so being the dependent variable. The results of an experiment, or information to be used to draw conclusions, are known as data. It is often important to consider which variables to allow, or directly control or eliminate, in the design of experiments.

There are also quasi-independent variables, which are used by researchers to group things without affecting the variable itself. For example, to separate people into groups by their sex does not change whether they are male or female. Or a researcher may separate people, arbitrarily, on the amount of coffee they had drunk before beginning an experiment. The researcher cannot change the past, but can use it to split people into groups.

While independent variables can refer to quantities and qualities that are under experimental control, they can also include extraneous factors that influence results in a confusing or undesired manner. In statistics the technique to work this out is called correlation.

If strongly confounding variables exist that can substantially change the result, it makes it harder to interpret. For example, a study on cancer against age will also have to take into account variables such as income, location, stress, and lifestyle. Without considering these, the results could be grossly inaccurate deductions. Because of this, controlling unwanted variables is important in research.

In other scientific fields such as biology, chemistry, and physics, the word variable is used to refer to a measurable factor, characteristic, or attribute of an individual or a system. In a scientific experiment, so called "independent variables" are factors that can be altered or chosen by the scientist. For example, temperature is a common environmental factor that can be controlled in laboratory experiments. "Dependent variables" or "response variables" are those that are measured and collected as data. An independent variable is presumed to affect a dependent one.

In social sciences, variable is a logical set of attributes. A variable such as "gender" would have two attributes: male and female.

## 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. In mathematics, variables are usually represented by letters of the Roman alphabet, but are also represented by letters of other alphabets; as well as various other symbols. In computer programming, variables are usually represented by alphanumeric strings.

## Why are variables useful?

Variables are useful in mathematics because they allow instructions to be specified in a general way. If one were forced to use actual values, then the instructions would only apply in a more narrow, and specific set of situations. For example: specify a mathematical definition for finding the square of ANY number: square(x) = x · x.

Now, all we need to do to find the square of a number is replace x with any number we want.

• square(x) = x · x = y
• square(1) = 1 · 1 = 1
• square(2) = 2 · 2 = 4
• square(3) = 3 · 3 = 9

etc...

In the above example, the variable x is a "placeholder" for ANY number. One important thing we are assuming is that the value of each occurrence of x is the same -- that x does not get a new value between the first x and the second x. This page uses content from the English-language version of The Psychology Wiki. The original article was at variable. The list of authors can be seen in the page history. The text of both The Psychology Wiki and Wikipedia is available under the GNU Free Documentation License.