Generally speaking, in any given model or equation, variables can be divided into two categories:
- Independent variables are the variables that are changed in a given model or equation. One can also think of them as the ‘input’ which is then modified by the model to change the ‘output’ or dependent variable.
- Dependent variables are considered to be functions of the independent variables, changing only as the independent variable does.
Using Independent and Dependent Variables
While the definition is more-or-less universal, the application varies slightly between statistical experiments and mathematics.
For example:
- If a scientist conducts an experiment to test the theory that a vitamin could extend a person’s life-expectancy, then the independent variable is the amount of vitamin that is given to the subjects within the experiment. This is controlled by the experimenting scientist.
- The dependent variable, or the variable being affected by the independent variable in this case, is life span.
It varies from person to person within each group, and is what is being tested; that is, whether or not the people given the vitamin live, on average, longer than the people not given the vitamin. The scientist might then conduct further experiments to increase the number of independent variables -- gender, ethnicity, overall health, etc. -- in order to narrow down the specific effects of the vitamin.
Here are some other examples of dependent and independent variables in science:
- A scientist studies the impact of a drug on cancer. The independent variable is the administration of the drug. The dependent variable is the impact the drug has on cancer.
- A scientist studies the impact of withholding affection on rats. The independent variable is the affection. The dependent variable is the reaction of the rats.
- A scientist studies how many days people can eat soup until they get sick. The independent variable is the number of days of consuming soup. The dependent variable is the onset of illness.
Independent and Dependent Variables in Math
In mathematics, the x and y values in an equation or a graph are referred to as "variables."
- If an equation shows a relationship between x and y in which y is specified in terms of x, y is known as the dependent variable and is sometimes referred to as ‘function(x)’ or f(x).
- The final solution of the equation, y, depends on the value of x, the independent variable which can be changed.
Graphing Dependent and Independent Variables
In both math and science, these dependent and independent variables can be plotted on the x and y axes of a graph.
- When used in a graph, there is typically a clear and obvious relationship between x and y.
- While independent and dependent variables are at work in mathematics, the application is more theoretical than practical.
An example of this would be Boyle’s Gas Law wherein the pressure of a gas is directly proportionate to its temperature.
- Using the equation (y = kx), one can plot a graph that will yield a theoretical value for y when given any value for x, allowing one to accurately predict the affect the independent variable will have on the dependent variable.
In order to have come up with the equation for what is now Boyle’s Gas Law, Boyle himself would have had to conduct a series of experiments that measured the effect that altering the independent variable (temperature) had on the dependent variable (pressure). This would have put both independent and dependent variables into a real life, practical context. Boyle was then able to devise his equation based on his observations of the independent and dependent variables.