Generally speaking, in any given model or equation, there are two types of variables:
The definition of an independent or dependent variable is more or less universal in both statistical or scientific experiments and in mathematics; however, the way the variable is used varies slightly between experimental situations and mathematics.
If a scientist conducts an experiment to test the theory that a vitamin could extend a person's life-expectancy, then:
The independent variables and dependent variables can vary from person to person, and the variances are what are being tested; that is, whether the people given the vitamin live longer than the people not given the vitamin. The scientist might then conduct further experiments changing other independent variables -- gender, ethnicity, overall health, etc. -- in order to evaluate the resulting dependent variables and to narrow down the effects of the vitamin on life span under different circumstances.
Here are some other examples of dependent and independent variables in scientific experiments:
In mathematics, the "x" and "y" values in an equation or a graph are referred to as "variables."
In both math and science, dependent and independent variables can be plotted on the x and y axes of a graph. The convention is to use the independent variable as the x-axis and the dependent variable as the y-axis. There is typically a clear and obvious relationship between x and y shown on the graph.
An example of this would be Boyle's Gas Law where the pressure of a gas is inversely proportional to its volume as long as the temperature remains constant.
In order to have come up with the equation for what is now Boyle's Law, Boyle himself would have had to conduct a series of experiments that measured the effect that altering the independent variable (pressure) had on the dependent variable (volume). 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.
Knowing the differences between independent and dependent variables will help as you sharpen your problem solving skills and explore new concepts within the fields of mathematics and the science