To know about independent and dependent variable, first we have to know about variables.
In mathematics, a variable is an event, idea, period or a type of category which we trying to measure. So we can say that a variable is anything that can be changed, like time,height,weight, attention etc.
In mathematics, we have two types of variables, independent variable and dependent variable. These two variables are the mathematical tools, used in an experiment. By the use of these tools, we control over the experiment and measure the result. These variables are related to one another.

In Math, independent variables are those values that determine the value of other variables.

A variable, which manipulated or controlled by human being or the experimenter is known as independent variable. It stands alone and isn't changed by the other variable(which we are trying to calculate). This is also called " factors".

This type of variable manipulated by the experimenter in an experiment. So we can say that,
independent variables are variables that are systematically controlled by any researcher to determine the variable’s overall effect on the final outcome or the dependent variable.

For example, someone's weight might be an independent variable. Other factors (such as what they eat, how much they eat, how is the food) aren't going to change a person's weight. In fact, when we are looking for some kind of relationship between variables we are trying to see if the independent variable causes some kind of change in the other variables, or dependent variable.

There are three ways to manipulate independent variables: presence or absence technique, amount technique and type technique.

In presence or absence technique, the independent variable can be manipulated by presenting a condition or treatment to one group of individuals and withholding the condition or treatment from another group of individuals.

In amount technique, the independent variable can be manipulated by varying the amount of a condition or variable such as the amount of a drug which is given to children within a learning disorder.

In type technique, the independent variable is to vary the type of the condition or treatment administered.
In math, dependent variables are those variables, whose values are determined with the help of the independent variable.

Dependent variables are the focus of any project and this is influenced by the independent variables. In an experiment we wish to find out or measure the value of dependent variable with the help of independent variable. Any dependent variable will be affected by the independent variable and will serve as the outcome of the measured.

In an experiment, the experimenter is looking for the possible effect on the dependent variable that might be caused by changing the independent variable.

Example:
A test score could be a dependent variable because it could change depending on several factors such as how much student studied, how much sleep. Usually when we are looking for a relationship between two things we are trying to find out what makes the dependent variable change the way it does

Every experiment has at least two types of variables: an independent and dependent.
“If one variable is describing things that occur before the things described by another variable happen, then the first variable can be usually taken as the independent variable and the second as the dependent variable”.
Here are some helpful tips to determine which variable is which:
  • An independent variable might be a variable, which is selected by the experimenter to determine its relationship to an observed phenomenon. It can be manipulated by a person(researcher). The dependent variable is the outcome of experiment.
  • In study or in an experiment, where one variable causes the other, the independent variable is the cause and dependent variable is the effect. In a study where groups are being compared, the independent variable is the group classification and dependent variable is the factor which is observed and measured to determine the effect of the independent variable, that is, the factor that appears,disappears, or varies as the experimenter introduces, removes, or varies the independent variable.
  • An independent variable is the presumed cause, whereas the dependent variable is the presumed effect.
  • In an experiment, the independent variable is the variable that is varied or manipulated by a person, and the dependent variable is the response that is measured.
  • The dependent variable refers to the outcome(effect), in which the experimenter is interested and the independent variable refers to the presumed 'cause', changes in which lead to changes in the status of the dependent variable.
So any event or condition can be conceptualized as either an independent or a dependent variable.

Given below are some of differences between independent and dependent variables.


To understand more about independent and dependent variable, lets take some examples:
  1. A scientist studies the impact of a drug on blood-cancer. The independent variable is the administration of the drug. The dependent variable is the impact the drug has on blood-cancer.
  2. The circumference of a circle decreases as the radius( independent variable) of the circle decreases and circumference is the dependent variable.
  3. Someone's weight might be a dependent variable. Other factors (such as what they eat, how much they eat, how is the food) are going to change a person's weight.
Graphing Dependent and Independent Variables:

In both math and science, these independent and dependent variables can be plotted on the x and y axes of a graph.
When we 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.

Example 1:
If we take an equation y = f(x) = In x, i.e. y depends on x. if we take different
different values of x then we find some different values of y.
x = 1 then y = In 1 = 0, x = 2 then y = 0.693
x = 3 then y = 1.09, x = 5 then y = 1.60
x = 7 then y = 1.945


Example 2:
Let y = sin x be a function, where y depends on x. Then
x = 0 then y = sin(0) = 0,
x = 1 then y = 0.84
x = -2 then y = -0.909,
x = 3 then y = 0.141
x = 4 then y = -0.75,
x = 6 then y = 0.27
x = 7 then y = 0.65
we get some values of y corresponding to x. Now ploy a graph for the help of these points:


In Mathematics, independent variables are those values that determine the value of other variables. Dependent variables are those, whose values are determined with the help of the independent variable.