Dependent and independent variables with examples
This article will be about The concept of dependent and independent variables, with examples and how to identify each type of variable.
The dependent and independent variables are a concepts use mainly in mathematics and statistics when we are talking about the relation between two variables, where the change of a variable affects the value of other. It is really important to learn how to identify this two types of variables so we can make a right analyses, specially in inferential statistic, where what we are looking for is to change a situation in a population by taking different actions to counteract bad tendencies or a not wanted behavior. This is accomplished by locating the different dependent and independent variables.
The independent variables are the variables that does not depend on another, this types of variables are the variables that we want to manipulate with the objective of having an expected result. The independent variables are not the objective of the study, but are the way that gets us to the main objective of a study, because by making changes in this variables we are going to get to the expected result.
The dependent variables are the variables which value depends on the value of another variable. This variables are, in a study, what we want to change. These variables depend on the value of another variable, this means that when we change the value of the variable this depends on, the value of the dependent variable is going to change as well.
In a study there could be multiple dependent and independent variables, even there could be dependent variables that depend on more than one independent variable, and also, independent variables that have effect on multiple dependent variables, this is why it is so important to know what is the result we are looking for in the study, so we can identify the corrects variables.
If there is somebody that is payed per worked hour, and this person have the option of working the hours he wants, in this example, we have 2 variables, one of the is the hours this person works, and the other is the money this person earns. If we analyze this example we can understand that the money he makes will depend on the hours the person works, so the independent variable are the worked hours and the dependent variable are the earning.
As we can see in the previous example, the objective of the dependent and independent variables is to change a situation, for example, if the current situation of the person is that the earned money is not enough to buy a new cellphone, we understand that the problem is the money, because is not enough, but, to change the earned money we have to increase the worked hours, so we can increase the earnings as well, therefore, even when what we want is to change the earnings, first we have to manipulate the worked hours.
Dependent and independent variables examples
Example 1: In a work group they are celebrating the anniversary of the group, and they are planning to buy pizza, and they send a person to buy the pizzas, and when this person arrives to the pizza shop it turns out that each pizza is $5.
In this example we could take as the dependent variable the total price of the pizzas they are going to buy, and as the independent variable the quantity of pizzas, because the total to pay will depend on the number of pizzas they are going to get, for example if they only want one pizza, then the price would be 5$, but if they buy 2 pizzas, then the price would be 10$.
- Function of the price
- price(quantity) = $5 * quantity
- If we buy 1
- price(1) = $5 * 1
- price(1) = $5
- If we buy 3
- price(3) = $5 * 3
- price(3) = $15
- If we buy 8
- price(5) = $5 * 8
- price(5) = $40
In the previous case we can see that the manipulated variable is the number of pizzas, and every time that it changes, then the total price changes as well.
As we said before there is not only one way of defining this variables, in the previous example we took the number of pizzas as independent and the price as dependent, but we could take this variables of another way, if the work group collected a certain money, and they told the person to buy as many pizzas as possible, in this case the independent variable would be the collected money while the number of pizzas in this case would be the dependent variable.
Example 2: an example of the dependent and independent variables in mathematics are the function, this functions are an equation with a value that changes, where this value can take any value, and depending on this value the result of the function will change.
- Example of a linear function
- f(x) = 4x
- When x is 4
- f(4) = 4(4)
- f(4) = 8
- When x is 12
- f(12) = 4(12)
- f(12) = 48
- When x is 100
- f(100) = 4(100)
- f(100) = 400