How do I identify the variables of a relation or function and how do I determine if they are independent or dependent?
Normally, a relation or a function is created when a student or scientist collects data during a scientific experiment to test a hypothesis to see if there is a relationship between 2 variables: an independent variable and a dependent variable.
Many scientists create these relations or functions in hopes that they will be able to predict events with accuracy. When the independent variable is manipulated, a scientist might hope to predict what the outcome will be depending upon the magnitude of the change in the independent variable.
For example, if you heat a gas like air in a bottle covered over with a balloon, as the temperature increases, the balloon will blow up and the volume of the “container” will increase. The variables in this natural phenomenon are temperature and volume of the container. The independent variable is the temperature because it controls the size of the container. The dependent variable is the volume of the container because it is controlled by the independent variable (temperature). A function in this case would allow the scientist to predict the size to which a container would “grow” at a given temperature.
Normally data from an experiment can take the form of a graph or table, and if a relationship is established, data can take the form of an equation.
The independent variable on a graph will always lie on the x-axis of a Cartesian coordinate graph. The dependent variable will always lie on the y-axis.
The independent value of an ordered pair is the first number in the set (the x-value). Take for example the ordered pair (3, 5). 3 would be the x value also known as the independent variable value. The 5 would be the y value also known as the dependent variable value.
In a vertical table, the left column is usually designated for the independent variable values and the right column is usually designated for the dependent variable value.
In a horizontal table, the top column is usually designated for the independent variable values and the bottom column is usually designated for the dependent variable value.
In an equation, for example y=2x + 7, the x is the place where an independent value would go to find the value for y which would be a dependent variable value.
Remember one more important thing about variables. They must be quantifiable and measurable. In other words a number value must be associated with the variable. For example if you said the independent variable for a situation was “students,” it may be more appropriate to label the independent variable “number of students,” so that I can measure the independent variable.
Let’s take a look at a few problems where we not only identify the variables of a situation or experiment, but we also determine whether they are independent or dependent.
Independent and dependent variables: Practice worksheet
Please identify the independent and dependent variables in the following descriptions of experiments:
1) Students watched a cartoon either alone or with others and then rated how funny they found the cartoon to be.
Independent Variable:
Dependent Variable:
2) A comprehension test was given to students after they had studied textbook material either in silence or with the television turned on.
Independent Variable:
Dependent Variable:
3) Some elementary school teachers were told that a child’s parents were college graduates, and other teachers were told that the child’s parents had not finished high school; they then rated the child’s academic potential.
Independent Variable:
Dependent Variable:
4) Workers at a company were assigned to one of two conditions: One group completed a stress management training program; another group of workers did not participate in the training. The number of sick days taken by these workers was examined for the two subsequent months.
Independent Variable:
Dependent Variable:
5) Students at a University were split into two groups and each received a different text for a philosophy course. Once group received a traditional text book, while the other received an interactive textbook on a tablet computer. After the course, the final exam marks between the two groups of students was compared.
Independent Variable:
Dependent Variable:
Determine the independent and dependent variable in each of the following scenarios.
1. The more time people spend using social media, the less able they are to express themselves in conversation. Experiment:
Independent Variable:
Dependent Variable:
1. Drinking energy drinks makes people more aggressive.
Independent Variable:
Dependent Variable:
2. Taking a nap in the afternoon makes people more relaxed and less irritable for the rest of the day.
Independent Variable:
Dependent Variable:
3. Spending time with a cat or dog decreases the amount of stress someone is feeling and allows them to perform better on tests.
Independent Variable:
Dependent Variable:
4. Eating breakfast in the morning increases the ability to learn in school.
Independent Variable:
Dependent Variable: