  In an equation, there are two types of variables: independent and dependent. These values represent mathematical tools that are used in an experiment. Independent and dependent variables allow a researcher to maintain control, measure results, and draw accurate conclusions.

The basic definition of independent and dependent variables is universal in both science and math. However, the way the variables are used differs depending on whether you are conducting a scientific experiment, performing a math problem, or studying statistics.

Independent variables are values that can be changed in a given equation or experiment. Think of an independent variable as your input. An independent variable represents information that you put in to the equation.

Dependent variables are values that result directly from the independent variable. Ultimately, they depend on the independent variable. You do not put this information into the equation or experiment but instead observe or discover it.

A simple equation used in the field of physics can be used to demonstrate the relationship between independent and dependent variables.

Newton’s Second Law of Motion states the following:

F = ma

(Force equals mass multiplied by acceleration.)

When measuring the acceleration of an object, the mass does not change. Therefore, it remains constant. The independent variable in this formula would be force. Force can be changed, and a greater force results in a greater acceleration.

## Independent and Dependent Variables in Science

Let’s imagine that a scientist is conducting an experiment to test if a vitamin enriched water will result in more growth than plain water.

The independent variable is the variable that is manipulated by the researcher during an experiment. In this case, the independent variable is the vitamin substance that is being given to the plant. This is controlled by the experimenting scientist.

The dependent variable is the amount of plant growth. This is affected directly by the vitamin substance or independent variable. It is important to note that there can be more than one dependent variable. For example, in the above experiment,  the daily growth rate could be measured as well as the overall height of the plant after a number of days.  Width or other factors to measure health such as could be measured as well.  All of these variables are dependent upon the independent variable (the vitamin substance).

Outside of some advanced forms of research, you cannot have more than one independent variable for a valid experiment. In order to receive accurate results, the researcher needs to know the one factor that is causing the results of the experiment.

When conducting an experiment,  control variables or constants come into play.  The control variables are variables that must be held constant or neutralized from the beginning to the end of the experiment for the results to be reliable. Everything except the independent and dependent variables need to stay the same throughout the experiment. Some control variables would be the amount of liquid given to the plant, the tools used, location, soil quality, sunlight, and temperature.

## Independent and Dependent Variables in Math

You probably remember being introduced to variables during an introductory Algebra lesson. In math, variables are the x and y values in an equation or graph. The term function is often used when using independent and dependent variables in math. Functions are examined algebraically or graphically by either looking at equations or graphs. A function represents a mathematical relationship where the value of a single, dependent variable is determined by one or more independent variables.

The independent variable is often designated by x. The dependent variable is often designated by y.

We say y is a function of x. This means y depends on or is determined by x.

Mathematically, we write y = f(x). This means that mathematically y depends on x. If we know the value of x, then we can find the value of y. Equations show relationships. The final solution of the equation (y) depends on the value of (x) or the independent variable which can be changed.

Let’s look at the equation y = 4x – 3. The dependent variable is y because it depends upon the value chosen for x. The dependent variable is usually isolated on one side of the equation.

If you are looking to learn basic Algebra or brush up on your knowledge, check out this course.

## Graphing Independent and Dependent Variables

Throughout the practice of both math and science, dependent and independent variables can be plotted on the x and y axes of a graph. A graph shows a clear relationship between the x and y variables.

A simple and effective way to represent data using an independent and dependent variable would be a two-dimensional graph. When graphing information, traditionally the independent variable is placed on the y axis and the dependent variable is placed on the x axis. These variables are usually studied to determine if there is a correlation in the data. The independent variables are the input into the mathematical problem or system and are not changed by the process.

Graphs are often used in descriptive statistics to summarize data and discover patterns. If you are looking to learn concepts, calculations and applications of descriptive statistics, check out this course offered by Udemy.

The following examples of independent and dependent variables can easily be shown on a graph.

### Dependent Variable

Hours Worked

Amount of Money Earned

Total Calories Consumed

Total Weight Gain

Number of Assignments Completed

## Summary of Differences

1. In science, for one independent variable, there may be more than one dependent variable. However, for more than one dependent variable, there is always one independent variable.
2. The value of an independent value can be changed. You cannot change of the value of a dependent variable.
3. The independent variable is the value which is manipulated in an experiment.  The dependent variable is the value observed by the researcher during an experiment.

Knowing the differences between independent and dependent variables will help as you as you sharpen your problem solving skills and continue to explore new concepts within the fields of mathematics and the science. If you are brushing up on your knowledge in preparation of an SAT test, this teaching and coaching course would help to improve your SAT score or just broaden your general knowledge when it comes to high school level subject matter.

Page Last Updated: February 2020

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