# What is Bivariate Data? - Definition & Examples

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• 0:01 Bivariate Data
• 1:00 Bivariate Data Defined
• 4:07 Understanding…
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Lesson Transcript
Instructor: Cathryn Jackson

Cat has taught a variety of subjects, including communications, mathematics, and technology. Cat has a master's degree in education and is currently working on her Ph.D.

In this lesson, you will be learning about the definition and uses of bivariate data. We will also compare and contrast the characteristics of univariate data and bivariate data.

## Bivariate Data

Mindy is a college student who works as a teacher's assistant at an elementary school. She is helping the third grade teacher grade a reading test. Mindy notices that the grades on the reading test are all over the place, meaning that there are some students who did very well, some students who did average and some students who did poorly. These are the results of the test: 55, 32, 67, 100, 98, 75, 46, 82, 72, 93, 44, 26, 67.

Later, Mindy is grading a questionnaire. The students are answering questions about what they do at home. One of the questions asks the student to track how much they read outside of school. These are the number of hours that each student reported on his or her questionnaire: 1, 2, 0, 3, 4, 6, 1, 2, 5, 0, 1, 1, 2.

Mindy wonders if there is a relationship between the number of hours a student spends each week reading and the reading test scores.

In this lesson, you will be learning about the definition and uses of bivariate data. We will also compare and contrast the characteristics of univariate data and bivariate data.

## Bivariate Data Defined

Bivariate data deals with two variables that can change and are compared to find relationships. If one variable is influencing another variable, then you will have bivariate data that has an independent and a dependent variable. This is because one variable depends on the other for change. An independent variable is a condition or piece of data in an experiment that can be controlled or changed. A dependent variable is a condition or piece of data in an experiment that is controlled or influenced by an outside factor, most often the independent variable.

This is very different from univariate data, which is one variable in a data set that is analyzed to describe a scenario or experiment.

For example, if Mindy was studying for a college test and tracks her study time and her test scores, she might see that the more time she spends studying, the better her test scores become. Therefore, in this scenario, Mindy's test scores are the dependent variable because they depend on the number of hours she studies. Likewise, the number of study hours would be considered the independent variable. For that reason, we can see the relationship in this bivariate data set:

In this case, we can compare the number of hours the third grade students spend reading with his or her test score, like this:

We can also display this data visually, like this:

Notice that most of the points increase both vertically and horizontally. You may notice that we have graphed the number of reading hours on the x-axis, horizontally, and the test scores on the y-axis, vertically. When a bivariate data set shows an overall increase in numbers like this, it is called a positive correlation, where the dependent variables and independent variables in a data set increase or decrease together.

This means that there is a positive relationship between the number of hours spent reading during the week and the test score of the student. In other words, the more a student reads, the better they score on the reading test. Therefore, in this case the independent variable is the amount the student reads during the week, because that is something they can control. The dependent variable is the score on the test; they can only control this variable if they change the independent variable.

If the numbers sloped downward, like the bivariate data in the graph below, then you have a data set with a negative correlation, where the dependent variables and independent variables in a data set either increase or decrease opposite from one another. That means if the independent variable decreases, then the dependent variable would increase and vice versa.

If there is no relationship between the numbers, as shown in the graph below, then the data set has no correlation. You can learn more about correlation in the Regression & Correlation Chapter of this course!

## Understanding Bivariate and Univariate Data

The third graders in Mindy's class are studying plants. Each student records the amount of water they give the plant each day and the height of the plant. Are the students studying bivariate data? Yes, they are studying two separate variables in which each variable can change.

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