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Statistics 101: Principles of Statistics11 chapters | 144 lessons | 9 flashcard sets

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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.

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** 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!

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.

Let's look at the characteristics of bivariate data in comparison to univariate data. First, bivariate data deals with two variables while univariate data deals with only one variable. You can remember this by looking at the prefix 'bi,' which means two; just like the word bicycle means that there are two wheels. If Mindy wanted to collect data on the ages of the students in her class, that would be univariate data because she is only looking at one data set with one variable.

Second, bivariate data and univariate data serve two different functions or purposes. The primary purpose of bivariate data is to compare the two sets of data to find a relationship between the two variables. Remember, if one variable influences the change in another variable, then you have an independent and dependent variable. The primary function or purpose of univariate data is to describe an experiment. If we wanted to describe the ages of a third grader, then we would collect the ages of third grade students and then analyze the data. Since there is only one variable in this experiment, the data is univariate.

Third, bivariate data and univariate data can be analyzed using visual representations. Although both types of data can be displayed in a multitude of visual representations, let's talk about the most common ones you will see. You will probably see bivariate data represented in scatterplots like you saw in an earlier example. For univariate data, there are many ways to display information. You may see univariate data in a stem-and-leaf display or in a box-and-whisker plot.

Mindy can find many examples of both univariate and bivariate data in her classroom. **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 dependent variable. 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.

Bivariate data deals with two variables. The primary purpose of bivariate data is to compare the two sets of data or to find a relationship between the two variables. Bivariate data is most often analyzed visually using scatterplots.

On the other hand, **univariate data** is when one variable is analyzed to describe a scenario or experiment. Univariate data only has one data set with one variable. The primary function or purpose of univariate data is to describe an experiment. You may see univariate data in a stem-and-leaf display or in a box-and-whisker plot.

Lastly, when a bivariate data set shows a relationship, it can be either a positive or negative correlation. A **positive correlation** is where the dependent variables and independent variables in a data set increase together. A **negative correlation** is where the dependent variables and independent variables in a data set either increase or decrease opposite from one another. If there is no relationship between the numbers, as shown in this graph, then the data set has no correlation:

Through this lesson, expand your knowledge along with your capacity to:

- Define bivariate data and identify how it is used
- Characterize the independent and dependent variables in bivariate data
- Know what is meant by positive correlation, negative correlation and no correlation
- Compare and contrast bivariate and univariate data

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Statistics 101: Principles of Statistics11 chapters | 144 lessons | 9 flashcard sets

- Frequency & Relative Frequency Tables: Definition & Examples 4:48
- Cumulative Frequency Tables: Definition, Uses & Examples 5:17
- How to Calculate Percent Increase with Relative & Cumulative Frequency Tables 5:47
- Creating & Reading Stem & Leaf Displays 4:27
- Creating & Interpreting Histograms: Process & Examples 5:43
- Creating & Interpreting Frequency Polygons: Process & Examples 5:48
- Creating & Interpreting Dot Plots: Process & Examples 7:35
- Creating & Interpreting Box Plots: Process & Examples 6:29
- Understanding Bar Graphs and Pie Charts 9:36
- Making Arguments & Predictions from Univariate Data 8:35
- What is Bivariate Data? - Definition & Examples 8:12
- Joint, Marginal & Conditional Frequencies: Definitions, Differences & Examples 9:57
- Go to Tables and Plots

- Go to Probability

- Go to Sampling

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