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Statistics 101: Principles of Statistics11 chapters | 141 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.

Scatterplots are a great visual representation of two sets of data. In this lesson, you will learn how to interpret bivariate data to create scatterplots and understand the relationship between the two variables.

Liam is a soccer player getting ready to try out for his varsity high school team. Each night he will scrimmage with a different group of players. Liam tracks his practice time during the day and the number of goals he makes each night.

Liam wonders if there is a way to visually display this information and to analyze the relationship between the number of hours he practices and the number of goals he makes. Liam can do this by creating a scatterplot. A **scatterplot** is a graph of ordered pairs showing a relationship between two sets of data. In this lesson, you will learn how to interpret bivariate data to create scatterplots.

When creating a scatterplot, you will be looking at two sets of data. This data is known as **bivariate data**, which are two sets of variables that can change and are compared to find relationships.

Take a look at this graph:

Notice that there is an *x*-axis (the horizontal line in a graph) and a *y*-axis (the vertical line in a graph). Each point on this graph is called an ordered pair, which is two numbers that indicate a location on the coordinate plane. The first number is the location on the *x*-axis, and the second number is the location on the *y*-axis.

This graph represents the relationship between the number of hours Liam practiced and the number of goals he made each night during the scrimmage. This is called a **correlation**, which is the relationship between two variables or sets of data. Notice that the more hours Liam spends practicing, the more goals he makes that night.

Each ordered pair is the number of practice hours and the number of goals. This ordered pair represents the number of hours Liam spent practicing on Tuesday and the number of goals he made Tuesday night. When you are creating a scatterplot, each set of variables must have something in common. In this case, the variables have Liam and the day Liam practiced in common. We can't create an ordered pair out of someone else's practice hours and Liam's number of goals. They don't have anything in common!

Ideally, when you create a scatterplot, you want to identify the independent and dependent variables in the scenario. An **independent variable** is a condition or piece of data in an experiment that can be controlled or changed. In this case, the independent variable would be the number of hours Liam spent practicing. Liam has total control over his practice time. 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.

In this case, the dependent variable would be the number of goals that Liam makes during the game. Now, you could make the argument that Liam has control over the number of goals he makes and therefore the goals would also be an independent variable, and this is true. However, Liam can't simply make a wish to improve his performance, right? He has to practice to get better! Therefore, the only way Liam can control his performance and make it better is to increase his practice time, and that is where we get the relationship between the independent and dependent variables. Make sure, that when you are creating a scatterplot, to put the independent variable on the *x*-axis and the dependent variable on the *y*-axis.

To create a scatterplot, you want to take a close look at your two sets of data. Liam is now tracking two different sets of data: his practice time and his endurance. He wants to see how long he can run each night after practicing in the morning. Take a look at the table Liam has created:

Can we make a scatterplot from this data? Absolutely!

First, create ordered pairs from the two variables. In this case, we want to put the practice hours on the *x*-axis and the endurance time on the *y*-axis. Therefore, the first set of numbers, 2 and 10, would make up our first pair and so on and so forth.

Next, plot each point on your graph. This will show if there is a correlation between your two variables. If the points seem to move in the same direction and are close together, then they likely will have a correlation. Notice that most of the points increase both vertically and horizontally:

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 together. If the graph sloped downward, like the bivariate data in the graph below, then you have a data set with a **negative correlation**.

If there is no relationship between the numbers, as shown in the graph below, then the data set has no correlation. We will talk about this more in later chapters, so be sure to check out the other lessons in this chapter!

A **scatterplot** is a graph of ordered pairs showing a relationship between two sets of data. When creating a scatterplot, you will have two sets of information, known as **bivariate data**, which is two sets of variables that can change and are compared to find relationships.

Each point on this graph is called an **ordered pair**, which is two numbers that indicate a location on the coordinate plane. The first number is the location on the *x*-axis, and the second number is the location on the *y*-axis. To create a scatterplot, first create ordered pairs from the two variables. Put the **independent variable** on the *x*-axis and the **dependent variable** on the *y*-axis.

Next, plot each point on your graph. This will show if there is a correlation between your two variables. If the points seem to move in the same direction and are close together, then they likely will have a **correlation**.

After you've completed this lesson, you'll be able to:

- Define scatterplot and bivariate data
- Explain how to create a scatterplot of bivariate data
- Differentiate between independent and dependent variables
- Describe the different types of correlation that can be seen in a scatterplot

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Statistics 101: Principles of Statistics11 chapters | 141 lessons | 9 flashcard sets

- Go to Probability

- Go to Sampling

- Creating & Interpreting Scatterplots: Process & Examples 6:14
- Analyzing Residuals: Process & Examples 5:30
- Interpreting the Slope & Intercept of a Linear Model 8:05
- The Correlation Coefficient: Definition, Formula & Example 9:57
- The Correlation Coefficient: Practice Problems 8:14
- How to Interpret Correlations in Research Results 14:31
- Correlation vs. Causation: Differences & Definition 7:27
- Interpreting Linear Relationships Using Data: Practice Problems 6:15
- Transforming Nonlinear Data: Steps & Examples 9:25
- Coefficient of Determination: Definition, Formula & Example 5:21
- Pearson Correlation Coefficient: Formula, Example & Significance 6:31
- Go to Regression & Correlation

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