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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.

Dot plots are a visual way to display the frequency distribution in a data set. In this lesson, you will learn how to construct a dot plot and understand its uses.

Jason is a writer for a local magazine. He is collecting research about some of the trends among college students. Jason asks the students about their favorite study snacks, what they do to relax, how many hours they spend studying and how many hours they work during the week. Jason wants to organize this information in a visual way that shows the popularity of each choice. Jason can do this by creating a dot plot.

In this lesson, learn how to create and interpret a dot plot to visually analyze your data.

A **dot plot** is a visual representation of data using intervals or categories of variables; the dots represent an observation in the data.

A dot plot can be used to analyze frequency in a data distribution. Jason's data is all about frequency. He is asking questions about the frequency, or amount, of students that select each option. A dot plot can quickly and easily tell you how popular a certain choice or item is in your data set. Take a look at the results of Jason's survey:

Notice that there are two distinct types of data. There are numbers, such as the number of study hours or the number of work hours; and there are things or categories, such as the snacks and the relaxation activities.

These two different types of data are categorical and numerical. ** Categorical data** is data that is grouped by type or object, not by numbers. **Numerical data** is information that is measurable. It is always collected in number form. Let's look at different examples of numerical and categorical data when creating a dot plot.

When creating a dot plot, first label all of the data categories. If you are working with categorical data, then this will be the options that were given in the data set. For example, Jason asked the college students which snacks they prefer. Therefore, the categories in this dot plot would be Twizzlers, Payday, Doritos, Honey Buns, Whoppers, Hershey and Skittles.

Next, place a divider line over the top of your categories. This will separate the data from the labels.

Finally, place a dot for each selection in your data set. You'll notice that there are three dots above the Twizzlers option. Therefore, three people selected Twizzlers as their favorite study snack. Each dot represents one person that selected that option.

This is Jason's dot plot for what the college students do to relax:

Notice that three students selected sleep as their preferred method of relaxation, two students selected watch TV and one student each selected go to the movies, hang out with friends and go home.

Notice that this dot plot contains number labels rather than categories:

That is because this data set is numerical data rather than categorical. Each number represents the number of hours each student spends studying each week. Each dot represents the student that chose that option. Notice that there are no dots on the zero and three labels. That means that no students selected zero or three hours as the number of hours they spend each week studying.

This is another example of numerical data:

This dot plot represents the data set when Jason asked the students how many hours they worked each week. Notice that three students selected zero, which would likely tell Jason that they do not work.

Jason is now conducting a second interview for a follow up article. His readers want to know the following information:

- Ages of 20 college students surveyed
- Number of class hours each student was taking
- Amount of money spent on books in this semester

When you are analyzing dot plots with numerical data, you can analyze the shape of that particular dot plot. Your dot plot may be symmetrical or skewed.

**Symmetry** is where the shape created is mirrored nearly perfectly across a line. In statistics, you'll find that visual representations of data will be nearly perfect, but not always perfect. That is why we define symmetry as being nearly perfect. When a data set is symmetrical, then the mean, median and mode all occur in the same point. The mean is the average. The median is the middle value. The mode is the number that appears most.

This is an example of a dot plot that is symmetrical:

Notice that the middle option is the tallest, and each side of the middle option mirrors the other side. This tells us that the mean, median and mode of Jason's data set are 20.

Okay, if your dot plot is not symmetrical, then it might be **skewed**, which is when the shape of a graph peaks to the left or the right of the center. If a dot plot shows skewness, then the data is considered either skewed left or skewed right. Distributions that are skewed to the right have fewer observations, or numbers, that are higher values.

This is an example of a dot plot that is skewed right:

Notice that more people surveyed are taking between 12 and 14 hours than taking between 15 and 18 hours.

Distributions that are skewed to the left have fewer observations, or numbers, that are lower values. This is an example of a dot plot that is skewed left:

Notice that the majority of the observations are on the right, telling us that more people have to spend between $500 and $700 on books.

You can tell if the data is skewed left or right by looking at the tail of the data.

If the tail is on the left side of the graph, then the distribution is skewed left. If the tail is on the right side of the graph, then the distribution is skewed right.

A dot plot is a great way to create a visual representation of data, especially when you are analyzing frequency in a data distribution. A **dot plot** is a visual representation of data using intervals or categories of variables; the dots represent an observation in the data. To create a dot plot, simply list your labels or categories. Then, draw a line across the top of the categories. Finally, place a dot over each category for each observation in the data set.

There are two different types of data: categorical and numerical. **Categorical data** is data that is grouped by type or object, not by numbers. **Numerical data** is information that is measurable. It is always collected in number form.

When analyzing numerical data, you'll find that the distribution may be **symmetrical**, where the shape created is mirrored nearly perfectly across a line. Data isn't always perfectly symmetrical, but it may get very close. When a data set is symmetrical, then the mean, median and mode all occur in the same point.

Your distribution could also be **skewed**, which is where the shape of a graph peaks to the left or the right of the center. Distributions that are skewed to the right have fewer observations, or numbers, that are higher values. Distributions that are skewed to the left have fewer observations, or numbers, that are lower values. You can remember this by looking at the tail of the data. Dot plots are a great way to visualize the frequency distributions in a data set, so use them if you want to display this type of data!

After you have finished with this lesson, you'll be able to:

- Define dot plot and identify the purpose of using dot plots
- Summarize how to create a dot plot
- Differentiate between categorical and numerical data
- Describe what a symmetrical dot plot looks like and what it means for the data
- Explain what is meant by skewed and what skewed left or skewed right means for the 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
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