## Chapter 2Graphs

"Education is the most powerful tool we can use to change the world."-Nelson Mandela

Graphs are an essential part to learning mathematics. Graphs show data and allow people to understand that data. Their are many different types of graphs that will be taught in this chapter; circle graphs, bar graphs, line graphs, and scatter plot graphs. The goal of this chapter is to teach each one of these graphs and for students to understand how to read these graphs. They will also be able to know how to create each graph based on data they are given. They will learn each step in order to make each graph.

The objective of each section is to show these graphs and teach about the current history and past history at Saint Joseph's University. Another objective is for the students to be able to read, understand, and create their own circle, bar, line, and scatter plot graphs.

Saint Joseph's University, Barbellin Hall/Sweeney Field

### Section 1: Circle Graphs

This circle graph is showing the Business Majors at Saint Joseph's University. Along with each major this university provides, it is also showing how many other areas you can go into under that major. Business is a very popular major at this university and as you can see from this graph, there are many different business majors and minors that students can go into for their academics.

This circle graph shows certain data that was collected. Once the data was collected, the graph was then made. Circle graphs are used to show the results of data in a proportional manner. You can see the percentages of each result and how it compares to other results.

Vocabulary to know:

Circle Graph- A circle chart divided into sections which represent a value out of the overall value.

Percentage- Any proportion or share in relation to a whole.

Data- Facts and statistics collected together for reference or analysis.

Average- Obtaining the result by adding all of the quantities together and then dividing by how many quantities there are.

Degree- A unit of measurement of angles.

This video is a good quick lesson on how to make circle graphs. You can watch this for more help! The following are detailed steps in order to make this circle graph.

To read a circle graph, you look at each category and see what percentage of the circle it has. This is out of 360%, because a circle is 360 degrees. You can see how much each category is by comparing them to each other category.

Step 1: Collect data and have the data separated into categories that can be split up.

Step2: Once the data is split up, take each category and their values (numbers) and order them from the largest to the least. You will need to take the average of them all to see how much each category will take up of the graph. For example, the circle graph shown of the business majors would be each number of majors and their minors, which is 17. After you have the total of the whole circle graph, you will use that number, 17 in this case, and divide each major by 17 to get the average of each major. For Marketing, you will do 4 (value of marketing) divided by 17 (total values for the graph). This equals 0.23529. After doing this for each category/major, you will now get a percentage for each major. You will take each percentage and multiply each by 360 degrees because a circle is 360 degrees. For Marketing, you take the 0.23529 and multiply that by 360, which equals 84.7%. That is how much of the graph, out of 360%, is marketing. Once you have each percentage, you will take a protractor and measure each degree that you have gotten for each value.

Step 3: You make each part of the circle graph and label each part with what it represents. Make sure to have a title for the graph as well. You can color code the chart so it is easier to read and see each different type of data.

This is another video explaining pie charts.

#### Questions:

1.) What do you need to divide each value by in order to get a percentage of the circle graph?

2.) Make a circle graph with the following data of students favorite ice cream flavors: Chocolate-6, Vanilla-10, Mint Chocolate Chip-12, Rocky Road-4, Cookies and Cream-5

### Section 2: Bar Graphs

Many objects can look like graphs too!

Bar graphs are used by many people to easily show the results of some type of experiment. Using bar graphs, it makes it easier to see the comparison between different results.

Vocabulary to know:

Bar Graph- A graphical display of data using bars or different heights.

Y-Intercept- The axis that is vertical of a system of coordinates.

X-Intercept- The horizontal axis of a system of coordinates.

Interval- The consistent space in between numbers.

Below is an example of a bar graph that you can look at. You can use this website to make your own graphs.

This bar graph shows the Men's Varsity sports teams at Saint Joseph's. As you can see, there are many teams and many students that play on each team. Sports are a great extra-curricular activity and a great way to make friends and stay in shape! Sports are a big part of this university and are important to many students.

SJU sports teams

Bar graphs are used for data that need to be compared. The data is separated into categories and you can compare each category separately.

In order to read a bar graph you look at the x-axis and that is your category you are trying to find the value of. You look to see where the bar goes until and look at the y-axis to see what value it is at. This is your data that was graphed.

Each category has a certain value and that value is what is being shown by the bar graph. To start making a bar graph, you need the data and to separate them into categories. Once you have your categories, see how many is in each and that is the value. Once you have the values for each category, you will begin to make the bar graph.

Start with drawing your x-axis (horizontal) and y-axis (vertical) and label them with what you are graphing. Shown below.

Next, look at your values and try and figure out what interval you will go by on your graph. This will be on your y-axis, numbers going from 0 to your highest value. Once you have your interval, start labeling the graph with the values on the y-axis.

Now, label your x-axis with your category name or with what you are graphing. You may need to find an interval for this axis as well.

After your graph is completely labeled, you can now start to draw the bars of data. Start from the left and see what your data is showing you, and draw a bar where the value is (y-axis). Continue this for each category and make sure all of your data is showing on the graph.

#### Questions:

1.) Explain the difference between the x-axis and y-axis.

2.) What are bar graphs used for?

### Section 3: Line Graphs

Line graphs are used for seeing a relationship of two variables over periods of time. They show the change over time for a quantity. Below is an example of a line graph of Saint Joseph's enrollment over the past 17 years. You can see the increase in students as the years go on. Starting in 2000 there were just about 3,647 students attending SJU and now in 2017 there are about 5,395 students. This is a great graph to show this type of data.

Vocabulary to know:

Correlate- Having a mutual relationship or connection, where one thing affects or depends on another.

Line Graph- Shows how much a quantity changes over time.

Plot- A point to represent a location on a graph.

This video is a little introduction for understanding line graphs and how to make them.

A line graph shows relationships so reading this graph is a little different than a circle graph or bar graph. When reading a line graph, you need to look at the x-axis and see the category that is being shown and follow the line on the graph. This line is representing the change of that category over time. You look at both axes and the point that is shown between them both. Start at a point and follow that to the x-axis and then y-axis to see what the category is and what the value is.

In order to make a line graph, you do the same as a bar graph and make the axes first. Make the x-axis and y-axis and label them both. Your value number intervals will go on the y-axis and your year or category will be on the x-axis.

Once you have these axes labeled, you will now start to plot your data. You will look at the x-axis or y-axis and follow the data point to your data point on the other axis. When they meet, that is where you place a dot. You will continue this for all of your data points and once you are done, you will create a line connecting all of the dots. The line will start with the first dot and go in order of the data from left to right.

Now that you have your line, the graph is finished. Even though it is finished, you can read the graph and decide wether it is increasing, decreasing, or remaining the same. When a line is remaining the same, it is a flat line across the graph. A line that is increasing (Figure 1) is a line moving from the lower left of the graph to the upper right of the graph. A line that is decreasing (Figure 2) is going from the upper left of the graph to the lower right. See below for the visuals of these two line graphs.

Figure 1: Increasing
Figure 2: Decreasing

The following is another video to watch on how to make a line graph.

#### Questions:

1.) Why are line graphs sometimes referred to as correlating graphs?

2.) What is the order to connecting the dots of data?

### Section 4: Scatter Plot Graphs

Scatter plot graphs are used to represent how much one variable is affected by another. It shows a relationship between two variables and their correlation, which can be positive, negative, or no correlation. These graphs are similar to line graphs in which they correlate with each other.

Vocabulary to know:

Scatter plot graph- A graph that has points that show the relationship between two sets of data.

Positive correlation- This exists as both variables are decreasing or when both variables are increasing.

Negative correlation- This exists when one variable is increasing and the other is decreasing.

Figure 1

Figure 1 graph shows height and weight and how they relate with each other. It shows that when someone is taller, they tend to weigh more than someone who is shorter. To see this, you look at a dot and see where it is located at the x-axis and y-axis and that is what your dot is representing. This is an example of a positive correlation because the points are going from bottom left to top right, moving upwards.

Figure 1 represents height versus weight and is showing a positive correlation. To make a scatter plot graph, it is similar to a line graph. First, you need to make and label your axes the same way you did for a line graph and bar graph. Get the x-axis labeled with your one variable and your y-axis labeled with your other variable. Since these two correlate, when you look at your data, there will be one data point that represent both axes. For example, looking at the scatter plot of Height vs. Weight, look at the point where the dot is at 5'3 and 130. This one point correlates with both of the axes. It is showing that a person that is 5'3 weighs 130 pounds. When you get each data point on the graph and match them with the axes, your graph is complete.

Scatter plot graphs will have a positive correlation, negative correlation, or no correlation. The graph in figure 1 shows a positive correlation. This is because the data points are moving in the direction of upwards toward the top right of the graph. A negative correlation is when the dots are in a clustered line going from the top left of the graph to the bottom right of the graph. No correlation is when the dots are scattered and are in no formation all over the graph.

The video below can also help with understanding and making a scatter plot.

The following video is explaining scatter plots and correlations.

### Practice Test:

1.) Is this line graph increasing, decreasing, or remaining constant?

2.) Given this data, create a bar graph:

Flowers- 4 tulips, 7 daisies, 12 roses, 10 white roses, 10 carnations, 9 gingers, 22 orchids.

3.) Draw an example of a negative correlation for a scatter plot graph. (Just the graph, you do not need to use data.)

4.) What type of graph should be used when you are trying to compare different categories and their percentages?

5.) For a circle graph, what do you multiply each value by in order to get your percentages for each category? Explain why.

6.) If someone is making a scatter plot graph, explain the data that they are graphing and why they need to use a scatter plot graph.

7.) What is a line graph best used to show? Explain why.

The following two questions relate to Figure 1.

8.) When the speed is 30 m/s, what time is it at?

Figure 1

9.) When the time is on 2 seconds, about what speed is it going? (Do not forget units!)

Credits:

Created with images by jimmiehomeschoolmom - "bar graph of traffic" • SJU Undergraduate Admissions - "Barbelin2" • PublicDomainPictures - "achievement bar business" • Search Engine People Blog - "cacherank bar chart" • blprnt_van - "Twittergrams: Morning Tweet Graph" • SJU Undergraduate Admissions - "New live greater lanyards" • Tom Anderson - "Quality vs Slashiness"

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