Parts of a graph

Task 1: Create a broken-line graph

What is a broken-line graph?

A broken-line graph is a type of graph that helps us to understand the relationship between two variables. Explore the broken-line graph titled ‘Push-Ups’.

Making a broken-line graph

Start by labelling your x-axis and y-axis using a graph paper. You may also use TVO Mathify or use another method of your choice.

The horizontal axis or x-axis is for the independent variable. The vertical axis or y-axis is for the dependent variable.

It is helpful to label your x-axis and y-axis. Explore the following example.

Often the data you are given for broken-line graphs deals with the rate at which something changes over time. This makes it easier to identify your dependent and independent variables because time is always independent. You can’t do anything to affect time, so time will be labelled on the x-axis.

Once you have determined the appropriate scales and labelled both your x-axis and y-axis, you will use your data to plot your (x, y) coordinates.

When you’ve plotted all the points, you connect them together to create a broken-line.

Your turn!

Use the data in the following table to create or describe a broken-line graph:

If you would like, you can complete this task using TVO Mathify.

Press ‘Example’ to see a sample answer.

Example

Task 2: Create a circle graph

What is a circle graph?

Circle graphs are most commonly used to show how parts are related to a whole. A circle graph is divided into parts or sections that represent a category. They are helpful to provide a representation of the data as a whole in relation to its parts. Circle graphs can help to easily compare the values of the data set.

For example, consider the following circle graph divided in four sections according to following percentages: 37%, 25%, 23% and 15%.

Creating a circle graph

Suppose we wanted to survey teenagers on their most preferred interest. We would start by choosing a sample size for our survey and then conducting the survey with that sample of teenagers. Let’s assume that the sample size is a Grade 8 class of 30 students.

We would collect our data into a table of values so that we could organize it in an efficient way to create the circle graph. The following example explains one way of creating our table of values.

Now we can use a tool such as a protractor or a digital tool to help us accurately draw that portion of the circle graph within a 360-degree circle.

We can continue this process for the rest of the interests used in the survey. Be sure to label each portion of the graph with the name of the category and its percentage value of the whole.

Your turn!

Complete the Teenagers' Preferred Interests using the following fillable and printable documents or another method of your choice.

Press ‘Answer’ to reveal the solution.

Answer

Using the table you just completed, create the circle graph using TVO Mathify or another method of your choice.

Press ‘Sample Response’ to reveal the an example of the completed table.

Sample Response

Task 3: Create a bar graph

What is a bar graph?

Like a circle graph, the data for a bar graph can be collected through a survey and organized into a table of values. Rectangular bars are then used to represent the total value for data in each category on the x-axis and y-axis. Categories are on the x-axis only. The y-axis shows frequency.

Making a bar graph

A bar graph is made using an x-axis and y-axis. Choose a scale for your y-axis based on the values of the table. Your x-axis will be used to display the different categories of data and the y-axis will be used to represent the value of the data in each category. Ensure that your bars are evenly spaced out on your x-axis and label each bar on the x-axis so that we know which category it represents. The height of each bar will represent the value or tally of each category.

Your Turn!

The data of this chart was collected from responses to the question, “What type of transportation do you use on a daily basis to get to work?” The results are listed in this table.

Use the data in the following table to create a bar graph using a method of your choice.

Press ‘Example’ to reveal a sample answer.

Example

Task 4: Create a histogram

What is a histogram?

A histogram is similar in some ways to a bar graph. However, it displays the independent variable in equal intervals of data. The x-axis will display the interval categories of the data and the bars will be the same width, but will be touching one another, unlike in a bar graph.

Creating a histogram

If you are given raw data, the most important aspect of a histogram is to create a frequency table that organizes the data into equal intervals. Then, using the frequency table, you would follow the same steps as creating a bar graph to graph the data. As previously mentioned, the x-axis will display the interval categories of the data and the bars will be the same width, but will be touching one another, unlike in a bar graph.

Your Turn!

Create a histogram from following frequency table using your notebook or TVO Mathify.

Notice that each interval is the same by having range of 20 units in each.

Press ‘Answer’ to reveal a sample answer.

Answer

Task 5: Create a scatter plot

What is a scatter plot?

Scatter plots are graphs that are used to plot a variety of (x, y) coordinates. This graph is useful when you want to investigate patterns or trends. It helps to determine whether one value increases while the other decreases, or if both decrease. Sometimes there is no apparent relationship between the two variables, and no trend or pattern can be identified.

Creating a scatter plot

In a scatter plot, it is important to organize the data set in order of value, increasing from least to greatest.

The independent variable will be on the x-axis and the dependent variable will be on the y-axis. Remember that an independent variable is one that changes naturally and does not depend on the other variable. For example, in the table below, the number of games played would be the independent variable. A dependent variable is the variable that is being studied or measured and depends upon the independent variable. For this table, the dependent variable we are studying is the number of points the player has accumulated and we are trying to identify if there is a correlation with the number of games played.

Also, after plotting the points on a scatter plot, you do not connect them with a line. Instead, a line of best fit is used when trying to determine if there are any patterns or trends in the data set. Try to have the line as close as possible to all points, and with as many points above the line as below.

Your turn!

Create a scatter plot using the data in the table. You can use TVO Mathify or any other method of your choice. Sort your data in order before you start to graph, making sure it increases from least to greatest value.

Sometimes you will be provided with a data source for the data set.

When a data source is provided, state this at the bottom of your graph.

This data was collected from the following website: https://www.tsn.ca/nhl/team/toronto-maple-leafs/statistics(Opens in a new window)

Press ‘Answer’ to reveal the sample answer.

Answer

Task 1: Which is the most appropriate graph?

Determine which type of graph (a bar graph, broken-line graph, scatter plot, histogram, or circle graph) you would use to display the data for the following purposes:

• to predict the world’s population growth in the future.
• to compare the percent of Canada’s total population with the population in each province.
• to compare the number of vehicles that pass through an intersection in four hour intervals throughout the day.

Task 2: Construct the appropriate graph based on the data

For one of the three following sets of data, analyze the data provided and determine whether you should construct a circle graph, bar graph, histogram, line graph, or scatter plot to display the data. Then create the graph using the Interactive Mathify whiteboard, graph paper or another method of your choice.

Data set 1

The table below displays the results by percent when Canadian teens were asked: “What is your top priority when it comes to global relationships?”:

What are some conclusions about Canadian teens and concerns that your graph helps you to make?

• Why did you choose your type of graph to represent this data set?

Data set 2

The speed at which a car is driven affects the amount of gasoline that the car uses. The following table displays the relationship between the speed of a car and its gasoline consumption:

• Analyze the graph to determine which speed uses the least amount of gasoline per 100 kms.
• Why did you choose your type of graph to represent this data set?

Data set 3

An individual’s average net worth total is calculated by determining the difference between what they own (such as a house or money in their retirement account) versus what they owe (for example, student loans, credit card debt). The following table records the average net worth by age:

• Analyze the graph to determine which age groups have similar net worth.
• Why might this be?
• Why did you choose your type of graph to represent this data set?

Create the graph for the data set you have chosen.

Reflection

As you read the following descriptions, select the one that best describes your current understanding of the learning in this activity. Press the corresponding button once you have made your choice.

Now, expand on your ideas by recording your thoughts using a voice recorder, speech-to-text, or writing tool.

When you review your notes on this learning activity later, reflect on whether you would select a different description based on your further review of the material in this learning activity.

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