Review of Bar Graphs

After completing this unit you should be able to:

• Identify the bar graph title.
• Identify labels for the bar graph axes.
• Identify information given by a designated bar
• Make statements about data trends from a bar graph.

A bar graph is a visual display used to compare the amounts or frequency of occurrence of different characteristics of data. This type of display allows us to:

• compare groups of data, and
• to make generalizations about the data quickly.

This unit will introduce basic bar graphs, how to read bar graphs. An example of a bar graph is given on the right. When reading a bar graph there are several things we must pay attention to: the graph title, two axes, including axes labels and scale, and the bars. Since bar graphs are used to graph frequencies or amounts of data in discrete groups, we will need to determine which axis is the grouped data axis, as well as what the specific groups are, and which is the frequency axis.

Price of Corn versus Quantity Demanded

The height of the bars are particularly important since they give us information about specific data.

Now let's look at the components of a bar graph individually. There is a lot of information in this section so you may wish to jot down some short notes to yourself.

Graph Title--The graph title gives an overview of the information being presented in the graph. The title is given at the top of the graph. Axes and their labels--Each graph has two axes. The axes labels tell us what information is presented on each axis. One axis represents data groups, the other represents the amounts or frequency of data groups. Grouped Data Axis--The grouped data axis is always at the base of the bars. This axis displays the type of data being graphed.

• Frequency Data Axis--The frequency axis has a scale that is a measure of the frequency or amounts of the different data groups.
• Axes Scale-- Scale is the range of values being presented along the frequency axis.
• Bars--The bars are rectangular blocks that can have their base at either vertical axis or horizontal axis (as in this example). Each bar represents the data for one of the data groups.

Now let's look more closely at how the elements of a bar graph help us get a handle on the information presented in a graph. While there are several ways to do this, here we will present one way to get an overview of a graph using the graph above.

• Graph Title--provides an overview of the type of information given in the bar graph.
  For the bar graph given, the title indicates that we are looking at data on:
  Price of Corn versus Quantity Demanded

Axes and their labels--The axes labels tell us what information is presented on each axis. One axis represents data groups is labeled Price per Bushel. The other axis is labeled Quantity Demanded. Bar--rectangular blocks that can have their base at either the vertical axis or horizontal axis. For this graph we can see that the base of the bars are on the horizontal axis. This means that the grouped data axis is the horizontal axis and the frequency axis is the vertical axis.

• Vertical axis--This axis is the frequency axis and contains the quantity demanded given in units of bushels.
• Grouped Data Axis--Since the the grouped data axis is always at the base of the bars, the grouped data axis is the horizontal axis. The axis label tells us that along the horizontal grouped data axis we have the price per bushel, with each data group being a different dollar amount from $1 to $5.
  Two important pieces of information we must determine are the:
  • type of data being counted, and
  • how the data is grouped.
• Frequency Data Axis--The scale is the range of frequency values shown on the graph. The span of values represented is determined by the lowest and greatest values you wish to include on the graph.

  When looking at this axis, look to see where the range begins and ends, as well as at the interval between tick marks. For a further discussion on scale, read the section on Scale. The vertical axis is the quantity demanded given in units of bushels. In this case, the frequency scale goes from 0 to 80, and uses an interval of units of 10. The frequency of our data groups range over nearly the entire scale so we are able to get a good picture of our data.

Now that we understand all the pieces that go into a bar graph we are ready to discuss the analysis of a bar graph. As you can see, being able to do some data analysis of bar graphs can be more complicated then it initially looks. Keep in mind that parts of this process, such as doing an overview of the titles of the table and axes, are done quickly. The parts that may take more practice are determining the type of data groups being presented, whether the scale is appropriate, and making comparisons between groups of data. For example, in the bar graph Price of Corn versus Quantity Demanded, what information is being displayed in this bar graph?

Price of Corn versus Quantity Demanded

If we begin by looking at the axes we notice that the data groups are ordinal, going from a low of $1 to a high of $5. We also may notice that there does not appear to be any trend in going from low to high values of Price per Bushel. One thing we can see here is how difficult it can be to determine exact amounts from a bar graph. For example, at a price per bushel of $3, it is hard to tell whether the quantity demanded is 19, 20, or 21. While specific information of data groups may be difficult to determine, we can make a quick comparison. Now let's take a look at an example of analyzing a bar graph.

Given the graph at right, below, answer the following questions.

Which course has the most students enrolled in it? Order the courses by enrollment from lowest to highest. The enrollment in Econ is approximately how many times bigger than the enrollment in Chem? Approximately how many students were enrolled in the course with the most students? Approximately how many more students are in Econ than in Physics?

Enrollment in Introductory Courses at Union University

1. Which course has the most students enrolled in it?
   Econ has the most students enrolled.
2. Order the courses by enrollment from lowest to highest.
   From lowest to highest: Physics, Chem, Psych, Poly Sci, Econ.
3. The enrollment in Econ is approximately how many times bigger than the enrollment in Chem?
   The enrollment is approximately two times larger.
4. Approximately, how many students were enrolled in the course with the most students?
   There are approximately 340 students enrolled in the course with the most students, which is Econ.
5. Approximately how many more students are there in Econ than in Physics?
   There are approximately 200 more students in Econ than in Physics.
   
   (You can also view the Detailed Discussion of this example.)

When you are ready, try the practice for this unit. When you feel confident you understand the material presented in this unit you should move onto the next unit.

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