Review of Bar Graphs
Objectives
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.
What is 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.
Parts of a Bar Graph
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 TitleThe 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 labelsEach
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 AxisThe
grouped data axis is always at the base of the bars. This axis
displays the type of data being graphed.


 Frequency Data AxisThe
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.
 BarsThe 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 Titleprovides
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 labelsThe
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.
 Barrectangular 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 axisThis axis
is the frequency axis and contains the quantity demanded given
in units of bushels.
 Grouped Data AxisSince
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:
 Frequency Data AxisThe 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. 

Analysis of the Bar Graph
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.
Example
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

Answers to Example
 Which course has the most students
enrolled in it?
Econ has the most students
enrolled.
 Order the courses by enrollment from
lowest to highest.
From lowest to highest: Physics,
Chem, Psych, Poly Sci, Econ.
 The enrollment in Econ is approximately
how many times bigger than the enrollment in Chem?
The enrollment is approximately
two times larger.
 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.
 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.