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Bar Graph

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Source: Normal Distribution Graph, Public Domain: http://commons.wikimedia.org/wiki/File:The_Normal_Distribution.svg Bar graph created by Jonathan Osters

This tutorial is going to teach you how to construct and interpret bar graphs. Qualitative, which is categorical data, can be displayed visually in a bar graph. This is not the only way to display categorical data, but it's one way. And what it does is it compares the number of values in each category.

So suppose we have these courses in a college and these number of students in each course. What we do is we begin by drawing a horizontal axis and labeling the categories beneath it. We could also label it on the vertical axis and label the categories from top to bottom. But we have it set up this way. So we wrote economics, biology, chemistry, and visually separated them.

Then, we're going to create a vertical axis with frequency on it. The highest number that we have is 444. That's why I chose to have my frequencies go up to 500. Finally, you set up a bar that goes up to the number that corresponds to that category. So economics will have a bar that goes up to 321. It will peak out right about here. Biology will go all the way up to almost 450. The full bar graph looks like this.

We can also use relative frequency. Relative frequency shows how much of the whole this is. So for instance, biology has over 20% of the students, between 20% and 25% of the students. This is assuming that no student is in both biology and chemistry. This might not be true, in which case relative frequency might not be the way to go.

Notice that in the previous example with counts, and in this example with relative frequency, the shape and size of the bars didn't change. The only thing that changed was the vertical axis and what it was measuring.

Another example-- suppose that we have data in a table like this. We can create multiple bar graphs on the same set of axes and compare them by category. Suppose that this was the results of a sample of 100 students that I took. And I wanted to know about their work habits. I wanted to know if they were male or female, and whether they had a job, not at all, during summer only, or had a job all year long.

One way to display these in a bar graph would be to break it up by male and female and choose green to be males and yellow to be females. And break the horizontal axis into no job, summer only, and job all year. And create both bar graphs, side-by-side, within each category.

The males had 25 that had no job. The females had 28 that never had a job, and et cetera. Now that's one way to do it. The other way would be to flip-flop which category means colors and which category goes on the axis. I could put male and female on the axis and have the job status be the colors. In that case, it would look like this.

Both of these tell me some interesting things. This graph tells me that both males and females have a tendency mostly to have no job, then have a summer job, then have a job all year. That's true for both males and females. What this one tells me is that males are more likely than females to have a job all year and in summer, and a little bit less likely than females to never have had a job.

And so to recap. Bar graphs are a nice way to view the counts in a category for a qualitative data set. We can use frequencies or we can use relative frequencies, if there's no overlap between the categories. And we can show how each category relates to the others. We can also put multiple bar graphs on the same set of axes.

Good luck. And we'll see you next time.