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Visually Representing Numerical Data | Splitting up the Whole with Pie Graphs | Showing the overlap with Venn Diagrams | Comparing Categories with Bar Graphs | Seeking Trends with Line Graphs | Showing Orderly Data with Histograms | Functions as Graphs in the Coordinate System | Summary Comparing Categories with Bar Graphs
Bar graphs are used to quickly demonstrate "which type had how much." Unlike a pie graph, there is no implication that a "whole" is being split up. For example, if I want to compare the average incomes of people who work in fire departments, police departments, and public schools, it would be very appropriate to use a bar graph – its not like these are the only three types of workers or that their average salaries are the only salaries that exist. A bar graph has a bar for each of the types, or categories, being considered, so this bar graph would have one bar for police, one for fire, and one for school. Each bar’s length is determined by the information given, with larger numbers associated with larger salaries. If we find out that cops earn $62,000, firefighters earn $58,000, and teachers earn $45,000, one possible bar chart for that data follows:
We can see that there’s not much difference between the salaries of police and firefighters but there’s some gap for teachers. One very interesting thing about visually representing numerical data is that we can manipulate the graph to influence the viewer. For example, if I was an advocate for teachers and I wanted to emphasize the fact that their salaries were much lower, I could use the following bar graph:
Isn’t that a much more dramatic presentation of the salary differences? All I had to do was to manipulate the scale of the numerical data, giving a scale from 40 to 65, instead of the original 0 to 70. When you view numerical data, always be sure to be a little skeptical and realize that although the numbers can’t lie to you, the way they are presented can certainly mislead or influence you. Bar charts can be useful in making comparisons within categories. One example would be to take the data on salaries given above and break it down by the gender of the worker. If I find out that in police departments, men earn an average of $64,000 while women earn $52,000, in fire departments, men earn $61,000 and women earn $52,000, and in public schools, men earn $46,000 and women earn $44,000, I have several different ways to draw a bar chart to represent that data. I might use the following graph to emphasize that females are earning less than males in all three professions:
If I wanted to focus on the fact that teachers are paid less than cops and firefighters, regardless of gender, I might organize my data differently:
Notice that in both cases, I’ve kept the scale that emphasizes the salary differences. Also note that in both of the previous graphs, the same 6 heights are used for the bars – only the way they are grouped together changes. There are some other slightly more complex ways of doing bar graphs, but the above two, by category, and by category with comparisons, are the important ones. Below are some other types of bar graph with very brief explanations for each.
Three-dimensional bar graph.
Horizontal bar graph – exactly the same data but presented sideways.
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