Example

An insurance company determines vehicle insurance premiums based on known risk factors. If a person is considered a higher risk, their premiums will be higher. One potential factor is the color of your car. The insurance company believes that people with some color cars are more likely to get in accidents. To research this, they examine police reports for recent total-loss collisions. The data is summarized in the frequency table below.

Color	Frequency
Blue	25
Green	52
Red	41
White	36
Black	39
Grey	23

example

Using our car data from above, note the highest frequency is 52, so our vertical axis needs to go from 0 to 52, but we might as well use 0 to 55, so that we can put a hash mark every 5 units: Notice that the height of each bar is determined by the frequency of the corresponding color.  The horizontal gridlines are a nice touch, but not necessary.  In practice, you will find it useful to draw bar graphs using graph paper, so the gridlines will already be in place, or using technology.  Instead of gridlines, we might also list the frequencies at the top of each bar, like this: The following video explains the process and value of moving data from a table to a bar graph. https://youtu.be/vwxKf_O3ui0

Examples

Transforming our bar graph from earlier into a Pareto chart, we get: The following video addressed Pareto charts. https://youtu.be/Tsvru8DPxBE

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In a survey[footnote]Gallup Poll. March 5-8, 2009. http://www.pollingreport.com/enviro.htm[/footnote], adults were asked whether they personally worried about a variety of environmental concerns. The numbers (out of 1012 surveyed) who indicated that they worried “a great deal” about some selected concerns are summarized below.

Environmental Issue	Frequency
Pollution of drinking water	597
Contamination of soil and water by toxic waste	526
Air pollution	455
Global warming	354

This data could be shown graphically in a bar graph:

examples

For our vehicle color data, a pie chart might look like this: Pie charts can often benefit from including frequencies or relative frequencies (percents) in the chart next to the pie slices. Often having the category names next to the pie slices also makes the chart clearer. This video demonstrates how to create pie charts like the ones above. https://youtu.be/__1f8dKh6yo

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The pie chart below shows the percentage of voters supporting each candidate running for a local senate seat. If there are 20,000 voters in the district, the pie chart shows that about 11% of those, about 2,200 voters, support Reeves. The following video addresses how to read a pie chart like the one above. https://youtu.be/mwa8vQnGr3I

example

A labor union might produce the graph to the right to show the difference between the average manager salary and the average worker salary. Looking at the picture, it would be reasonable to guess that the manager salaries is 4 times as large as the worker salaries – the area of the bag looks about 4 times as large. However, the manager salaries are in fact only twice as large as worker salaries, which were reflected in the picture by making the manager bag twice as tall. This video reviews the two examples of ineffective data representation in more detail. https://youtu.be/bFwTZNGNLKs

example

Compare the two graphs below showing support for same-sex marriage rights from a poll taken in December 2008[footnote]CNN/Opinion Research Corporation Poll. Dec 19-21, 2008, from http://www.pollingreport.com/civil.htm[/footnote]. The difference in the vertical scale on the first graph suggests a different story than the true differences in percentages; the second graph makes it look like twice as many people oppose marriage rights as support it.