Review of Circle Graphs

After completing this unit, you should be able to:

• Identify the title of a circle graph.
• Identify the sectors of a circle graph.
• Identify the sector labels of a circle graph.
• Critically read circle graphs, particularly to compare parts to a whole.

Circle graphs, also called pie charts, are a type of graph used to represent a part to whole relationship. Properties of Circle Graphs:

• They are circular shaped graphs with the entire circle representing the whole.
• The circle is then split into parts, or sectors.
• Each sector represents a part of the whole.
• Each sector is proportional in size to the amount each sector represents, therefore it is easy to make generalizations and comparisons.

In this unit we will review how to read a circle graph. An example of a circle graph is given below.

Revenue Sources for the Federal Government

When reading this circle graph we look for the following pieces of information: the graph title, individual sectors and their relative sizes, and the sector labels (one for each sector). Let's take a closer look at each of these.

Graph Title--A graph title gives an overview of the information displayed in the graph. The title is given at the top of the graph. Sectors--Each sector represents one part of the whole. The size of each sector represents its fraction of the whole. Sector Labels--The label of each sector indicates the category of information it refers to, and may also give numeric data (often a percentage) so we know the size of each sector.

Let's use the circle graph given here as an example of how to get information from a circle graph. Looking at the elements of this graph we find:

• Graph Title--The title gives an overview of the information displayed in the graph.
  The title of this graph is:
  Revenue Sources for the Federal Government

  We would expect the graph associated with this title to contain the names of different sources of revenue for the federal government, with some information on the relative amounts from each revenue source.

   

• Sectors--Each sector represents one part of the whole.

  The graph below contains four different sectors. This means the graph displays four different sources of revenue. The largest sector is a little less than half of the whole circle. There is another source that is also relatively large, and then there are two smaller sources of revenue.

  
  
• Sector Labels--Sector labels indicate the category of information represented in the sector and may also give numeric data (often a percentage).

  The graph has a label for each sector. Each label shows what type of revenue it corresponds to, and the percentage of the whole for that sector. From the graph we can see:

  The largest sector, 45% of the total revenue, comes from individual income tax. The smallest sector, 8%, comes from sources listed as other. Individual income tax provides four and a half times as much income as corporate income tax Revenue Sources for the Federal Government

We determine this by finding the ratio of Individual Income Tax to Corporate Income Tax. From the circle graph we know this is 45:10, which is 4.5:1. (If you have any problem understanding ratios you should review the units on ratios and proportions.)

When we are presented with a circle graph, we want to be able to make statements about the sectors of the graph, relative to one another, and relative to the entire circle. From this one example, we can see the amount of information we can get, and all from looking at one circle graph! Now, let's try an example of reading a circle graph and answering specific questions about the data presented.

Based on the circle graph given below, answer the following questions.

What type of information is being presented on this graph? If the total spending is $50,000, how much money was spent on highways? Approximately how many times the amount of spending on highways is spent on education? Approximately what fraction of the total expenditures are spent on highways and public welfare combined?

Expenditures for State and Local Governments

Below are the answers to the example above. To view the detailed soluntion to a specific
question, click on that question, or you may also what the vew the solution from the beginning by clicking the link: [view detailed discussion of the solution]

1. What type of information is being presented on this graph?
   The graph title is Expenditures for State and Local Governments. The circle is cut into four sectors, each representing one category of expenditures, with the percentage of the total for each category.
   
2. If the total spending is $50,000, how much money was spent on highways?
   Money spent on highways is $3,500
   
3. Approximately how many times the amount of spending on highways is spent on education?
   State and local governments spent approximately five times more on education than on highways.
   
4. Approximately what fraction of the expenditures are spent on highways and public welfare combined?
   Approximately 1/5 of the total is spent on highways and welfare combined.
   

Now try the practice for this unit. When you feel you are ready, move on to the next unit on construction circle graphs.

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