Bar Charts and Pie Charts

Bar charts and pie charts are commonly used to describe categorical data. If our intent is to draw attention to the frequency of each category, then we will most likely draw a bar chart. If our intent is to emphasize the proportion of each category, then a pie chart is a likely choice. In a bar chart, the height of a rectangle represents this frequency. There is no need for the bars to touch.

An interesting and useful extension to the simple bar chart can be used when components of individual categories are also of interest. For example, Table 5 shows the number of students enrolled in three business majors for two different years at one small private university.

This information can be shown in a bar chart by breaking down the total number of students for each year so that the three components are distinguished by differences shading as shown in Figure 2. This kind of chart is called a component or stacked bar chart. Figure 3 shows the same data in a bar chart that is called a cluster or side-by-side bar chart. Both graphs allow us to make visual comparisons of totals and individual components.  In this example, it appears that the increase in enrollment between 2000 and 2005 was fairly uniform over the three majors.

Table 8: Student Enrollment in Three Business Majors, 2000 and 2005

Major	2000	2005
Financing	160	250
Marketing	140	200
Accounting	100	150

Figure 2: Finance, Marketing and Accounting Majors, 2000, 2005 (Component Bar Chart)

If we want to draw attention to the proportion of frequencies in each category, then we will probably use a pie chart to depict the division of the whole into its constituent parts. The circle (or “pie”) represents the total, and the segments (or “pieces of the pie”) cut from its center depict shares of that total. The pie chart is constructed so that the area of each segment is proportional to the corresponding frequency.

Figure 3: Finance, Marketing, and Accounting Majors, 2000, 2005 (Cluster Bar Chart).

Example: Travel Expenditures
A university administrator requested a breakdown of travel expenses for faculty to attend various professional meetings.  It was found that 31% of the travel expenses were spent for transportation costs, 25% for lodging, 12% for food, 20% for conference registration fees; the remainder was spent for miscellaneous costs. Graph this data.

Figure: Travel expenses (Pie Chart)