11.3: Pie Charts

Pie charts are a visual method for displaying the frequency distribution of a variable measured on a nominal or ordinal scale. Consider a variable with a corresponding frequency distribution that includes the percentage of observations equal to each of the possible outcomes of the variable. One way to visually represent these percentages is to construct a circular figure that has been divided into pieces where the area of each piece is proportional to the percentage from the frequency distribution for each possible outcome of the variable. The corresponding chart resembles a pie that has been cut into pieces of various sizes.

Definition: Pie Chart

A pie chart of a frequency distribution is a circular graph whose “slices” corresponds to the possible outcomes for a qualitative variable. The area of the slice compared to the area of the entire pie is equal to the percentage (or relative frequency) of that response.

Earlier we looked at a survey on gender discrimination. The responses to the question are scored on a five-point Likert scale, and the frequency distribution for the first question is given in Table 11.1. A pie chart of the corresponding frequency distribution is shown in Figure \(\PageIndex{1}\). In the figure we can observe a circle with slices labeled for each of the five possible observed responses. The chart has been constructed so that the area of each slice, relative to the area of the entire circle, is the same as the ratio of the corresponding frequency of the response relative to the number of responses. For example, from Table 11.1 we can observe that the number of individuals who responded with a 1 to the first question is 5, which is 20% of all the responses to the question. Therefore, when the pie chart was constructed, it was done so in such a way that the area of the slice that is labeled 1 takes up 20% of the entire area of the circle. Note that the areas labeled for responses 1 and 3 are equal. This is because both responses have the same frequency. From a pie chart one can quickly see what responses had high or low frequencies. If the slices are all about the same size, then all the frequencies are very similar. From Figure \(\PageIndex{1}\) we can observe that all the frequencies are similar, but response 5 has a higher frequency than the other responses.

Figure \(\PageIndex{1}\): Pie Chart for Question 1 in Table 10.5. The numbers on the pie chart refer to the responses from the question (Public domain image created by Alan M. Polansky).

In some cases, you will see pie charts that have been enhanced for visual appeal. These enhancements are often unnecessary and, in some cases, can be used to manipulate the visual conclusions that one might make from looking at the chart. For example, some pie charts are given a three-dimensional representation as a disk. The pie chart in Figure \(\PageIndex{2}\): is a three-dimensional pie chart representing the same frequency data as was used to create Figure \(\PageIndex{1}\). Because of the illusion of perspective as well as the thickness of the disk used to represent the pie, the areas for responses 4 and 5 seem overrepresented by the amount of area that the eye perceives in the plot. Consequently, the remaining responses are underemphasized since they are at the rear of the disk.

Figure \(\PageIndex{2}\): Three-dimensional pie Chart for Question 1 in Table 10.5. The numbers on the pie chart refer to the responses from the question (Public domain image created by Alan M. Polansky).

Often it is beneficial to list the relative frequencies of percentages for our categories on the pie chart. This is because categories can have an extremely small number of responses, and we would like to know which has the smallest. To do this, you list the category's name (in our case, 1 through 5 for the possible responses), then the percentage or relative frequency associated with that value. This is displayed in Figure \(\PageIndex{3}\). Notice that the areas remain unchanged. You can also list the percentage in the pie slice itself.

Figure \(\PageIndex{3}\): Pie Chart for Question 1 in Table 10.5. The numbers on the pie chart refer to the responses from the question. The percentage of each response is also indicated (Public domain image created by Alan M. Polansky).

Pie charts are not typically the best method for displaying frequency information, though they can be useful in some contexts. Bar charts provide a much easier way to compare frequencies as the relative heights of the bars are easy to distinguish as they are plotted next to one another. It is difficult, for example, to determine visually if one pie slice has twice the area of another, whereas it is relatively easy to determine visually that one bar might be twice as high as another.

Pie charts can be used when comparing frequencies that are repeating over many situations or responses. For example, Figure \(\PageIndex{4}\) shows a sequence of four pie charts showing the frequency distributions of the responses for each of the first four questions. Recall that the Likert scale for this survey indicates how much the individual agrees with the question. In considering the sequence of pie charts shown in Figure \(\PageIndex{4}\), we see that more people strongly disagree with questions 2 and 3 than with questions 1 and 4. Further, we can note that more people strongly agree with questions 1 and 4 than with questions 2 and 3.

Figure \(\PageIndex{4}\): Pie Chart for Questions 1–4 in Table 10.5. The numbers on the pie chart refer to the responses from the question. The percentage of each response is also indicated (Public domain image created by Alan M. Polansky).