All of the graphical methods shown in this section are derived from frequency tables. Table 1 shows a frequency table for the results of the iMac study; it shows the frequencies of the various response categories. It also shows the relative frequencies, which are the proportion of responses in each category. For example, the relative frequency for "none" of 0.17=85/500 0.17 85500 .

The pie chart in Figure 1 shows the results of the iMac study. In a pie chart, each category is represented by a slice of the pie. The area of the slice is proportional to the percentage of responses in the category. This is simply the relative frequency multiplied by 100. Although most iMac purchasers were Macintosh owners, Apple was encouraged by the 12% of purchasers who were former Windows users, and by the 17% of purchasers who were buying a computer for the first time.

Figure 1: Pie chart of iMac purchases illustrating frequencies of previous computer ownership.

Here is another important point about pie charts. If they are based on a small number of observations, it can be misleading to label the pie slices with percentages. For example, if just 5 people had been interviewed by Apple Computers, and 3 were former Windows users, it would be misleading to display a pie chart with the Windows slice showing 60%. With so few people interviewed, such a large percentage of Windows users might easily have accord since chance can cause large errors with small samples. In this case, it is better to alert the user of the pie chart to the actual numbers involved. The slices should therefore be labeled with the actual frequencies observed (e.g., 3) instead of with percentages.

Bar charts can also be used to represent frequencies of different categories. A bar chart of the iMac purchases is shown in Figure 2. Frequencies are shown on the Y axis and the type of computer previously owned is shown on the X axis. Typically the Y-axis shows the number of observations rather than the percentage of observations in each category as is typical in pie charts.

Figure 2: Bar chart of iMac purchases as a function of previous computer ownership.

Comparing Distributions

Often we need to compare the results of different surveys, or of different conditions within the same overall survey. In this case, we are comparing the distributions of responses between the surveys or conditions. Bar charts are often excellent for illustrating differences between two distributions. Figure 3 shows the number of people playing card games at the Yahoo website on a Sunday and on a Wednesday on a day in the Spring of 2001. We see that there were more players overall on Wednesday compared to Sunday. The number of people playing Pinochle was nonetheless the same on these two days. In contrast, there were about twice as many people playing hearts on Wednesday as on Sunday. Facts like these emerge clearly from a well-designed bar chart.

Figure 3: A bar chart of the number of people playing different card games on Sunday and Wednesday.

The bars in Figure 3 are oriented horizontally rather than vertically. The horizontal format is useful when you have many categories because there is more room for the category labels. Such horizontal bar charts may be contrasted with vertical bar charts like the one in Figure 4.

Example:

Another example using bar charts to compare distributions.

We'll have more to say about bar charts when we consider numerical quantities later in this chapter. (See Bar Charts.)

Don't get fancy! People sometimes add features to graphs that don't help to convey their information. For example, 3-dimensional bar charts like the one shown in Figure 4 are usually not as effective as their two-dimensional counterparts.

Figure 4: A three-dimensional version of Figure 2.

Figure 5: A redrawing of Figure 2 with a lie factor greater than 8.

Figure 6: A redrawing of Figure 2 with a baseline of 50.

Figure 7: A line graph of the number of people playing different card games on Sunday and Wednesday.

Pie charts and bar charts can both be effective methods of portraying qualitative data. Bar charts are better when there are more than just a few categories and for comparing two or more distributions. Be careful to avoid creating misleading graphs.