# Circle graphs/pie charts

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A circle graph/pie chart is a way of summarizing a set of categorical data or displaying the different values of a given variable (e.g., percentage distribution). This type of chart is a circle divided into a series of segments. Each segment represents a particular category. The area of each segment is the same proportion of a circle as the category is of the total data set.

Circle graphs/pie charts usually show the component parts of a whole. Often you will see a segment of the drawing separated from the rest of the pie in order to emphasize an important piece of information.

The circle graph/pie chart above clearly shows that 90% of all students and faculty members at Avenue High School do not want to have a uniform dress code and that only 10% of the school population would like to adopt school uniforms. This point is clearly emphasized by its visual separation from the rest of the pie.

The use of the circle graph/pie chart is quite popular, as the circle provides a visual concept of the whole (100%). Circle graphs/pie charts are also one of the most commonly used charts because they are simple to use. Despite its popularity, circle graphs/pie charts should be used sparingly for two reasons. First, they are best used for displaying statistical information when there are no more than six components only—otherwise, the resulting picture will be too complex to understand. Second, circle graphs/pie charts are not useful when the values of each component are similar because it is difficult to see the differences between slice sizes.

A circle graph/pie chart uses percentages to compare information. Percentages are used because they are the easiest way to represent a whole. The whole is equal to 100%. For example, if you spend 7 hours at school and 55 minutes of that time is spent eating lunch, then 13.1% of your school day was spent eating lunch. To present this in a circle graph/pie chart, you would need to find out how many degrees represent 13.1%. This calculation is done by developing the equation:

percent ÷ 100 x 360 degrees = the number of degrees

This ratio works because the total percent of the circle graph/pie chart represents 100% and there are 360 degrees in a circle. Therefore 47.1 degrees of the circle (13.1%) represents the time spent eating lunch.

## Constructing a circle graph/pie chart

A circle graph/pie chart is constructed by converting the share of each component into a percentage of 360 degrees. In Figure 2, music preferences in 14- to 19-year-olds are clearly shown.

The circle graph/pie chart quickly tells you that

• half of students like rap best (50%), and
• the remaining students prefer alternative (25%), rock and roll (13%), country (10%) and classical (2%).

Tip! When drawing a circle graph/pie chart, ensure that the segments are ordered by size (largest to smallest) and in a clockwise direction.

In order to reproduce this circle graph/pie chart, follow this step-by-step approach:

If 50% of the students liked rap, then 50% of the whole circle graph/pie chart (360 degrees) would equal 180 degrees.

1. Draw a circle with your protractor.
2. Starting from the 12 o'clock position on the circle, measure an angle of 180 degrees with your protractor. The rap component should make up half of your circle. Mark this radius off with your ruler.
3. Repeat the process for each remaining music category, drawing in the radius according to its percentage of 360 degrees. The final category need not be measured as its radius is already in position.

Labeling the segments with percentage values often makes it easier to tell quickly which segment is bigger. Whenever possible, the percentage and the category label should be indicated beside their corresponding segments. This way, users do not have to constantly look back at the legend in order to identify what category each colour represents.

The circle graph/pie chart above conveys a clear message to the user—that 88% of all students in the World Religions class celebrate Easter. We can easily tell what the message is by simply looking at the accompanying percentages. Unfortunately, the category labels are too long to fit beside the pie segments, so they had to be placed in the legend. Ideally, these labels would also accompany the pie segments.

It is more difficult to understand the message behind Figure 4 because there are no percentage figures given for each slice of the pie. This is why it is important to label the slices with actual values.

The user can still develop a picture of what is being said about the type of pets sold by this store, but the message is not as clear as it would have been had the parts of the pie been labelled.

In the circle graph/pie chart above, the legend is formatted properly and the percentages are included for each of the pie segments. However, there are too many items in the circle graph/pie chart to quickly give a clear picture of the distribution of movie genres. If there are more than five or six categories, consider using a another graph to display the information. Figure 5 would certainly be easier to read as a bar graph.

Tip! Many software programs will draw circle graphs/pie charts for you quickly and easily. However, research has shown that many people can make mistakes when trying to compare circle graph/pie chart values. In general, bar graphs communicate the same message with less chance for misunderstanding.

## Circle graphs/pie charts versus bar graphs

When displaying statistical information, refrain from using more than one circle graph/pie chart for each figure.

Figure 6 shows two circle graphs/pie charts side-by-side, where a split bar graph (two bar graphs back-to-back) would have shown the information more clearly. A user might find it difficult to compare a segment from one circle graph/pie chart to the corresponding segment of the other circle graph/pie chart. However, in a split bar graph, these segments become bars which are lined up back-to-back, making it much easier to make comparisons.

Figure 7 shows how a split bar graph would be a better choice for displaying information than a double circle graph/pie chart. The key point in preparing this type of graph is to ensure that you are using the same scale for both sides of the bar graph. You'll notice that the information is much clearer in Figure 7 than in Figure 6.