2.2 Displaying and Describing Categorical Distributions
2.2 Displaying and Describing Categorical Distributions
Descriptive Statistics for Categorical Data
Working with categorical data is typically more straightforward. Recall that descriptive statistics consists of visual and numerical methods. We usually start with visual methods and then move on to numerical.
Graphical Methods for Categorical Data
Below are tables comparing the number of part-time and full-time students at De Anza College and Foothill College enrolled for the spring 2010 quarter. The tables display counts (frequencies) and percentages or proportions (relative frequencies). The percent columns make it easier to compare the same categories across colleges. Displaying percentages along with the numbers is often helpful, but it is particularly important when comparing sets of data that do not have the same totals, such as the total enrollments for both colleges in this example. Notice how much larger the percentage for part-time students at Foothill College is compared to De Anza College.
| De Anza College | Foothill College | |||||
|---|---|---|---|---|---|---|
| Number | Percent | Number | Percent | |||
| Full-time | 9,200 | 40.9% | Full-time | 4,059 | 28.6% | |
| Part-time | 13,296 | 59.1% | Part-time | 10,124 | 71.4% | |
| Total | 22,496 | 100% | Total | 14,183 | 100% |
Figure 2.4: Full- and part-time students
Tables are a good way of organizing and displaying data, but graphs can be even more helpful in understanding the data. There are no strict rules concerning which graphs to use. Two graphs that are used to display categorical data are pie charts and bar graphs.
Pie Charts
In a pie chart, categories of data are represented by wedges in a circle and are proportional in size to the percent of individuals in each category. Suppose a statistics professor collects information about the classification of her students about which of her students are freshmen, sophomores, juniors, or seniors. The data she collects is summarized in the pie chart below.
Bar Graphs
Bar graphs are made up of separate bars representing categories, where the length of the bar for each category is proportional to the number or percent of individuals in that category. The bars can be rectangles, or they can be rectangular boxes (used in three-dimensional plots), and they can be vertical or horizontal. In the bar graph shown in Figure 2.7 below, age groups are represented on the x-axis and proportions on the y-axis
By the end of 2011, Facebook had over 146 million users in the United States. The figure below shows three age groups, the number of users in each age group, and the proportion (%) of users in each age group.
| Age groups | Number of Facebook users | Proportion (%) of Facebook users |
|---|---|---|
| 13–25 | 65,082,280 | 45% |
| 26–44 | 53,300,200 | 36% |
| 45–64 | 27,885,100 | 19% |
Figure 2.6: Facebook users
Pie vs. Bar Charts
It is a good idea to consider a variety of graphs to determine which will be the most helpful in displaying our data. Our