2.2 Displaying and Describing Categorical Data
Descriptive Statistics for Categorical Data
Categorical data is typically more straightforward to work with. Recall descriptive statistics consists of visual and numerical methods. We usually start with visual methods and then move into 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 comparing the same categories in the colleges easier. 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% |
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 as freshmen, sophomores, juniors, or seniors. The data she collects are summarized in the pie chart below.
Bar Graphs
Bar graphs consist of bars that are separated from each other. The length of the bar for each category is proportional to the number or percent of individuals in each category. The bars can be rectangles or they can be rectangular boxes (used in three-dimensional plots), and they can be vertical or horizontal. The bar graph shown in the figure below has age groups 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. Construct a bar graph using this data.
| 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% |
Pie vs. Bar Charts
It is a good idea to look at a variety of graphs to see which is the most helpful in displaying the data. We might make different choices of what we think is the “best” graph depending on the data and the cont