EXAMPLE 1 How to make a histogram
Table 11.1 presents the percentage of residents aged 65 years and over in each of the 50 states. To make a histogram of this distribution, proceed as follows.
Step 1. Divide the range of the data into classes of equal width. The data in Table 11.1 range from 7.3 to 17.4, so we choose as our classes
7.0 ≤ percentage over 65 < 8.0
8.0 ≤ percentage over 65 < 9.0
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17.0 ≤ percentage over 65 < 18.0
Be sure to specify the classes precisely so that each individual falls into exactly one class. In other words, be sure that the classes are exclusive (no individual is in more than one class) and exhaustive (every individual appears in some class). A state with 7.9% of its residents aged 65 or older would fall into the first class, but 8.0% fall into the second.
| State | Percent | State | Percent | State | Percent |
|---|---|---|---|---|---|
| Alabama | 13.8 | Louisiana | 12.3 | Ohio | 13.7 |
| Alaska | 7.3 | Maine | 15.1 | Oklahoma | 13.5 |
| Arizona | 13.3 | Maryland | 12.1 | Oregon | 13.3 |
| Arkansas | 14.3 | Massachusetts | 13.4 | Pennsylvania | 15.4 |
| California | 11.2 | Michigan | 13.0 | Rhode Island | 14.1 |
| Colorado | 10.4 | Minnesota | 12.5 | South Carolina | 13.3 |
| Connecticut | 13.7 | Mississippi | 12.7 | South Dakota | 14.4 |
| Delaware | 13.9 | Missouri | 13.6 | Tennessee | 13.2 |
| Florida | 17.4 | Montana | 14.2 | Texas | 10.2 |
| Georgia | 10.1 | Nebraska | 13.5 | Utah | 9.0 |
| Hawaii | 14.8 | Nevada | 11.4 | Vermont | 14.0 |
| Idaho | 12.0 | New Hampshire | 12.9 | Virginia | 12.1 |
| Illinois | 12.2 | New Jersey | 13.3 | Washington | 12.0 |
| Indiana | 12.8 | New Mexico | 13.1 | West Virginia | 15.7 |
| Iowa | 14.8 | New York | 13.4 | Wisconsin | 13.3 |
| Kansas | 13.1 | North Carolina | 12.4 | Wyoming | 12.3 |
| Kentucky | 13.3 | North Dakota | 14.7 | ||
| Source: 2010 Statistical Abstract of the United States; available online at www.census.gov/library/publications/2009/compendia/statab/129ed.html. | |||||
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Step 2. Count the number of individuals in each class. Here are the counts:
| Class | Count | Class | Count | Class | Count |
|---|---|---|---|---|---|
| 7.0 to 7.9 | 1 | 11.0 to 11.9 | 2 | 15.0 to 15.9 | 3 |
| 8.0 to 8.9 | 0 | 12.0 to 12.9 | 12 | 16.0 to 16.9 | 0 |
| 9.0 to 9.9 | 1 | 13.0 to 13.9 | 19 | 17.0 to 17.9 | 1 |
| 10.0 to 10.9 | 3 | 14.0 to 14.9 | 8 |
Step 3. Draw the histogram. Mark on the horizontal axis the scale for the variable whose distribution you are displaying. That’s “percentage of residents aged 65 and over” in this example. The scale runs from 5 to 20 because that range spans the classes we chose. The vertical axis contains the scale of counts. Each bar represents a class. The base of the bar covers the class, and the bar height is the class count. There is no horizontal space between the bars unless a class is empty, so that its bar has height zero. Figure 11.1 is our histogram.