EXAMPLE 8 Stemplot of the Percentage of Hispanics

To make a stemplot of the percentage of Hispanics from the data in Table 5.5 (page 189), take the whole-number part of the percentage as the stem and the final digit (in this case, the tenths place) as the leaf. Figure 5.11 is the complete stemplot for the data in Table 5.5. The entries for Idaho and Oregon, 9|01, represent 9.0% and 9.1%, respectively.

If we rotate Figure 5.11 a quarter-turn counterclockwise, the stemplot would look like a histogram (of a distribution skewed to the right). Comparing the stemplot in Figure 5.11 with the histogram in Figure 5.4 (page 191) reveals the strengths and weaknesses of stemplots. The stemplot, unlike the histogram, preserves the actual value of each observation, at least in cases where the data values have not been truncated or rounded. But you can choose the classes in a histogram, whereas the classes (the stems) of a stemplot are not as flexible. Whether the large number of classes in Figure 5.11 is an improvement over Figure 5.4 is a matter of taste. To change the classes on the stemplot, we could truncate the tenths place; for example, 11.3% and 11.6% both become 11% when the tenths place is truncated. In Figure 5.12, we construct a stemplot of the truncated data. Notice that now the leaves represent 1% so that 0|1 and 1|0 represent 1% and 10%, respectively.

There are too many leaves on the first stem in Figure 5.12, and no outliers are obvious. Just as we might zoom in on a digital map to view added detail, we can zoom in by expanding each stem into two stems, using the first stem for leaves 0, 1, 2, 3, and 4 and the second stem for leaves 5, 6, 7, 8, and 9. Figure 5.13 shows the result.

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Now our stemplot reveals the same information as the histogram in Figure 5.3 but gives the added detail of the truncated data values.