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Lesson 1.4 %u2022 Displaying Quantitative Data: Stemplots 39 Comparing Distributions with Stemplots You can use a back-to-back stemplot with common stems to compare the distribution of a quantitative variable in two groups. The leaves on each side are placed in order leading out from the common stem. Which states have more electoral votes? Describing a stemplot PROBLEM: Use the stemplot in Figure 1.5(b) and the data table from the preceding example to answer these questions. (a) What percentage of states (plus the District of Columbia) get 10 or more electoral votes? (b) Describe the distribution of electoral votes. SOLUTION: (a) 22/51 0.431 = . About 43.1% of states (plus the District of Columbia) get 10 or more electoral votes. (b) Shape: The distribution of electoral votes is skewed to the right with a single peak on the 05%u201309 stem and three clear gaps%u2014from%u00a019 to 28, from 30 to 40, and from 40 to 54. Outliers: 40 (Texas) and 54 (California) appear to be outliers. Center: The middle value (median) is 8 electoral votes. Variability: The number of electoral votes in a state (plus the District of Columbia) varies from 3 to 54. EXAMPLE Note that skewed right always means skewed toward the larger values, regardless of the orientation of the graph. Imagine rotating the graph 90 degrees counterclockwise to see the shape of the graph more clearly. FOR PRACTICE TRY EXERCISE 11. How can we distinguish oak trees? Comparing distributions with stemplots PROBLEM: Of the many species of oak trees in the United States, 28 species grow on the Atlantic Coast and 11 species grow in California. How does the distribution of acorn sizes compare for oak trees in these two regions? Here are data on the average volumes of acorns (in cubic centimeters, cm3 ) for these 39%u00a0oak species: 39 Atlantic 0.3 0.4 0.6 0.8 0.9 0.9 1.1 1.1 1.1 1.1 1.1 1.2 1.4 1.6 1.8 1.8 1.8 2.0 2.5 3.0 3.4 3.6 3.6 4.8 6.8 8.1 9.1 10.5 California 0.4 1.0 1.6 2.0 2.6 4.1 5.5 5.9 6.0 7.1 17.1 (a) Make a back-to-back stemplot for these data. (b) Which of the two regions%u2019 oak tree species typically has the larger acorns? (c) Are the shapes of the acorn size distributions similar or different in the two regions? Justify your answer. EXAMPLE Cindy Rabinowitz%u00a9 Bedford, Freeman & Worth Publishers. For review purposes only. Do not distribute.