138 Chapter 3 Numerical Summaries of Data 29. Caffeine: Following are the number of grams of carbohydrates in 12-ounce espresso beverages offered at Starbucks. 14 43 38 44 31 27 39 59 9 10 54 14 25 26 9 46 30 24 41 26 27 14 Source: www.starbucks.com a. Find the first and third quartiles of these data. b. Find the median of these data. c. Find the upper and lower outlier boundaries. d. The beverage with the most carbohydrates is a Peppermint White Chocolate Mocha, with 59 grams. Is this an outlier? e. The beverages with the least carbohydrates are an Iced Skinny Flavored Latte, and a Cappuccino, each with 9 grams. Are these outliers? f. Construct a boxplot for these data. g. Describe the shape of this distribution. h. What is the 31st percentile? i. What is the 71st percentile? j. There are 38 grams of carbohydrates in an Iced Dark Cherry Mocha. What percentile is this? 30. Nuclear power: The following table presents the number of nuclear reactors as of December 31, 2007, in each country that had one or more reactors. Number of Number of Country Reactors Country Reactors Argentina 2 Mexico 2 Armenia 1 Netherlands 1 Belgium 7 Pakistan 2 Brazil 2 Romania 2 Bulgaria 2 Russia 31 Canada 18 Slovakia 5 China 11 Slovenia 1 Czech Republic 6 South Africa 2 Finland 4 Spain 8 France 59 Sweden 10 Germany 17 Switzerland 5 Hungary 4 Taiwan 6 India 17 Ukraine 15 Japan 55 United Kingdom 19 South Korea 20 United States 104 Lithuania 1 Source: International Atomic Energy Agency a. Find the first and third quartiles of these data. b. Find the median of these data. c. Find the upper and lower outlier boundaries. d. Which countries are outliers? e. Construct a boxplot for these data. f. Describe the shape of this distribution. g. What is the 45th percentile? h. What is the 88th percentile? i. India has 17 nuclear reactors. What percentile is this? 31. Playback time: Following are the playback times (in hours) for a sample of 20 MP3 players. 29 25 23 21 47 46 66 43 35 47 35 40 13 38 34 23 42 38 29 25 Source: Consumer Reports a. Find the first and third quartiles of these data. b. Find the median of these data. c. Find the upper and lower outlier boundaries. d. Are there any outliers? If so, list them. e. Construct a boxplot for these data. f. Describe the shape of this distribution. g. What is the 35th percentile? h. What is the 70th percentile? i. The Apple iPod Nano has a playback time of 34 hours. What percentile is this? 32. Hail to the chief: There have been 56 presidential inaugurations in U.S. history. At each one, the president has made an inaugural address. Following are the number of words spoken in each of these addresses. 1425 135 2308 1729 2158 1175 1209 3217 4467 2906 1125 1172 3838 8445 4776 996 3319 2821 3634 698 1128 1337 2480 2978 1681 4388 2015 3967 2217 985 5433 1802 1526 3318 4059 3801 1883 1807 1340 559 2242 2446 2449 1355 1437 2130 1668 1087 2463 2546 2283 1507 2170 1571 2073 2406 Source: www.infoplease.com a. Find the first and third quartiles of these data. b. Find the median of these data. c. Find the upper and lower outlier boundaries. d. The two shortest speeches were 135 words, by George Washington in 1793, and 559 words, by Franklin Roosevelt in 1945. Are either of these outliers? e. The two longest speeches were 8445 words, by William Henry Harrison in 1841, and 5433 words, by William Howard Taft in 1909. Are either of these outliers? f. Construct a boxplot for these data. g. Describe the shape of this distribution. h. What is the 15th percentile? i. What is the 65th percentile? j. Barack Obama used 2406 words in his inauguration speech in 2009. What percentile is this? 33. Bragging rights: After learning his score on a recent statistics exam, Ed bragged to his friends: “My score is the first quartile of the class.” Did Ed have a good reason to brag? Explain. 34. Who scored the highest? On a final exam in a large statistics class, Tom’s score was the tenth percentile, Dick’s was the median, and Harry’s was the third quartile. Which of the three scores was the highest? Which was the lowest? 35. Baseball salaries: In 2008, the Philadelphia Phillies won the World Series to become the champions of Major League Baseball. The New York Yankees, who had been expected to do well, did not qualify for the playoffs. Following are the salaries, in millions of dollars, of the players on each of these teams.
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