11.8 Lightning storms. Figure 11.10 comes from a study of lightning storms in Colorado. It shows the distribution of the hour of the day during which the first lightning flash for that day occurred. Describe the shape, center, and variability of this distribution. Are there any outliers?

11.9 Where do 18- to 34-year-olds live? Figure 11.11 is a stemplot of the percentage of residents aged 18 to 34 in each of the 50 states in July 2008. As in Figure 11.6 (page 256) for older residents, the stems are whole percents and the leaves are tenths of a percent.

11.10 Minority students in engineering. Figure 11.12 is a histogram of the number of minority students (black, Hispanic, Native American) who earned doctorate degrees in engineering from each of 152 universities in the years 2000 through 2002. Briefly describe the shape, center, and variability of this distribution. The classes for Figure 11.12 are 1–5, 6–10, and so on.

11.11 Returns on common stocks. The total return on a stock is the change in its market price plus any dividend payments made. Total return is usually expressed as a percentage of the beginning price. Figure 11.13 is a histogram of the distribution of total returns for all 1528 common stocks listed on the New York Stock Exchange in one year.

260

11.12 More lake levels. Figure 11.14 contains average monthly lake levels for Lake Murray in South Carolina. Describe the shape, center, and variability of the distribution of lake levels.

11.13 Automobile fuel economy. Government regulations require automakers to give the city and highway gas mileages for each model of car. Table 11.2 gives the combined highway and city mileages (miles per gallon) for 31 model year 2015 sedans. Make a stemplot of the combined gas mileages of these cars. What can you say about the overall shape of the distribution? Where is the center (the value such that half the cars have better gas mileage and half have worse gas mileage)? Some of these cars are electric and the reported milage is the electric equivalent. These cars have far higher mileage. How many electric cars are in this data set?

11.14 The obesity epidemic. Medical authorities describe the spread of obesity in the United States as an epidemic. Table 11.3 gives the percentage of adults who were obese in each of the 50 states in 2009. Display the distribution in a graph and briefly describe its shape, center, and variability.

11.15 Yankee money. Table 11.4 gives the salaries of the players on the New York Yankees baseball team for the 2015 season. Make a histogram of these data. Is the distribution roughly symmetric, skewed to the right, or skewed to the left? Explain.

11.16 The statistics of writing style. Numerical data can distinguish different types of writing, and sometimes even individual authors. Here are data collected by students on the percentages of words of 1 to 15 letters used in articles in Popular Science magazine:

11.17 What’s my shape? Do you expect the distribution of the total player payroll for each of the 30 teams in Major League Baseball to be roughly symmetric, clearly skewed to the right, or clearly skewed to the left? Why?

11.18 Asians in the eastern states. Here are the percentages of the population who are of Asian origin in each state east of the Mississippi River in 2008:

Make a stemplot of these data. Describe the overall pattern of the distribution. Are there any outliers?

11.19 How many calories does a hot dog have? Consumer Reports magazine presented the following data on the number of calories in a hot dog for each of 17 brands of meat hot dogs:

Make a stemplot of the distribution of calories in meat hot dogs and briefly describe the shape of the distribution. Most brands of meat hot dogs contain a mixture of beef and pork, with up to 15% poultry allowed by government regulations. The only brand with a different makeup was Eat Slim Veal Hot Dogs. Which point on your stemplot do you think represents this brand?

11.20 The changing age distribution of the United States. The distribution of the ages of a nation’s population has a strong influence on economic and social conditions. Table 11.5 shows the age distribution of U.S. residents in 1950 and 2050, in millions of persons. The 1950 data come from that year’s census. The 2050 data are projections made by the Census Bureau.

11.21 Babe Ruth’s home runs. Here are the numbers of home runs that Babe Ruth hit in his 15 years with the New York Yankees, 1920 to 1934:

Make a stemplot of these data. Is the distribution roughly symmetric, clearly skewed, or neither? About how many home runs did Ruth hit in a typical year? Is his famous 60 home runs in 1927 an outlier?

11.22 Back-to-back stemplot. The current major league single-season home run record is held by Barry Bonds of the San Francisco Giants. Here are Bonds’s home run counts for 1986 to 2007:

A back-to-back stemplot helps us compare two distributions. Write the stems as usual, but with a vertical line both to their left and to their right. On the right, put leaves for Ruth (Exercise 11.21). On the left, put leaves for Bonds. Arrange the leaves on each stem in increasing order out from the stem. Now write a brief comparison of Ruth and Bonds as home run hitters.

11.23 When it rains, it pours. On July 25 to 26, 1979, 42.00 inches of rain fell on Alvin, Texas. That’s the most rain ever recorded in Texas for a 24-hour period. Table 11.6 gives the maximum precipitation ever recorded in 24 hours (through 2010) at any weather station in each state. The record amount varies a great deal from state to state—hurricanes bring extreme rains on the Atlantic coast, and the mountain West is generally dry. Make a graph to display the distribution of records for the states. Mark where your state lies in this distribution. Briefly describe the distribution.