Description
Complete problems 1.9 – 1.17
1.9 Bear markets. Investors speak of a “bear market" when stock prices drop substantially. Here are data on all declines of at least 10% in the Standard & Poor's 500-stock index between 1940 and 2005. The data show how far the index fell from its peak and how long the decline in stock prices lasted.
Decline Duration Decline Duration
Year (percent) (months) Year (percent) (months)
1940-1942 42 28 1966 22 8
1946 27 5 1968-1970 36 18
1950 14 1 1973-1974 48 21
1953 15 8 1981-1982 26 19
1955 10 1 1983-1984 14 10
1956-1957 22 15 1987 34 3
1959-1960 14 15 1990 20 3
1962 26 6 1998 20 3
2000-2003 31 50
(a) Make a stem plot of the percent declines in stock prices during these bear markets. Make a second stem plot, splitting the stems. Which graph do you prefer? Why?
(b) The shape of this distribution is irregular, but we could describe it as somewhat skewed. Is the distribution skewed to the right or to the left? Are there any outliers?
(c) Describe the center and spread of the data. What would you tell an investor about how far stocks fall in a bear market?
1.10 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:
54 59 35 41 46 25 47 60 54 46 49 46 41 34 22
Make a stemplot for 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?
1.11 Back-to-back stem plot. A leading recent home run hitter was Mark McGwire, who retired after the 2001 season. Here are McGwire's home run counts for 1987 to 2001:
49 32 33 39 22 42 9 9 39 52 58 70 65 32 29
Make a stem plot for McGwire's home run counts. McGwire was injured in 1993 and there was a baseball strike in 1994. How do these events appear in the data? How does McGwire compare with Babe Ruth?
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1.13 Vanishing lands. Garbage that is not recycled is buried in lands. Here are time series data that emphasize the need for recycling: the number of lands operating in the United States in the years 1988 to 2002
Year Land Year Lands Year Lands
1988 7924 1993 4482 1998 2314
1989 7379 1994 3558 1999 2216
1990 6326 1995 3197 2000 1967
1991 5812 1996 3091 2001 1858
1992 5386 1997 2514 2002 1767
Make a time plot of these data. Describe the trend that your plot shows. Why does the trend emphasize the need for recycling?
1.14 The influenza epidemic of 1918 (EESEE). In 1918 and 1919 a worldwide outbreak of influenza killed more than 25 million people. Here are data on the number of new influenza cases and the number of deaths from the epidemic in San Francisco week by week from October 5, 1918, to January 25, 1919. The date given is the last day of the week.6
Date Oct. 5 Oct. 12 Oct. 19 Oct. 26 Nov. 2 Nov. 9 Nov. 16 Nov. 23 Nov. 30
Cases 36 531 4233 8682 7164 2229 600 164 57
Deaths 0 0 130 552 738 414 198 90 56
Date Dec. 7 Dec. 14 Dec. 21 Dec. 28 Jan. 4 Jan. 11 Jan. 18 Jan. 25
Cases 722 1517 1828 1539 2416 3148 3465 1440
Deaths 50 71 137 178 194 290 310 149
(a) Make a time plot of weekly new cases. Based on your plot, describe the progress of the epidemic.
(b) We would
like to compare the patterns over time of number of new cases and number of
deaths. To make the two variables similar in size for easier comparison, plot
the number of deaths against time for October 5 to January 25, then plot the
number of cases divided by 10 on the same graph using a di
erent color. What do you see? In particular, about how long is the lag between
changes in the number of
cases and corresponding changes in deaths?
1.15 Poverty in the states. The table below gives the percents of people living below the poverty line in 2000 in the 26 states east of the Mississippi River.7 Make a stem plot of these data. Is the distribution roughly symmetric, skewed to the right, or skewed to the left? Which states (if any) are outliers?
State Percent State Percent State Percent
Alabama 14.6 Maryland 7.3 Pennsylvania 9.9
Connecticut 7.6 Massachusetts 10.2 Rhode Island 10.0
Delaware 9.8 Michigan 10.2 South Carolina 11.9
Florida 12.1 Mississippi 15.5 Tennessee 13.3
Georgia 12.6 New Hampshire 7.4 Vermont 10.1
Illinois 10.5 New Jersey 8.1 Virginia 8.1
Indiana 8.2 New York 14.7 West Virginia 15.8
Kentucky 12.5 North Carolina 13.2 Wisconsin 8.8
Maine 9.8 Ohio 11.1
1.16 Split the stems. Make another stem plot of the poverty data in the previous exercise, splitting the stems to double the number of classes. Do you prefer this stem plot or that from the previous exercise? Why?
1.17 The Boston Marathon. Women were allowed to enter the Boston Marathon in 1972. The times (in minutes, rounded to the nearest minute) for the winning woman from 1972 to 2006 appear below. The fastest time to date is 2 hours, 20 minutes, and 43 seconds, by Margaret Okayo of Kenya in 2002.
(a) Make a time plot of the winning times.
(b) Give a brief description of the pattern of Boston Marathon winning times over these years. Has the rate of improvement in times slowed in recent years?
Year Time Year Time Year Time Year Time
1972 190 1981 147 1990 145 1999 143
1973 186 1982 150 1991 144 2000 146
1974 167 1983 143 1992 144 2001 144
1975 162 1984 149 1993 145 2002 141
1976 167 1985 154 1994 142 2003 145
1977 168 1986 145 1995 145 2004 144
1978 165 1987 146 1996 147 2005 145
1979 155 1988 145 1997 146 2006 144
1980 154 1989 144 1998 143