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