120 Chapter 3 Numerical Summaries of Data a. Find the population standard deviation of the ratings for 1997–1998. b. Find the population standard deviation of the ratings for 2007–2008. c. Compute the range for the ratings for both seasons. d. Based on the standard deviations, did the spread in ratings increase or decrease over the two seasons? e. Based on the ranges, did the spread in ratings increase or decrease over the two seasons? 36. House prices: The following table presents prices, in thousands of dollars, of single-family homes for 24 of the 25 largest metropolitan area in the United States for the third quarter of 2007 and the third quarter of 2008 (information for Detroit was unavailable). Metro Area 2007 2008 Metro Area 2007 2008 Atlanta, GA 175.3 151.3 New York, NY 476.1 452.5 Baltimore, MD 291.4 279.2 Philadelphia, PA 243.0 241.1 Boston, MA 414.7 373.4 Phoenix, AZ 255.5 185.1 Chicago, IL 286.4 250.8 Pittsburgh, PA 127.7 122.7 Cincinnati, OH 145.3 136.0 Portland, OR 299.7 278.6 Cleveland, OH 132.7 116.4 Riverside, CA 375.1 227.2 Dallas, TX 153.7 150.2 St. Louis, MO 150.5 142.7 Denver, CO 254.1 225.1 San Diego, CA 589.3 377.3 Houston, TX 155.8 160.2 San Francisco, CA 824.2 615.7 Los Angeles, CA 602.9 391.4 Seattle, WA 394.7 350.0 Miami, FL 346.3 287.8 Tampa, FL 218.3 173.4 Minneapolis, MN 229.6 205.1 Washington, DC 438.0 332.7 Source: National Realtors Association a. Find the population standard deviation for 2007. b. Find the population standard deviation for 2008. c. In general, house prices decreased from 2007 to 2008. Did the spread in house prices decrease as well, or did it increase? 37. Stock prices: Following are the closing prices of Google stock for each trading day in June and July 2010. June 482.37 493.37 505.60 498.72 485.52 484.78 474.02 487.01 488.50 483.19 497.99 501.27 500.08 500.03 488.56 486.25 482.05 475.10 472.68 472.08 454.26 444.95 July 439.49 436.55 436.07 450.20 456.56 467.49 475.83 489.20 491.34 494.02 459.61 466.18 481.59 477.50 484.81 490.06 488.97 492.63 484.35 484.99 484.85 a. Find the population standard deviation for the prices in June. b. Find the population standard deviation for the prices in July. c. Financial analysts use the word volatility to refer to the variation in prices of assets such as stocks. In which month was the price of Google stock more volatile? 38. Stocks or bonds? Following are the annual percentage returns for the years 1990–2009 for three categories of investment: stocks, Treasury bills, and Treasury bonds. Stocks are represented by the Dow Jones Industrial Average. Year Stocks Bills Bonds Year Stocks Bills Bonds 1990 −4.34 7.55 6.24 2000 −6.18 5.76 16.66 1991 20.32 5.61 15.00 2001 −7.10 3.67 5.57 1992 4.17 3.41 9.36 2002 −16.76 1.66 15.12 1993 13.72 2.98 14.21 2003 25.32 1.03 0.38 1994 2.14 3.99 −8.04 2004 3.15 1.23 4.49 1995 33.45 5.52 23.48 2005 −0.61 3.01 2.87 1996 26.01 5.02 1.43 2006 16.29 4.68 1.96 1997 22.64 5.05 9.94 2007 6.43 4.64 10.21 1998 16.10 4.73 14.92 2008 −33.84 1.59 20.10 1999 25.22 4.51 −8.25 2009 18.82 0.14 −11.12 Source: Federal Reserve a. The standard deviation of the return is a measure of the risk of an investment. Compute the population standard deviation for each type of investment. Which is the riskiest? Which is least risky? b. Treasury bills are short-term (1 year or less) loans to the U.S. government. Treasury bonds are long-term (30-year) loans to the government. Finance theory states that long-term loans are riskier than short-term loans. Do the results agree with the theory? c. Finance theory states that the more risk an investment has, the higher its mean return must be. Compute the mean return for each class of investment. Do the results follow the theory?
navidi_monk_essential_statistics_1e_ch1_3
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