Similarly identify those states that fall into the upper 10th percentile of homeownership

Engin. 3.54 The Insurance Institute for Highway Safety published data on the total damage suffered by compact automobiles in a series of controlled, low-speed collisions. The data, in dollars, with brand names removed are as follows: 361 393 430 543 566 610 763 851 886 887 976 1,039 1,124 1,267 1,328 1,415 1,425 1,444 1,476 1,542 1,544 2,048 2,197 a. Draw a histogram of the data using six or seven categories. b. On the basis of the histogram, what would you guess the mean to be? c. Calculate the median and mean. d. What does the relation between the mean and median indicate about the shape of the data? Soc. 3.55 Data are collected on the weekly expenditures of a sample of urban households on food including restaurant expenditures. The data, obtained from diaries kept by each household, are grouped by number of members of the household. The expenditures are as follows: 1 member: 67 62 168 128 131 118 80 53 99 68 76 55 84 77 70 140 84 65 67 183 2 members: 129 116 122 70 141 102 120 75 114 81 106 95 94 98 85 81 67 69 119 105 94 94 92 3 members: 79 99 171 145 86 100 116 125 82 142 82 94 85 191 100 116 4 members: 139 251 93 155 158 114 108 111 106 99 132 62 129 91 5⫹ members: 121 128 129 140 206 111 104 109 135 136 a. Calculate the mean expenditure separately for each number of members. b. Calculate the median expenditure separately for each number of members. 3.56 Answer the following for the data in Exercise 3.55: a. Calculate the mean of the combined data, using the raw data. b. Can the combined mean be calculated from the means for each number of members? c. Calculate the median of the combined data using the raw data. d. Can the combined median be calculated from the medians for each number of members? Gov. 3.57 Federal authorities have destroyed considerable amounts of wild and cultivated marijuana plants. The following table shows the number of plants destroyed and the number of arrests for a 12-month period for 15 states. State Plants Arrests 1 110,010 280 2 256,000 460 3 665 6 4 367,000 66 5 4,700,000 15 6 4,500 8 7 247,000 36 8 300,200 300 9 3,100 9 10 1,250 4 11 3,900,200 14 12 68,100 185 13 450 5 14 2,600 4 15 205,844

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a. Discuss the appropriateness of using the sample mean to describe these two

variables.

b. Compute the sample mean, 10 trimmed mean, and 20 trimmed mean. Which

trimmed mean seems more appropriate for each variable? Why?

c. Does there appear to be a relation between the number of plants destroyed and the

number of arrests? How might you examine this question? What other variables might be related to the number of plants destroyed? Bus. 3.58 The most widely reported index of the performance of the New York Stock Exchange NYSE is the Dow Jones Industrial Average DJIA. This index is computed from the stock prices of 30 companies. When the DJIA was invented in 1896, the index was the average price of 12 stocks. The index was modified over the years as new companies were added and dropped from the index and was also altered to reflect when a company splits its stock. The closing New York Stock Exchange NYSE prices for the 30 components as of May 2004 of the DJIA are given in the following table. a. Compute the average price of the 30 stock prices in the DJIA. b. Compute the range of the 30 stock prices in the DJIA.

c. The DJIA is no longer an average; the name includes the word “average” only for his-

torical reasons. The index is computed by summing the stock prices and dividing by a constant, which is changed as stocks are added or removed from the index and when stocks split. where y i is the closing price for stock i, and C ⫽ .1409017. Using the stock prices given, compute the DJIA for May 27, 2004.

d. The DJIA is a summary of data. Does the DJIA provide information about a popula-

tion using sampled data? If so, to what population? Is the sample a random sample? Components of DJIA NYSE Stock Company Percent of DJIA Price 52704 3M Co. 5.9078 84.95 Alcoa Inc. 2.1642 31.12 Altria Group Inc. 3.3673 48.42 American Express Co. 3.5482 51.02 American International Group Inc. 5.0628 72.8 Boeing Co. 3.213 46.2 Caterpillar Inc. 5.2277 75.17 Citigroup Inc. 3.2352 46.52 Coca-Cola Co. 3.569 51.32 E.I. DuPont de Numours Co. 3.0057 43.22 Exxon Mobil Corp. 3.0161 43.37 General Electric Co. 2.174 31.26 General Motors Corp. 3.1601 45.44 Hewlett-Packard Co. 1.4702 21.14 Home Depot Inc. 2.4925 35.84 Honeywell International Inc. 2.3499 33.79 Intel Corp. 1.9785 28.45 International Business Machines Corp. 6.1609 88.59 J.P. Morgan Chase Co. 2.5697 36.95 Johnson Johnson 3.8799 55.79 McDonald’s Corp. 1.8269 26.27 Merck Co. Inc. 3.2985 47.43 DJIA ⫽ a 30 i⫽1 y i C continued