142 Chapter 3 Numerical Summaries of Data a. Find the mean annual amount of federal aid from 2000 to 2006. b. Find the median annual amount of federal aid from 2000 to 2006. 2. Corporate profits: The following table presents the profit, in billions of dollars, for the year 2007 for each of the 15 largest U.S. corporations in terms of revenue. Corporation Profit Corporation Profit Wal-Mart 12.7 Bank of America 15.0 Exxon Mobil 40.6 AT&T 12.0 Chevron 18.7 Berkshire Hathaway 13.2 General Motors −38.7 J.P. Morgan Chase 15.3 ConocoPhillips 11.9 American International Group 6.2 General Electric 22.2 Hewlett-Packard 7.2 Ford Motor −2.8 IBM 10.4 Citigroup 3.6 Source: Fortune a. Find the mean profit. b. Find the median profit. c. Are these data skewed to the right, skewed to the left, or approximately symmetric? Explain. 3. Computer chips: A computer chip is a wafer made of silicon that contains complex electronic circuitry made up of microscopic components. The wafers are coated with a very thin coating of silicon dioxide. It is important that the coating be of uniform thickness over the wafer. To check this, engineers measured the thickness of the coating, in millionths of a meter, for samples of wafers made with two different processes. Process 1: 90.0 92.2 94.9 92.7 91.6 88.2 92.0 98.2 96.0 Process 2: 76.1 90.2 96.8 84.6 93.3 95.7 90.9 100.3 95.2 a. Find the mean of the thicknesses for each process. b. Find the median of the thicknesses for each process. c. If it is desired to obtain as thin a coating as possible, is one process much better than the other? Or are they about the same? 4. More computer chips: Using the data in Exercise 3: a. Find the sample variance of the thicknesses for each process. b. Find the sample standard deviation of the thicknesses for each process. c. Which process appears to be better in producing a uniform thickness? Explain. 5. Stock prices: Following are the closing prices of Microsoft stock for each trading day in September and October 2010. September 23.90 23.94 24.29 23.96 23.93 24.01 23.85 25.11 25.03 25.12 25.33 25.22 25.43 25.15 24.61 24.43 24.78 24.73 24.68 24.50 24.49 October 24.38 23.91 24.35 24.43 24.53 24.57 24.59 24.83 25.34 25.23 25.54 25.82 25.10 25.31 25.42 25.38 25.19 25.90 26.05 26.28 26.67 a. Find the mean and median price in September. b. Find the mean and median price in October. c. Does there appear to be a substantial difference in price between September and October? Or are the prices about the same? 6. More stock prices: Using the data in Exercise 5: a. Find the population standard deviation of the prices in September. b. Find the population standard deviation of the prices in October. c. Financial analysts use the word volatility to refer to the variation in stock prices. Was the volatility for the price of Microsoft stock greater in September or October? 7. Measure that ball: Each of 16 students measured the circumference of a tennis ball by two different methods: A: Estimate the circumference by eye. B: Measure the circumference by rolling the ball along a ruler. The results (in centimeters) are given below, in increasing order for each method: A: 18.0 18.0 18.0 20.0 22.0 22.0 22.5 23.0 24.0 24.0 25.0 25.0 25.0 25.0 26.0 26.4 B: 20.0 20.0 20.0 20.0 20.2 20.5 20.5 20.7 20.7 20.7 21.0 21.1 21.5 21.6 22.1 22.3 a. Compute the sample standard deviation of the measurements for each method. b. For which method is the sample standard deviation larger? Why should one expect this method to have the larger standard deviation?
navidi_monk_essential_statistics_1e_ch1_3
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