102 Chapter 3 Numerical Summaries of Data 44. Age distribution: The ages of residents of Banks City, Oregon, are given in the following frequency distribution. Age Frequency 0–9 283 10–19 203 20–29 217 30–39 256 40–49 176 50–59 92 60–69 21 70–79 23 80–89 12 90–99 3 Source: U.S. Census Bureau a. Approximate the mean age. b. Assume all three people aged 90–99 were in fact 90 years old. Would this tend to make the approximate mean too large or too small? Explain. 45. Income: The personal income per capita of a state is the total income of all adults in the state, divided by the number of adults. The following table presents the personal income per capita (in thousands of dollars) for each of the 50 states and the District of Columbia. 32 40 33 30 42 41 54 41 61 38 33 39 31 40 34 35 37 31 35 34 46 49 35 41 29 34 32 36 40 42 49 31 47 34 35 35 34 35 39 39 31 34 33 37 31 37 41 38 30 36 43 Source: U.S. Bureau of Economic Analysis a. What is the mean state income? b. What is the median state income? c. Based on the mean and median, would you expect the data to be skewed to the left, skewed to the right, or approximately symmetric? Explain. d. Construct a frequency histogram. Do the results agree with your expectation? 46. Stock prices: The following table presents the stock prices for a sample of 43 companies at the close of business on Friday, September 11, 2009. 26.10 23.47 31.03 22.30 69.98 60.42 1.65 32.54 21.69 16.25 11.76 7.33 28.42 31.46 29.30 83.96 27.34 34.17 55.18 16.97 16.07 4.61 54.39 48.41 50.72 23.56 75.23 58.80 60.58 15.59 51.51 172.16 54.99 16.60 55.64 24.86 3.77 24.39 26.66 77.32 51.35 9.34 14.67 a. Find the mean and median of the stock prices. b. Based on the mean and median, would you expect that a histogram would be skewed to the left, skewed to the right, or approximately symmetric? Explain. c. Construct a frequency histogram. Do the results agree with your expectation? 47. Read any good books lately? The following data represent the responses of 24 library patrons when asked about their favorite type of book. Which type of book is the mode? Biography Fiction Biography Historical Fiction Biography Fiction Nonfiction Fiction Fiction Historical Biography How-to guide Nonfiction How-to guide Nonfiction Historical Nonfiction Fiction Fiction How-to guide How-to guide Biography How-to guide 48. Sources of news: A sample of 32 U.S. adults was surveyed and asked, “Do you get most of your information about current events from newspapers, magazines, the Internet, television, radio, or some other source?” The results are shown below. What is the mode? Television Internet Television Other Newspapers Internet Television Radio Magazines Newspapers Other Radio Radio Internet Other Television Internet Magazines Other Television Internet Newspapers Newspapers Internet Newspapers Other Television Newspapers Television Magazines Television Television Source: General Social Survey
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