Statistics

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4.1 A sample of 12 people was asked how much change they had in their pockets and wallets. The responses (in cents) are 52 25 15 0 104 44 60 30 33 81 40 5 Determine the mean, median, and mode for these data.

4.3 A random sample of 12 joggers was asked to keep track and report the number of miles they ran last week. The responses are 5.5 7.2 1.6 22.0 8.7 2.8 5.3 3.4 12.5 18.6 8.3 6.6 Compute the three statistics that measure central location. b. Briefly describe what each statistic tells you.

Count = 12 Mean = 8.542 Median = 6.900 Mode = N/A

4.9 An investment you made 5 years ago has realized the following rates of return. Year 12345 Rate of Return −.15 −.20 .15 −.08 .50 a. Compute the mean and median of the rates of return. b. Compute the geometric mean. c. Which one of the three statistics computed in parts (a) and (b) best describes the return over the 5-year period? Explain.

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4.19 Calculate the variance of the following data. 93741754

4.21 Determine the variance and standard deviation of the following sample. 12 6 22 31 23 13 15 17 21

4.25 A friend calculates a variance and reports that it is –25.0. How do you know that he has made a serious calculation error?

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4.37 ANES2008* The ANES in 2012 asked respondents to state their ages stored as AGE. A. Calculate the mean, variance, and standard deviation. B. Draw a histogram. C. Use the Empirical rule, if applicable, or Chebysheff ’s Theorem to interpret the mean and standard deviation.

4.43 Determine the first, second, and third quartiles of the following data.

10.5 14.7 15.3 14.1 13.9 18.5

17.7 15.9 12.2 10.0 13.9 15.1 14.7

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4.57 Xr04-57 In the United States, taxpayers are allowed to deduct mortgage interest from their incomes before calculating the amount of income tax they are required to pay. In 2008, the Internal Revenue Service sampled 500 tax returns that had a mort- gage interest deduction.

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4.77 Xr04-77 also recorded the average away attendance for each team in the 2012 season. Because visiting teams take a share of the gate, owners should be interested in this analysis.

a. Are visiting team attendance related to number of wins?

b. Estimate the marginal number of tickets sold for each additional game won.