796 CHAPTER 12 Statistics a) Compute the mean of each of the five sets of data. 8, 6.5, 2, 10, 66 b) Compute the mean of the five means in part (a). 18.5 c) Determine the mean of the 27 pieces of data. 19.926 ≈ d) Compare your answer in part (b) to your answer in part (c). Are the values the same? Does your answer make sense? No, the values are not the same. 73. Ruth Versus Mantle The tables below compare the batting performances for selected years for two well-known former baseball players, Babe Ruth and Mickey Mantle. m Babe Ruth Boston Red Sox 1914–1919 New York Yankees 1920–1934 Year At Bats Hits AVG 1925 359 104 1930 518 186 1933 459 138 1916 136 37 1922 406 128 Total 1878 593 m Mickey Mantle New York Yankees 1951–1968 Year At Bats Hits Pct. 1954 543 163 1957 474 173 1958 519 158 1960 527 145 1962 377 121 Total 2440 760 a) For each player, compute the batting average percent (pct.) for each year by dividing the number of hits by the number of at bats. Round to the nearest thousandth. Place the answers in the pct. column. * b) Going across each of the five horizontal lines (for example Ruth, 1925, vs. Mantle, 1954), compare the percents (pct.) and determine which is greater in each case. Mantle’s is greater in every case. c) For each player, compute the mean batting average percent for the 5 given years by dividing the total hits by the total at bats. Which is greater, Ruth’s or Mantle’s? Ruth: 0.316; Mantle: 0.311; Ruth’s is greater. d) Based on your answer in part (b), does your answer in part (c) make sense? Explain. Answers will vary. e) Determine the mean percent for each player by adding the five pcts. and dividing by 5. Which is greater, Ruth’s or Mantle’s? Ruth: 0.307; Mantle: 0.313; Mantle’s is greater. f) Why do the answers obtained in parts (c) and (e) differ? Explain. Answers will vary. g) Who would you say has the better batting average percent for the 5 years selected? Explain. Answers will vary. 74. Employee Salaries The following table gives the distribution of annual salaries for employees at DiLaura’s Home Improvement. Annual Salary Number Receiving Salary $100,000 1 85,000 2 24,000 6 21,000 4 18,000 5 17,000 7 Using the information provided in the table, determine the a) mean annual salary. $28,280 b) median annual salary. $21,000 c) mode annual salary. $17,000 d) midrange annual salary. $58,500 e) Which do you believe is the best measure of central tendency for this set of data? Explain your answer. Answers will vary. Weighted Average In Exercises 75 and 76 we use weighted averages. Sometimes when we wish to determine an average, we may wish to assign more importance, or weight, to some of the pieces of data. To calculate a weighted average, we use the formula: weighted average xw w , = Σ Σ where w is the weight of the piece of data, x; xw Σ is the sum of the products of each piece Pictorial Press Ltd/Alamy Stock Photo $ *See Instructor Answer Appendix AP Images
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