ODD ANSWERS A49 41. Class Frequency, f Relative frequency Cumulative frequency 52 – 55 6 0.1714 6 56 – 59 4 0.1143 10 60 – 63 6 0.1714 16 64 – 67 10 0.2857 26 68 – 71 5 0.1429 31 72 – 75 4 0.1143 35 Σf = 35 Σ f n = 1 Cumulative frequency Age 51.5 55.5 59.5 63.5 67.5 71.5 75.5 5 10 15 20 30 25 35 Retirement Ages Location of the greatest increase in frequency: 64–67 43. (a) Class Frequency, f Mid- point Relative frequency Cumulative frequency 65 – 74 4 69.5 0.1667 4 75 – 84 7 79.5 0.2917 11 85 – 94 4 89.5 0.1667 15 95 – 104 5 99.5 0.2083 20 105 – 114 3 109.5 0.1250 23 115 – 124 1 119.5 0.0417 24 Σf = 24 Σ f n ≈ 1 (b) Frequency Pulse rate 69.5 79.5 89.5 99.5 109.5 119.5 2 4 6 8 Pulse Rates (c) 2 4 6 8 Frequency Pulse rate 59.5 69.5 79.5 89.5 99.5 109.5 119.5 129.5 Pulse Rates (d) Relative frequency Pulse rate 69.5 79.5 89.5 99.5 109.5 119.5 0.10 0.20 0.30 0.05 0.15 0.25 Pulse Rates (e) Cumulative frequency Pulse rate 64.5 74.5 84.5 94.5 104.5 114.5 124.5 5 10 15 20 25 Pulse Rates 45. (a) Amount (in hundreds of dollars) Relative frequency 63.5 69.5 75.5 81.5 87.5 93.5 99.5 105.5 0.05 0.10 0.15 0.20 0.25 0.30 0.35 Daily Withdrawals (b) 16.7%, because the sum of the relative frequencies for the last three classes is 0.167. (c) $9700, because the sum of the relative frequencies for the last two classes is 0.10. 47. Data value Frequency 2 5 8 11 14 2 1 3 4 5 6 7 8 Histogram (5 Classes) Data value Frequency 1.5 5.5 9.5 13.5 17.5 2 1 3 4 5 6 Histogram (10 Classes) Data value Frequency 2 1 3 4 5 1 3 5 7 9 1113151719 Histogram (20 Classes) In general, a greater number of classes better preserves the actual values of the data set but is not as helpful for observing general trends and making conclusions. In choosing the number of classes, an important consideration is the size of the data set. For instance, you would not want to use 20 classes if your data set contained 20 entries. In this particular example, as the number of classes increases, the histogram shows more fluctuation. The histograms with 10 and 20 classes have classes with zero frequencies. Not much is gained by using more than five classes. Therefore, it appears that five classes would be best. Section 2.2 (page 62) 1. Quantitative: stem-and-leaf plot, dot plot, histogram, scatter plot, time series chart Qualitative: pie chart, Pareto chart 3. Both the stem-and-leaf plot and the dot plot allow you to see how data are distributed, to determine specific data entries, and to identify unusual data values. 5. b 6. d 7. a 8. c 9. 27, 32, 41, 43, 43, 44, 47, 47, 48, 50, 51, 51, 52, 53, 53, 53, 54, 54, 54, 54, 55, 56, 56, 58, 59, 68, 68, 68, 73, 78, 78, 85 Max: 85; Min: 27
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