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Unformatted text preview: Chapter 2: Descriptive Statistics CHAPTER 2Descriptive Statistics 2.1 a. Both halves are mirror images of each other and one peak in the middle, tapering on both ends. b. Two distinct high points. c. Having a long tail to the left. d. Having a long tail to the right. 2.2 a. Stemandleaf display: see page 41 Histogram: see page 46 Dot plot: see page 48 b. The class limits are the smallest and largest measurements that can fall in a class, where the class boundaries are set halfway between the class limits to include all measurements. The class midpoint is the middle value in a class. c. Outliers are unusually large or small observations that are well separated from the remaining observations. Outliers are handled differently depending on their cause. 2.3 a. StemandLeaf Display: Profit Margin Stemandleaf of Profit M N = 32 Leaf Unit = 0.10 4 1 1579 8 2 3357 14 3 122356 (5) 4 24479 13 5 22579 8 6 038 5 7 27 3 8 3 2 9 2 10 9 1 11 1 12 5 Skewed right. 7 Chapter 2: Descriptive Statistics b. StemandLeaf Display: Return on Capital Stemandleaf of Return o N = 32 Leaf Unit = 0.10 4 10 3339 8 11 5788 11 12 067 11 13 11 14 16 15 03478 16 16 157 13 17 4 12 18 12 19 7 11 20 333 8 21 8 22 8 7 23 01 5 24 5 25 5 26 5 4 27 4 28 5 3 29 3 30 5 2 31 2 32 2 1 33 1 34 1 35 1 36 1 37 1 38 1 39 4 Skewed to the right. c. The return on capital percentages are more spread out than the profit margin percentages. 2.4 a. Skewed with a tail to the right, one outlier. b. Skewed to the right with two or three outliers. 8 Chapter 2: Descriptive Statistics c. DotPlot0.5 0.5 1 1.5 2 Total Return Fairly symmetrical. 2.5 a. We have 64 2 6 = and . 128 2 7 = Since 6 2 < n = 65 and 7 2 > n = 65, we use K = 7 classes. Class length = 2 71 . 1 7 12 7 36 48 t measuremen smallest t measuremen largest = = = K Class Frequency Relative Frequency Boundaries Midpoint 36 37 1 1/65 = .0154 35.5, 37.5 36.5 38 39 7 7/65 = .1077 37.5, 39.5 38.5 40 41 11 11/65 = .1692 39.5, 41.5 40.5 42 43 14 14/65 = .2154 41.5, 43.5 42.5 44 45 21 21/65 = .3231 43.5, 45.5 44.5 46 47 10 10/65 = .1538 45.5, 47.5 46.5 48 49 1 1/65 = .0154 47.5, 49.5 48.5 b. The population of all possible customer satisfaction ratings is slightly skewed with a tail to the left. 9 Chapter 2: Descriptive Statistics c. The relative frequency histogram would be the same as the frequency histogram in Figure 2.15, except the heights of the rectangles would be the relative frequencies given in the table of part (a). This means the numbers on the vertical axis in Figure 2.15 0, 5, 10, 15, 20, 25 would be divided by 65. Thus, the numbers on the vertical axis would be 0, .077, .154, .231, .308, .385. Alternatively, if we have MINITAB construct a relative frequency histogram by choosing its own classes, we obtain the following: 2.6 a. We have 64 2 6 = and . 128 2 7 = Since 6 2 < n = 100 and 7 2 > n = 100, we use K = 7 classes....
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