E 3000 6000 9000 12000 15000 42 a mean 1057933 median

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e. 0 3,000 6,000 9,000 12,000 15,000 42. a. Mean = 105.7933 Median = 52.7 b. Q 1 = 15.7 Q 3 = 78.3 c. IQR = Q 3 - Q 1 = 78.3 - 15.7 = 62.6 Lower limit for box plot = Q 1 - 1.5(IQR) = 15.7 - 1.5(62.6) = -78.2 Upper limit for box plot = Q 3 + 1.5 (IQR) = 78.3 + 1.5(62.6) = 172.2 Note: Because the number of shares covered by options grants cannot be negative, the lower limit for the box plot is set at 0. Thus, outliers are values in the data set greater than 172.2.
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Descriptive Statistics: Numerical Methods Outliers: Silicon Graphics (188.8) and ToysRUs (247.6) d. Mean percentage = 26.73. The current percentage is much greater. 43. a. Five Number Summary (Midsize) 51 71.5 81.5 96.5 128 Five Number Summary (Small) 73 101 108.5 121 140 b. Box Plots Midsize 50 60 70 80 90 100 110 120 130 Small Size 50 60 70 80 90 100 110 120 130 140 150 c. The midsize cars appear to be safer than the small cars. 44. a. x = 37.48 Median = 23.67 b. Q 1 = 7.91 Q 3 = 51.92 c. IQR = 51.92 - 7.91 = 44.01 Lower Limit: Q 1 - 1.5(IQR) = 7.91 - 1.5(44.01) = -58.11 Upper Limit: Q 3 + 1.5(IQR) = 51.92 + 1.5(44.01) = 117.94 Russia, with a percent change of 125.89, is an outlier. With a percent change of 22.64, the United States is just below the 50th percentile - the median. 45. a. 0 10 20 30 40 50 60 70 0 5 10 15 20 x y
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Chapter 3 3 - 18 b. Negative relationship c/d. Σ Σ x x y y i i = = = = = = 40 40 5 8 230 230 5 46 Σ Σ Σ ( )( ) ( ) ( ) x x y y x x y y i i i i = − = = 240 118 520 2 2 2 2 ( )( ) 240 60 1 5 1 ( ) 118 5.4314 1 5 1 ( ) 520 11.4018 1 5 1 60 0.969 (5.4314)(11.4018) i i xy i x i y xy xy x y x x y y s n x x s n y y s n s r s s Σ = = = − Σ = = = Σ = = = = = = − There is a strong negative linear relationship. 46. a. 0 2 4 6 8 10 12 14 16 18 0 5 10 15 20 25 30 x y
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Descriptive Statistics: Numerical Methods 3 - 19 b. Positive relationship c/d. Σ Σ x x y y i i = = = = = = 80 80 5 16 50 50 5 10 Σ Σ Σ ( )( ) ( ) ( ) x x y y x x y y i i i i = = = 106 272 86 2 2 ( )( ) 106 26.5 1 5 1 i i xy x x y y s n Σ = = = 2 ( ) 272 8.2462 1 5 1 i x x x s n Σ = = = 2 ( ) 86 4.6368 1 5 1 i y y y s n Σ = = = 26.5 0.693 (8.2462)(4.6368) xy xy x y s r s s = = = A positive linear relationship 47. a. b. Positive relationship 400 450 500 550 600 650 700 750 2.6 2.8 3 3.2 3.4 3.6 3.8 x = GPA y = SAT
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Chapter 3 3 - 20 c/d. Σ Σ x x y y i i = = = = = = 19 8 19 8 6 33 3540 3540 6 590 . . . Σ Σ Σ ( )( ) ( ) . ( ) , x x y y x x y y i i i i = = = 143 0 74 36 400 2 2 2 2 ( )( ) 143 28.6 1 6 1 ( ) 0.74 0.3847 1 6 1 ( ) 36,400 85.3229 1 6 1 28.6 0.8713 (0.3847)(85.3229) i i xy i x i y xy xy x y x x y y s n x x s n y y s n s r s s Σ = = = Σ = = = Σ = = = = = = A positive linear relationship 48. Let x = driving speed and y = mileage 420 270 420 42 270 27 10 10 i i x x y y Σ = = = Σ = = = 2 2 ( )( ) 475 ( ) 1660 ( ) 164 i i i i x x y y x x y y Σ = − Σ = Σ = 2 2 ( )( ) 475 52.7778 1 10 1 ( ) 1660 13.5810 1 10 1 ( ) 164 4.2687 1 10 1 52.7778 .91 (13.5810)(4.2687) i i xy i x i y xy xy x y x x y y s n x x s n y y s n s r s s Σ = = = − Σ = = = Σ = = = = = = − A strong negative linear relationship 49. a. The sample correlation coefficient is .78. b. There is a positive linear relationship between the performance score and the overall rating. 50. a. The sample correlation coefficient is .92. b. There is a strong positive linear relationship between the two variables.
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Descriptive Statistics: Numerical Methods 3 - 21 51. The sample correlation coefficient is .88. This indicates a strong positive linear relationship between the daily high and low temperatures.
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  • Spring '08
  • Staff
  • Standard Deviation, Descriptive statistics, standard deviations, x=, Σxi

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