40th percentile 288 291 2 2895 8 a i x σ 695 695

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40th percentile = 28.8 + 29.1 2 = 28.95 8. a. i x Σ = 695 695 34.75 20 i x x n Σ = = = The modal age is 29; it appears 3 times. b. Median is average of 10th and 11th items. 33 36 Median 34.5 2 + = = Data suggest at - home workers are slightly younger. c. For Q 1 , 25 20 5 100 i = = Since i is integer, 1 25 26 25.5 2 Q + = = For Q 3 , 75 20 15 100 i = = Since i is integer, 3 42 45 43.5 2 Q + = = d. 32 20 6.4 100 i = = Since i is not an integer, we round up to the 7th position. 32nd percentile = 27
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Descriptive Statistics: Numerical Methods 3 - 5 9. a. 270,377 10,815.08 25 i x x n Σ = = = Median (Position 13) = 8296 b. Median would be better because of large data values. c. i = (25 / 100) 25 = 6.25 Q 1 (Position 7) = 5984 i = (75 / 100) 25 = 18.75 Q 3 (Position 19) = 14,330 d. i = (85/100) 25 = 21.25 85th percentile (position 22) = 15,593. Approximately 85% of the websites have less than 15,593 unique visitors. 10. a. Σ x i = 435 x x n i = = = Σ 435 9 48 33 . Data in ascending order: 28 42 45 48 49 50 55 58 60 Median = 49 Do not report a mode; each data value occurs once. The index could be considered good since both the mean and median are less than 50. b. 25 9 2.25 100 i = = Q 1 (3rd position) = 45 75 9 6.75 100 i = = Q 3 (7th position) = 55 11. Using the mean we get x city =15.58, x country = 18.92 For the samples we see that the mean mileage is better in the country than in the city.
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Chapter 3 3 - 6 City 13.2 14.4 15.2 15.3 15.3 15.3 15.9 16 16.1 16.2 16.2 16.7 16.8 Median Mode: 15.3 Country 17.2 17.4 18.3 18.5 18.6 18.6 18.7 19.0 19.2 19.4 19.4 20.6 21.1 Median Mode: 18.6, 19.4 The median and modal mileages are also better in the country than in the city. 12. a. 12,780 $639 20 i x x n Σ = = = b. 1976 98.8 20 i x x n Σ = = = pictures c. 2204 110.2 20 i x x n Σ = = = minutes d. This is not an easy choice because it is a multicriteria problem. If price was the only criterion, the lowest price camera (Fujifilm DX-10) would be preferred. If maximum picture capacity was the only criterion, the maximum picture capacity camera (Kodak DC280 Zoom) would be preferred. But, if battery life was the only criterion, the maximum battery life camera (Fujifilm DX10) would be preferred. There are many approaches used to select the best choice in a multicriteria situation. These approaches are discussed in more specialized books on decision analysis. 13. Range 20 - 10 = 10 10, 12, 16, 17, 20 25 (5) 1.25 100 i = = Q 1 (2nd position) = 12 75 (5) 3.75 100 i = = Q 3 (4th position) = 17 IQR = Q 3 - Q 1 = 17 - 12 = 5
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Descriptive Statistics: Numerical Methods 3 - 7 14. x x n i = = = Σ 75 5 15 s x x n i 2 2 1 64 4 16 = = = Σ ( ) s = = 16 4 15. 15, 20, 25, 25, 27, 28, 30, 34 Range = 34 - 15 = 19 25 (8) 2 100 i = = 1 20 25 22.5 2 Q + = = 75 (8) 6 100 i = = 3 28 30 29 2 Q + = = IQR = Q 3 - Q 1 = 29 - 22.5 = 6.5 x x n i = = = Σ 204 8 255 . s x x n i 2 2 1 242 7 34 57 = = = Σ ( ) . s = = 34 57 588 . . 16. a. Range = 190 - 168 = 22 b. 2 ( ) 376 i x x Σ = s 2 = 376 5 = 75.2 c. s = = 752 8 67 . . d. 8.67 Coefficient of Variation 100% 4.87% 178 = = 17. Range = 92-67 = 25 IQR = Q 3 - Q 1 = 80 - 77 = 3 x = 78.4667 ( ) 2 411.7333 i x x = ( ) 2 2 411.7333 29.4095 1 14 i x x s n = = = 29.4095 5.4231 s = =
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Chapter 3 3 - 8 18. a. x x n i = Σ 115.13 (Mainland); 36.62 (Asia) Median (7th and 8th position) Mainland = (110.87 + 112.25) / 2 = 111.56 Median (6th and 7th position) Asia = (32.98 + 40.41) / 2 = 36.695 b. Range = High - Low Mainland Asia Range 86.24 42.97 Standard Deviation 26.82 11.40 Coefficient of Variation 23.30% 31.13% c. Greater mean and standard deviation for Mainland. Greater coefficient of variation for Asia.
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  • Spring '08
  • Staff
  • Standard Deviation, Descriptive statistics, standard deviations, x=, Σxi

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