ch03 SOLUTION.pdf

# Term median 4 mode 4 q 3 p 75 i 75 12 17 100 75 q 3

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term Median = 4 Mode = 4 Q 3 = P 75 : i = 75 . 12 ) 17 ( 100 75 = Q 3 is located at the 13 th term Q 3 = 4 P 11 : i = 87 . 1 ) 17 ( 100 11 = P 11 is located 2 nd term P 11 = 1 P 35 : i = 95 . 5 ) 17 ( 100 35 = P 35 is located 6 th term P 35 = 3 P 58 : i = 86 . 9 ) 17 ( 100 58 = P 58 is located 10 th term P 58 = 4 P 67 :i = 39 . 11 ) 17 ( 100 67 = P 67 is located 12 th term P 67 = 4 3.11 x x -µ (x-µ) 2 6 6-4.2857 = 1.7143 2.9388 2 2.2857 5.2244 4 0.2857 .0816 9 4.7143 22.2246 1 3.2857 10.7958 3 1.2857 1.6530 5 0.7143 .5102 Σ x = 30 Σ x-µ = 14.2857 Σ (x -µ) 2 = 43.4284 2857 . 4 7 30 = = Σ = N x μ a.) Range = 9 - 1 = 8 b.) M.A.D. = = = Σ 7 2857 . 14 N x μ 2.041 c.) σ 2 = 7 4284 . 43 ) ( 2 = Σ N x μ = 6.204 d.) σ = 204 . 6 ) ( 2 = Σ N x μ = 2.491 e.) 1, 2, 3, 4, 5, 6, 9 Q 1 = P 25 i = ) 7 ( 100 25 = 1.75 Q 1 is located at the 1 + 1 = 2 th term, Q 1 = 2 Q 3 = P 75 :i = ) 7 ( 100 75 = 5.25 Q 3 is located at the 5 + 1 = 6 th term, Q 3 = 6 IQR = Q 3 - Q 1 = 6 - 2 = 4

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Chapter 3: Descriptive Statistics 3 3.12 x x x 2 ) ( x x 4 0 0 3 1 1 0 4 16 5 1 1 2 2 4 9 5 25 4 0 0 5 1 1 Σ x = 32 x x Σ = 14 2 ) ( x x Σ = 48 8 32 = Σ = n x x = 4 a) Range = 9 - 0 = 9 b) M.A.D. = 8 14 = Σ n x x = 1.75 c) s 2 = 7 48 1 ) ( 2 = Σ n x x = 6.857 d) s = 857 . 6 1 ) ( 2 = Σ n x x = 2.619 e) Numbers in order: 0, 2, 3, 4, 4, 5, 5, 9 Q 1 =P 25 i = ) 8 ( 100 25 =2 Q 1 is located at the average of the 2 nd and 3 rd terms, Q 1 = (2 + 3)/2 = 2.5 th term Q 1 = 2.5 Q 3 = P 75 i = ) 8 ( 100 75 = 6 Q 3 is located at the average of the 6 th and 7 th terms Q 3 = (5 + 5)/2 = 5 IQR = Q 3 - Q 1 = 5 - 2.5 = 2.5 3.13 a.) x (x-µ) (x -µ) 2 12 12-21.167= -9.167 84.034 23 1.833 3.360 19 -2.167 4.696 26 4.833 23.358 24 2.833 8.026 23 1.833 3.360 Σ x = 127 Σ (x -µ) = -0.002 Σ (x -µ) 2 = 126.834 μ = 6 127 = Σ N x = 21.167 σ = 139 . 21 6 834 . 126 ) ( 2 = = Σ N x μ = 4.598 ORIGINAL FORMULA b.) x x 2 12 144 23 529 19 361 26 676 24 576 23 529 Σ x = 127 Σ x 2 = 2815 σ = 138 . 21 6 83 . 126 6 17 . 2688 2815 6 6 ) 127 ( 2815 ) ( 2 2 2 = = = = Σ Σ N N x x = 4.598 SHORT-CUT FORMULA The short-cut formula is faster.
Chapter 3: Descriptive Statistics 4 3.14 s 2 = 433.9267 s = 20.8309 Σ x = 1387 Σ x 2 = 87,365 n = 25 x = 55.48 3.15 σ 2 = 58,631.359 σ = 242.139 Σ x = 6886 Σ x 2 = 3,901,664 n = 16 µ = 430.375 3.16 14, 15, 18, 19, 23, 24, 25, 27, 35, 37, 38, 39, 39, 40, 44, 46, 58, 59, 59, 70, 71, 73, 82, 84, 90 Q 1 = P 25 i = ) 25 ( 100 25 = 6.25 P 25 is located at the 6 + 1 = 7 th term Q 1 = 25 Q 3 = P 75 i = ) 25 ( 100 75 = 18.75 P 75 is located at the 18 + 1 = 19 th term Q 3 = 59 IQR = Q 3 - Q 1 = 59 - 25 = 34 3.17 a) 75 . 4 3 4 1 1 2 1 1 2 = = = b) 84 . 25 . 6 1 1 5 . 2 1 1 2 = = c) 609 . 56 . 2 1 1 6 . 1 1 1 2 = = d) 902 . 24 . 10 1 1 2 . 3 1 1 2 = = 3.18 Set 1: 5 . 65 4 262 1 = = Σ = N x μ 4 4 ) 262 ( 970 , 17 ) ( 2 2 2 1 = Σ Σ = N N x x σ = 14.2215 Set 2: 5 . 142 4 570 2 = = Σ = N x μ 4 4 ) 570 ( 070 , 82 ) ( 2 2 2 2 = Σ Σ = N N x x σ = 14.5344 CV 1 = ) 100 ( 5 . 65 2215 . 14 = 21.71% CV 2 = ) 100 ( 5 . 142 5344 . 14 = 10.20% 3.19 x x x 2 ) ( x x 7 1.833 3.361 5 3.833 14.694 10 1.167 1.361 12 3.167 10.028 9 0.167 0.028 8 0.833 0.694 14 5.167 26.694 3 5.833 34.028 11 2.167 4.694 13 4.167 17.361 8 0.833 0.694 6 2.833 8.028 106 32.000 121.665 12 106 = Σ = n x x = 8.833 a) MAD = 12 32 = Σ n x x = 2.667 b) s 2 = 11 665 . 121 1 ) ( 2 =

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