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ch6 - CHAPTER 6 Section 6-1 6-1 Sample average n xi x= i =1...

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6-1 CHAPTER 6 Section 6-1 6-1. Sample average: mm 0044 . 74 8 035 . 592 1 = = = ° = n x x n i i Sample variance: ( ) 2 2 2 1 1 2 2 8 1 2 8 1 ) mm ( 000022414 . 0 7 0001569 . 0 1 8 8 035 . 592 18031 . 43813 1 031 18 . 43813 035 . 592 = = - - = - ± ² ³ ´ µ - = = = ° ° ° ° = = = = n n x x s x x n i i n i i i i i i Sample standard deviation: mm 00473 . 0 000022414 . 0 = = s The sample standard deviation could also be found using ( ) s x x n i i n = - - = ° 2 1 1 where ( ) x x i i - = = ° 2 1 8 0 0001569 . Dot Diagram: .. ...: . -------+---------+---------+---------+---------+---------diameter 73.9920 74.0000 74.0080 74.0160 74.0240 74.0320 There appears to be a possible outlier in the data set.
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6-2 6-2. Sample average: min 359 . 14 19 82 . 272 19 19 1 = = = ° = i i x x Sample variance: ( ) 2 2 2 1 1 2 2 19 1 2 19 1 (min) 47 . 356 18 49 . 6416 1 19 19 82 . 272 8964 . 10333 1 8964 . 10333 82 . 272 = = - - = - ± ² ³ ´ µ - = = = ° ° ° ° = = = = n n x x s x x n i i n i i i i i i Sample standard deviation: min 88 . 18 47 . 356 = = s The sample standard deviation could also be found using ( ) s x x n i i n = - - = ° 2 1 1 where ( ) 49 . 6416 19 1 2 = - ° = i i x x
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6-3 6-3. Sample average: yards x 1 . 7068 12 84817 = = Sample variance: ( ) ( ) 2 2 2 1 1 2 2 19 1 2 12 1 265 . 51302 11 92 . 564324 1 12 12 84817 600057949 1 600057949 84817 yards n n x x s x x n i i n i i i i i i = = - - = - ± ² ³ ´ µ - = = = ° ° ° ° = = = = Sample standard deviation: yards s 5 . 226 265 . 51302 = = The sample standard deviation could also be found using ( ) 1 1 2 - - = ° = n x x s n i i where ( ) 92 . 564324 12 1 2 = - ° = i i x x Dot Diagram: (rounding was used to create the dot diagram) . . : .. .. : : -+---------+---------+---------+---------+---------+-----C1 6750 6900 7050 7200 7350 7500
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6-4 6-4. Sample mean: kN 22 . 126 18 2272 18 18 1 = = = ° = i i x x Sample variance: ( ) 2 2 2 1 1 2 2 18 1 2 18 1 ) kN ( 24 . 683 17 11 . 11615 1 18 18 2272 298392 1 298392 2272 = = - - = - ± ² ³ ´ µ - = = = ° ° ° ° = = = = n n x x s x x n i i n i i i i i i Sample standard deviation: kN 14 . 26 24 . 683 = = s The sample standard deviation could also be found using ( ) 1 1 2 - - = ° = n x x s n i i where ( ) 11 . 11615 18 1 2 = - ° = i i x x Dot Diagram: . : :: . :: . . : . . +---------+---------+---------+---------+---------+-------yield 90 105 120 135 150 165 6-5. Sample average:
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6-5 975 . 43 8 8 . 351 = = x Sample variance: ( ) 143 . 151 7 998 . 1057 1 8 8 8 . 351 043 . 16528 1 403 . 16528 8 . 351 2 2 1 1 2 2 19 1 2 8 1 = = - - = - ± ² ³ ´ µ - = = = ° ° ° ° = = = = n n x x s x x n i i n i i i i i i Sample standard deviation: 294 . 12 143 . 151 = = s The sample standard deviation could also be found using ( ) 1 1 2 - - = ° = n x x s n i i where ( ) 998 . 1057 8 1 2 = - ° = i i x x Dot Diagram: . . .. . .. . +---------+---------+---------+---------+---------+------- 24.0 32.0 40.0 48.0 56.0 64.0
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6-6 6-6. Sample average: 2 35 1 / 514 . 810 35 28368 35 m watts x x i i = = = ° = Sample variance: ( ) 2 2 2 2 1 1 2 2 19 1 2 19 1 ) / ( 61 . 16465 34 743 . 559830 1 35 35 28368 23552500 1 23552500 28368 m watts n n x x s x x n i i n i i i i i i = = - - = - ± ² ³ ´ µ - = = = ° ° ° ° = = = = Sample standard deviation: 2 / 32 . 128 61 . 16465 m watts s = = The sample standard deviation could also be found using ( ) 1 1 2 - - = ° = n x x s n i i where ( ) 743 . 559830 35 1 2 = - ° = i i x x 6-7. 44 . 5 1270 6905 = = μ ; The value 5.44 is the population mean since the actual physical population of all flight times during the operation is available.
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6-7 6-8 a.) Sample average: mm n x x n i i 173 . 2 9 56 . 19 1 = = = ° = b.) Sample variance: ( ) 2 2 2 1 1 2 2 9 1 2 9 1 ) ( 4303 . 0 8 443 . 3 1 9 9 56 . 19 953 . 45 1 953 . 45 56 . 19 mm n n x x s x x n i i n i i i i i i = = - - = - ± ² ³ ´ µ - = = = ° ° ° ° = = = = Sample standard deviation: mm s 6560 . 0 4303 . 0 = = c.) Dot Diagram . . . . . . . .. -------+---------+---------+---------+---------+---------crack length 1.40 1.75 2.10 2.45 2.80 3.15 6-9. Dot Diagram (rounding of the data is used to create the dot diagram) x . .
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