ch03 e SOLUTION - 10.doc

# ch03 e SOLUTION - 10.doc - Chapter 3 Descriptive Statistics...

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Chapter 3: Descriptive Statistics 1 Chapter 3 Descriptive Statistics SOLUTIONS TO PROBLEMS IN CHAPTER 3 3.1 Mode 2, 2, 3, 3, 4, 4, 4, 4, 5, 6, 7, 8, 8, 8, 9 The mode = 4 4 is the most frequently occurring value 3.2 Median for values in 3.1 Arrange in ascending order: 2, 2, 3, 3, 4, 4, 4, 4, 5, 6, 7, 8, 8, 8, 9 There are 15 terms. Since there are an odd number of terms, the median is the middle number. The median = 4 Using the formula, the median is located at the n + 1 th term = 15+1 = 16 = 8 th term 2 2 2 The 8 th term = 4 3.3 Median Arrange terms in ascending order: 073, 167, 199, 213, 243, 345, 444, 524, 609, 682 There are 10 terms. Since there are an even number of terms, the median is the average of the two middle terms: Median = 243 + 345 = 588 = 294 2 2 Using the formula, the median is located at the n + 1 th term. 2 n = 10 therefore 10 + 1 = 11 = 5.5 th term. 2 2 The median is located halfway between the 5 th and 6 th terms. 5 th term = 243 6 th term = 345 Halfway between 243 and 345 is the median = 294 3.4 Mean 17.3 44.5 µ = x/N = 333.6/8 = 41.7 31.6 40.0 52.8 x = x/n = 333.6/8 = 41.7 38.8 30.1 78.5 (It is not stated in the problem whether the x = 333.6 data represent as population or a sample). 3.5 Mean 7 -2 5 µ = x/N = -12/12 = -1 9 0 -3 -6 x = x/n = -12/12 = -1 -7 -4 -5 2 -8 (It is not stated in the problem whether the x = -12 data represent a population or a sample).

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Chapter 3: Descriptive Statistics 2 3.6 Rearranging the data into ascending order: 11, 13, 16, 17, 18, 19, 20, 25, 27, 28, 29, 30, 32, 33, 34 25 . 5 ) 15 ( 100 35 i P 35 is located at the 5 + 1 = 6 th term P 35 = 19 25 . 8 ) 15 ( 100 55 i P 55 is located at the 8 + 1 = 9 th term P 55 = 27 Q 1 = P 25 75 . 3 ) 15 ( 100 25 i Q 1 = P 25 is located at the 3 + 1 = 4 th term Q 1 = 17 Q 2 = Median The median is located at the term th th 8 2 1 15 Q 2 = 25 Q 3 = P 75 25 . 11 ) 15 ( 100 75 i Q 3 = P 75 is located at the 11 + 1 = 12 th term Q 3 = 30 3.7 Rearranging the data in ascending order: 80, 94, 97, 105, 107, 112, 116, 116, 118, 119, 120, 127, 128, 138, 138, 139, 142, 143, 144, 145, 150, 162, 171, 172 n = 24 8 . 4 ) 24 ( 100 20 i P 20 is located at the 4 + 1 = 5 th term P 20 = 107 28 . 11 ) 24 ( 100 47 i P 47 is located at the 11 + 1 = 12 th term P 47 = 127 92 . 19 ) 24 ( 100 83 i P 83 is located at the 19 + 1 = 20 th term P 83 = 145 Q 1 = P 25 6 ) 24 ( 100 25 i Q 1 is located at the 6.5 th term Q 1 = (112 + 116)/ 2 = 114 Q 2 = Median The median is located at the: term th th 5 . 12 2 1 24 Q 2 = (127 + 128)/ 2 = 127.5 Q 3 = P 75 18 ) 24 ( 100 75 i Q 3 is located at the 18.5 th term Q 3 = (143 + 144)/ 2 = 143.5 3.8 Mean = 87 . 870 , 2 15 063 , 43 N x The median is located at the th 2 1 15 = 8 th term Median = 2,264 Q 2 = Median = 2,264 45 . 9 ) 15 ( 100 63 i P 63 is located at the 9 + 1 = 10 th term P 63 = 2,646 3.9 The median is located at the th th 5 . 5 2 1 10 position The median = (595 + 653)/2 = 624 Q 3 = P 75 : 5 . 7 ) 10 ( 100 75 i P 75 is located at the 7+1 = 8 th term Q 3 = 751 For P 20 : 2 ) 10 ( 100 20 i P 20 is located at the 2.5 th term P 20 = (483 + 489)/2 = 486 For P 60 : 6 ) 10 ( 100 60 i P 60 is located at the 6.5 th term P 60 = (653 + 701)/2 = 677 For P 80 : 8 ) 10 ( 100 80 i P 80 is located at the 8.5 th term P 80 = (751 + 800)/2 = 775.5 For P 93 : 3 . 9 ) 10 ( 100 93 i P 93 is located at the 9+1 = 10 th term P 93 = 1096 3.10 n = 17 Mean = 59 . 3 17 61 N x The median is located at the th 2 1 17 = 9 th term Median = 4
Chapter 3: Descriptive Statistics 3

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