DS212_HW2_Solutions

# DS212_HW2_Solutions - DS 212 Business Statistics Soorapanth...

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Unformatted text preview: DS 212 Business Statistics Soorapanth Homework #2: Chapter 3 Descriptive Statistics 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 2 th term = 15 1 2 + = 8 th term The 8 th term = 4 3.4 Mean 17.3 44.5 µ = Σ x / N = (333.6)/8 = 41.7 31.6 40.0 52.8 x = Σ x / n = (333.6)/8 = 41.7 38.8 30.1 78.5 (It is not stated in the problem whether the Σ x = 333.6 data represent as population or a sample). 3.5 Mean 7 -2 5 µ = Σ x / N = -12/12 = -1 9 0 -3 -6 x = Σ x / n = -12/12 =-1-7-4 -5 2 -8 (It is not stated in the problem whether the Σ x = -12 data represent a population or a sample). 1 DS 212 Business Statistics Soorapanth 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 but 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 but: The median is located at the term th th 8 2 1 15 = + Q 2 = 25 Q 3 = P 75 but 25 . 11 ) 15 ( 100 75 = = i Q 3 = P 75 is located at the 11 + 1 = 12 th term, Q 3 = 30 3.8 Mean : 07 . 544 15 8161 = = = ∑ N x μ The mean is 544.07 The median is located at the th + 2 1 15 = 8 th term Median = 485 Q 2 = Median = 485 2 DS 212 Business Statistics Soorapanth For P 63 , 45 . 9 ) 15 ( 100 63 = = i P 63 is located at the 9 + 1 = 10 th term, P 63 = 524 For P 29 , 35 . 4 ) 15 ( 100 29 = = i P 29 is located at the 4 + 1 = 5 th term, P 29 = 459 3.11 x x- µ ( x- µ ) 2 6 6-4.2857 = 1.7143 2.9388 2 2.2857 5.2244 4 0.2857 0.0816 9 4.7143 22.2246 1 3.2857 10.7958 3 1.2857 1.6530 5 0.7143 0.5102 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 2.0408 c.) σ 2 = 7 4284 . 43 ) ( 2 =- Σ N x μ = 6.2041 d.) σ = 2041 . 6 ) ( 2 =- Σ N x μ = 2.4908 e.) Arranging the data in order: 1, 2, 3, 4, 5, 6, 9 Q 1 = P 25 i = ) 7 ( 100 25 = 1.75 Q 1 is located at the 2 nd term, Q 1 = 2 3 DS 212 Business Statistics Soorapanth Q 3 = P 75 : i = ) 7 ( 100 75 = 5.25 Q 3 is located at the 6 th term, Q 3 = 6 IQR = Q 3- Q 1 = 6 - 2 = 4 f.) z = 4908 . 2 2857 . 4 6- = 0.69 z = 4908 . 2 2857 . 4 2- = -0.92 z = 4908 . 2 2857 . 4 4- = - 0.11 z = 4908 . 2 2857 . 4 9- = 1.89 z = 4908 . 2 2857 . 4 1- = - 1.32 z = 4908 . 2 2857 . 4 3- = -0.52 z = 4908 . 2 2857 . 4 5- = 0.29 3.12 x x x- 2 ) ( x x- 4 0 3 1 1 4 16 5 1 1 2 2 4 9 5 25 4 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 4 DS 212 Business Statistics...
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DS212_HW2_Solutions - DS 212 Business Statistics Soorapanth...

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