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Unformatted text preview: 1 Homework 3 (11.6 pts) due Sept. 16 (2.4 pts.) 2.32abc. Reconsider the accompanying shear strength observations (MPa) introduced in Exercise 1 of this chapter: 22.2 40.4 16.4 73.7 36.6 109.9 30.0 4.4 33.1 66.7 81.5 a) What are the values of the quartiles, and what is the value of the IQR? The sorted data is: Value 4.4 16.4 22.2 30 33.1 36.6 40.4 66.7 73.7 81.5 109.9 point # 1 2 3 4 5 6 7 8 9 10 11 Since there are 11 points, the median is point 6 or Q2 = 36.6 ? 1 ??¡ ¡??¡ ¢£ ¤¢?¥?¦ 3 ¥§ 4 ¨ = 22.2 + 30 2 = 26.1 ? 3 ( ??¡ ¡??¡ ¢£ ¤¢?¥?¦ 8 ¥§ 9) = 66.7 + 73.7 2 = 70.2 IQR = Q3 – Q1 = 70.2 – 26.1 = 44.1 b) Construct a boxplot based on the fivenumber summary, and comment on its features. You actually have to do part c) before you do part b) so that you know that there are no outliers. SAS Code: data Problem2_32; infile 'H:\x2332.txt' ; input strength; run ; data Problem2_32_new; set Problem2_32; group = 1 ; run ; proc print data =Problem2_32_new; run ; proc boxplot data =Problem2_32_new; plot strength*group; run ; Output The SAS System 13:21 Thursday, September 15, 2011 2 Obs strength group 1 22.2 1 2 40.4 1 3 16.4 1 4 73.7 1 5 36.6 1 6 109.9 1 7 30.0 1 8 4.4 1 9 33.1 1 10 66.7 1 11 81.5 1 2 There are no outliers and the distribution is positively skewed. There also seems to be a large variation. c) How large or small does an observation have to be to qualify as an outlier? small: Q1 – 1.5 (IQR) = 26.1 – 1.5(44.1) = 26.1 – 66.15 = 40.05 large: Q3 + 1.5 (IQR) = 70.2 + 66.15 = 136.35 Therefore there are no outliers in this data set. As an extreme outlier? small: Q1 – 3 (IQR) = 26.1 – 3(44.1) = 26.1 – 132.3 = 106.2 large: Q3 + 3 (IQR) = 70.2 + 132.3 = 202.5 1 25 50 75 100 125 strength group 3 (1.7 pts.) 2.36 (you may use SAS). The amount of aluminum continuation (ppm) in plastic of a certain type was determined for a sample of 26 plastic specimens, resulting in the following data 30 30 60 63 70 79 87 90 101 102 115 118 119 119 120 125 140 145 172 182 183 191 222 244 291 511 Construct a boxplot that shows outliers, and comment on its features....
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 Spring '08
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 Statistics

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