The authors of the article “Predictive Model for Pitting Corrosion in Buried Oil and Gas Pipelines” (Corrosion, 2009: 332–342) provided the data on which their investigation was based. a. Consider the following sample of 61 observations on maximum pitting depth (mm) of pipeline specimens buried in clay loam soil. Construct a stem-and-leaf display in which the two largest values are shown in a last row labeled HI. b. Refer back to (a), and create a histogram based on eight classes with 0 as the lower limit of the first class and class widths of .5, .5, .5, .5, 1, 2, 5, and 5, respectively. c. The accompanying comparative boxplot from Minitab shows plots of pitting depth for four different types of soils. Describe its important features.
Solution: Step 1 : The given data is a sample of 61 observations on maximum pitting depth (mm) of pipeline specimens buried in clay loam soil. We have to construct a stem- leaf diagram based on the given data and a histogram based on eight classes with 0 as the lower limit of the first class and class widths of .5, .5, .5, .5, 1, 2, 5, and 5. Step 2 : a) In order to make a Stem- Leaf diagram first we have to arrange the given data into ascending order. The given data itsself in arranged format 0.41 0.41 0.41 0.41 0.43 0.43 0.43 0.48 0.48 0.48 0.58 0.79 0.79 0.81 0.81 0.81 0.91 0.94 0.94 1.02 1.04 1.04 1.17 1.17 1.17 1.17 1.17 1.17 1.19 1.19 1.27 1.40 1.40 1.59 1.59 1.60 1.68 1.91 1.96 1.96 1.96 2.10 2.21 2.31 2.46 2.49 2.57 2.79 3.10 3.18 3.30 3.58 3.58 4.15 4.75 5.33 7.65 7.70 8.13 10.41 13.44 To construct a Stem-Leaf diagram we take ones digit as stem and the remaining digits as leaf. Here we repeat each stem value twice by adding L to the stem with leaves from 00 to 49 and H to stem with leaves from 50 to 99. In the form b) By taking 0 as the lower limit of the first class and class widths of .5, .5, .5, .5, 1, 2, 5, and 5. We can make histogram for the data. Class frequency 0-0.5 9 0.5-1 9 1-2-1.5 15 1.5-2 8 2-3 7 3-5 7 5-10 4 10-15 2
