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Figure 6-10 A cumulative distribution plot of the compressive strength data from Minitab.
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CHAPTER 6 RANDOM SAMPLING AND DATA DESCRIPTION
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Figure 6-11 Histograms for symmetric and skewed distributions.
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Negative or left skew (a)
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distribution is skewed to the right, whereas mode median mean if the distribution is skewed to the left. Frequency distributions and histograms can also be used with qualitative or categorical data. In some applications there will be a natural ordering of the categories (such as freshman, sophomore, junior, and senior), whereas in others the order of the categories will be arbitrary (such as male and female). When using categorical data, the bins should have equal width. EXAMPLE 6-6 Figure 6-12 presents the production of transport aircraft by the Boeing Company in 1985. Notice that the 737 was the most popular model, followed by the 757, 747, 767, and 707. A chart of occurrences by category (in which the categories are ordered by the number of occurrences) is sometimes referred to as a Pareto chart. See Exercise 6-41. In this section we have concentrated on descriptive methods for the situation in which each observation in a data set is a single number or belongs to one category. In many cases, we work with data in which each observation consists of several measurements. For example, in a gasoline mileage study, each observation might consist of a measurement of miles per gallon, the size of the engine in the vehicle, engine horsepower, vehicle weight, and vehicle length. This is an example of multivariate data. In later chapters, we will discuss analyzing this type of data. EXERCISES FOR SECTION 6-4
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6-30. Construct a frequency distribution and histogram for the motor fuel octane data from Exercise 6-14. Use eight bins. 6-31. Construct a frequency distribution and histogram using the failure data from Exercise 6-15. 6-32. Construct a frequency distribution and histogram for the cotton content data in Exercise 6-16. 6-33. Construct a frequency distribution and histogram for the yield data in Exercise 6-17.
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Number of airplanes manufactured in 1985
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Figure 6-12 Airplane production in 1985. (Source: Boeing Company.)
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6-34. Construct a frequency distribution and histogram with 16 bins for the motor fuel octane data in Exercise 6-14. Compare its shape with that of the histogram with eight bins from Exercise 6-30. Do both histograms display similar information 6-35. Construct a histogram for the female student height data in Exercise 6-22. 6-36. Construct a histogram with 10 bins for the spot weld shear strength data in Exercise 6-23. Comment on the shape of the histogram. Does it convey the same information as the stem-and-leaf display 6-37. Construct a histogram for the water quality data in Exercise 6-24. Comment on the shape of the histogram. Does it convey the same information as the stem-and-leaf display 6-38. Construct a histogram with 10 bins for the overall distance data in Exercise 6-25. Comment on the shape of the histogram. Does it convey the same information as the stem-andleaf display 6-39. Construct a histogram for the semiconductor speed data in Exercise 6-26. Comment on the shape of the his-
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togram. Does it convey the same information as the stem-andleaf display 6-40. Construct a histogram for the pinot noir wine rating data in Exercise 6-27. Comment on the shape of the histogram. Does it convey the same information as the stem-and-leaf display 6-41. The Pareto Chart. An important variation of a histogram for categorical data is the Pareto chart. This chart is widely used in quality improvement efforts, and the categories usually represent different types of defects, failure modes, or product/process problems. The categories are ordered so that the category with the largest frequency is on the left, followed by the category with the second largest frequency and so forth. These charts are named after the Italian economist V Pareto, . and they usually exhibit Pareto s law ; that is, most of the defects can be accounted for by only a few categories. Suppose that the following information on structural defects in automobile doors is obtained: dents, 4; pits, 4; parts assembled out of sequence, 6; parts undertrimmed, 21; missing holes/slots, 8; parts not lubricated, 5; parts out of contour, 30; and parts not deburred, 3. Construct and interpret a Pareto chart.
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