chapter_07

chapter_07 - CHAPTER 7 SOLUTIONS AND MINI-PROJECT NOTES...

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CHAPTER 7 SOLUTIONS AND MINI-PROJECT NOTES CHAPTER 7 SUMMARIZING AND DISPLAYING MEASUREMENT DATA EXERCISE SOLUTIONS 7.1 a. 3|2 3| 4| 4| 5| 5|5 6|02441 6|8 7|3 7|5659898 8|43020 8|58 9|320 9|58 b. The outlier at 32 is much more apparent. Also, there appears to be a bimodal element, with a set of scores in the low 60’s, that was not evident in the stemplot in Figure 7.1. 7.2 a. 32, 66, 78.5, 84.5, 98 b. See the Figure below. 7.3 This histogram should have the same shape as the stemplot in Figure 7.1. The picture is skewed to the left due to the outlier. Ignoring the outlier, it is fairly evenly spread out over the range 55 to 98, with some clumping in the middle. Depending on how it is drawn, a bimodal shape may be evident. 7.4 Any measurement that is likely to have extreme outliers distorting the mean. Examples include sales prices of used cars, number of people killed in earthquakes of magnitude 4 or higher, salaries at companies with a few high-paid executives, and so on. 7.5 Any set in which all five numbers are equal. 7.6 10, 11, 30, 38, 39, 41, 65, 70, 72, 80 7.7 Whether or not there are any “outliers” – values more than 1.5 IQRs beyond the quartiles. Page 1 of 6

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CHAPTER 7 SOLUTIONS AND MINI-PROJECT NOTES 7.8 Mean = 25, variance = 125, so standard deviation = 11.18. 7.9 a. 65 b. 54, 62.5, 65, 70.5, 78 7.10 a. See the figure below. You could also draw them to be horizontal instead of vertical. b. Hours of sleep for males and females are similar except that there are a few males who are outliers because they slept so many hours. 7.11 a. Range = \$82,879 \$46,596 = \$36,283. b. Interquartile range = \$66,507 \$56,067 = \$10,440. c. Outliers are more than 1.5 interquartile ranges beyond the quartiles, in this case, more than (1.5) × \$10,440 = \$15,660 beyond the quartiles of \$56,067 and \$66,507. Thus, an outlier at the lower end is less than \$56,067 \$15,660 = \$40,407 and at the upper end is more than \$66,507 + \$15,660 = \$82,167. There are no outliers at the lower end. At the upper end, Connecticut (\$82,517) and Maryland (\$82,879) are outliers. d. See the figure below. Page 2 of 6
CHAPTER 7 SOLUTIONS AND MINI-PROJECT NOTES e. The histogram is more useful. Both plots capture the outliers and high values in the \$80,000s, but the histogram illustrates the approximate bell-shape for the remainder of the data. 7.12

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This note was uploaded on 10/15/2011 for the course STAT 100 at Penn State.

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chapter_07 - CHAPTER 7 SOLUTIONS AND MINI-PROJECT NOTES...

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