Section 3.3 Measures of Position 139 Phillies 14.2 10.0 8.6 8.0 8.0 7.8 6.4 6.0 5.5 5.0 3.3 3.0 2.4 1.7 1.4 0.90 0.90 0.60 0.50 0.48 0.45 0.44 0.43 0.42 0.42 0.40 0.39 0.39 0.39 Yankees 28.0 23.4 21.6 16.0 16.0 15.0 13.1 13.0 13.0 11.0 11.0 5.9 4.0 3.8 3.0 1.9 1.8 1.2 1.2 0.73 0.50 0.46 0.41 0.40 0.40 0.39 0.39 0.39 0.39 0.39 a. Find the median, the first quartile, and the third quartile of the Phillies’ salaries. b. Find the median, the first quartile, and the third quartile of the Yankees’ salaries. c. Find the upper and lower outlier bounds for the Phillies’ salaries. d. Find the upper and lower outlier bounds for the Yankees’ salaries. e. Construct comparative boxplots for the two data sets. What conclusions can you draw? 36. Automotive emissions: Following are levels of particulate emissions for 65 vehicles driven at sea level, and for 35 vehicles driven at high altitude. Sea Level 1.5 0.9 1.1 1.3 3.5 1.1 1.1 0.9 1.3 0.9 0.6 1.3 2.5 1.5 1.1 1.1 2.2 0.9 1.8 1.5 1.2 1.6 2.1 6.6 4.0 2.5 1.4 1.4 1.8 1.1 1.6 3.7 0.6 2.7 2.6 3.0 1.2 1.0 1.6 3.1 2.4 2.1 2.7 1.2 3.3 3.8 1.3 2.1 6.6 1.2 3.1 0.5 0.3 0.5 3.4 3.5 2.7 1.9 5.9 4.2 3.5 3.6 3.1 3.3 4.6 High Altitude 8.9 4.4 3.6 4.4 3.8 2.4 3.8 5.3 5.8 2.9 4.7 1.9 9.1 8.7 9.5 2.7 9.2 7.3 2.1 6.3 6.5 6.3 2.0 5.9 5.6 5.6 1.5 6.5 5.3 5.6 2.1 1.1 3.3 1.8 7.6 a. Find the median, the first quartile, and the third quartile of the sea-level emissions. b. Find the median, the first quartile, and the third quartile of the high-altitude emissions. c. Find the upper and lower outlier bounds for the sea-level emissions. d. Find the upper and lower outlier bounds for the high-altitude emissions. e. Construct comparative boxplots for the two data sets. What conclusions can you draw? Extending the Concepts 37. The vanishing outlier: Seven families live on a small street in a certain town. Their annual incomes (in $1000s) are 15, 20, 30, 35, 50, 60, and 150. a. Find the first and third quartiles, and the IQR. b. Show that 150 is an outlier. A big new house is built on the street, and the income (in $1000s) of the family that moves in is 200. c. Find the first and third quartiles, and the IQR of the eight incomes. d. Are there any outliers now? e. Explain how adding the value 200 to the data set eliminated the outliers. 38. Beyond quartiles and percentiles: If we divide a data set into four approximately equal parts, the three dividing points are called quartiles. If we divide a data set into 100 approximately equal parts, the 99 dividing points are called percentiles. In general, if we divide a data set into k approximately equal parts, we can call the dividing points k-tiles. How would you find the ith k-tile of a data set of size n? 39. z-scores and skewed data: Table 3.9 presents the February rainfalls in Los Angeles for the period 1965–2006. a. Show that the mean of these data is μ = 3.749 and the standard deviation is σ = 3.5808. b. Show that the z-score for a rainfall of 0 (rounded to two decimal places) is z = −1.05. c. Show that the z-score for a rainfall of 7.5 (rounded to two decimal places) is z = 1.05. d. What percentage of the years had rainfalls of 0? e. What percentage of the years had rainfalls of 7.5 or more? f. The z-scores indicate that a rainfall of 0 and a rainfall of 7.5 are about equally extreme. Is a rainfall of 7.5 really as extreme as a rainfall of 0, or is it less extreme? g. These data are skewed to the right. Explain how skewness causes the z-score to give misleading results. Answers to Check Your Understanding Exercises for Section 3.3 1. a. 70 b. 83 c. 30th d. Yes 2. 90% 3. a. 22 66 80 119 209 b. 53 c. Lower outlier bound is −13.5; upper bound is 198.5. d. 209 is the only outlier. 4. 0 50 100 150 200 250
navidi_monk_essential_statistics_1e_ch1_3
To see the actual publication please follow the link above