An insurance company experienced the following mobile home

In Exercise 6.1-7, lead concentrations near the San Diego Freeway in 1976 are given. During the fall of 1977, the weekday afternoon lead concentrations (in/m3) at the measurement station near the San Diego Freeway in Los Angeles were as follows: 9.5 10.7 8.3 9.8 9.1 9.4 9.6 11.9 9.5 12.6 10.5 8.9 11.4 12.0 12.4 9.9 10.9 12.3 11.0 9.2 9.3 9.3 10.5 9.4 9.4 8.2 10.4 9.3 8.7 9.8 9.1 2.9 9.8 5.7 8.2 8.1 8.8 9.7 8.1 8.8 10.3 8.6 10.2 9.4 14.8 9.9 9.3 8.2 9.9 11.6 8.7 5.0 9.9 6.3 6.5 10.2 8.8 8.0 8.7 8.9 6.8 6.6 7.3 16.7 (a) Construct a frequency distribution and display the results in the form of a histogram. Is this distribution symmetric? (b) Calculate the sample mean and sample standard deviation. (c) Locate , ± on your histogram. How many observations lie within one standard deviation of the mean? How many lie within two standard deviations of the mean? (d) Using the data from Exercise 6.1-7 and the data from this exercise, construct a back-to-back stem-and-leaf diagram with integer stems in the center and the leaves for 1976 going to the left and those for 1977 going to the right. (e) Construct box-and-whisker displays of both sets of data on the same graph. (f) Use your numerical and graphical results to interpret what you see.

When you purchase “1-pound bags” of carrots, you can buy either “baby” carrots or regular carrots. We shall compare the weights of 75 bags of each of these types of carrots. The following table gives the weights of the bags of baby carrots: 1.03 1.03 1.06 1.02 1.03 1.03 1.03 1.02 1.03 1.03 1.06 1.04 1.05 1.03 1.04 1.03 1.05 1.06 1.04 1.04 1.03 1.04 1.04 1.06 1.03 1.04 1.05 1.04 1.04 1.02 1.03 1.05 1.05 1.03 1.04 1.03 1.04 1.04 1.03 1.04 1.03 1.04 1.04 1.04 1.05 1.04 1.04 1.03 1.03 1.05 1.04 1.04 1.05 1.04 1.03 1.03 1.05 1.03 1.04 1.05 1.04 1.04 1.04 1.05 1.03 1.04 1.04 1.04 1.04 1.03 1.05 1.05 1.05 1.03 1.04 This table gives the weights of the regular-sized carrots: 1.29 1.10 1.28 1.29 1.23 1.20 1.31 1.25 1.13 1.26 1.19 1.33 1.24 1.20 1.26 1.24 1.11 1.14 1.15 1.15 1.19 1.26 1.14 1.20 1.20 1.20 1.24 1.25 1.28 1.24 1.26 1.20 1.30 1.23 1.26 1.16 1.34 1.10 1.22 1.27 1.21 1.09 1.23 1.03 1.32 1.21 1.23 1.34 1.19 1.18 1.20 1.20 1.13 1.43 1.19 1.05 1.16 1.19 1.07 1.21 1.36 1.21 1.00 1.23 1.22 1.13 1.24 1.10 1.18 1.26 1.12 1.10 1.19 1.10 1.24 (a) Calculate the five-number summary of each set of weights. (b) On the same graph, construct box plots for each set of weights. (c) If the carrots are the same price per package, which is the better buy? Which type of carrots would you select?

Here are underwater weights in kilograms for 82 male students: 3.7 3.6 4.0 4.3 3.8 3.4 4.1 4.0 3.7 3.4 3.5 3.8 3.7 4.9 3.5 3.8 3.3 4.8 3.4 4.6 3.5 5.3 4.4 4.2 2.5 3.1 5.2 3.8 3.3 3.4 4.1 4.6 4.0 1.4 4.3 3.8 4.7 4.4 5.0 3.2 3.1 4.2 4.9 4.5 3.8 4.2 2.7 3.8 3.8 2.0 3.4 4.9 3.3 4.3 5.6 3.2 4.7 4.5 5.2 5.0 5.0 4.0 3.8 5.3 4.5 3.8 3.8 3.4 3.6 3.3 4.2 5.1 4.0 4.7 6.5 4.4 3.6 4.7 4.5 2.3 4.0 3.7 Here are underwater weights in kilograms for 100 female students: 2.0 2.0 2.1 1.6 1.9 2.0 2.0 1.3 1.3 1.2 2.3 1.9 2.1 1.2 2.0 1.6 1.1 2.2 2.2 1.4 1.7 2.4 1.8 1.7 2.0 2.1 1.6 1.7 1.8 0.7 1.9 1.7 1.7 1.1 2.0 2.3 0.5 1.3 2.7 1.8 2.0 1.7 1.2 0.7 1.1 1.1 1.7 1.7 1.2 1.2 0.7 2.3 1.7 2.4 1.0 2.4 1.4 1.9 2.5 2.2 2.1 1.4 2.4 1.8 2.5 1.3 0.5 1.7 1.9 1.8 1.3 2.0 2.2 1.7 2.0 2.5 1.2 1.4 1.4 1.2 2.2 2.0 1.8 1.4 1.9 1.4 1.3 2.5 1.2 1.5 0.8 2.0 2.2 1.8 2.0 1.6 1.5 1.6 1.5 2.6 (a) Group each set of data into classes with a class width of 0.5 kilograms and in which the class marks are 0.5, 1.0, 1.5, . . . . (b) Draw histograms of the grouped data. (c) Construct box-and-whisker diagrams of the data and draw them on the same graph. Describe what this graph shows.

In Exercise 6.1-3, measurements for 96 plungers are given. Use those measurements to (a) Construct a stem-and-leaf diagram using integer stems. (b) Find the five-number summary of the data. (c) Construct a box-and-whisker diagram. Are there any outliers?

An insurance company experienced the following mobile home losses in \(10,000 ' s\) of dollars for 50 catastrophic events: 1 2 2 3 3 4 4 5 5 5 5 6 7 7 9 9 9 10 11 12 22 24 28 29 31 33 36 38 38 38 39 41 48 49 53 55 74 82 117 134 192 207 224 225 236 280 301 308 351 527 (a) Find the five-number summary of the data and draw a box-and-whisker diagram. (b) Calculate the IQR and the locations of the inner and outer fences. (c) Draw a box plot that shows the fences, suspected outliers, and outliers. (d) Describe the distribution of losses. (See Exercise 6.1-6.) Equation Transcription: Text Transcription: 10,000’s

In Exercise 6.1-5, data are given for the number of $1 bets a player can make in roulette before losing $5. Use those data to respond to the following: (a) Determine the order statistics. (b) Find the five-number summary of the data. (c) Draw a box-and-whisker diagram. (d) Find the locations of the inner and outer fences, and draw a box plot that shows the fences, the suspected outliers, and the outliers. (e) In your opinion, does the median or sample mean give a better measure of the center of the data?

Let \(X\) denote the concentration of calcium carbonate \(\left(\mathrm{CaCO}_{3}\right)\) in milligrams per liter. Following are 20 observations of \(X\): 130.8 129.9 131.5 131.2 129.5 132.7 131.5 127.8 133.7 132.2 134.8 131.7 133.9 129.8 131.4 128.8 132.7 132.8 131.4 131.3 (a) Construct an ordered stem-and-leaf display, using stems of \(127,128, \ldots, 134\). (b) Find the midrange, range, interquartile range, median, sample mean, and sample variance. (c) Draw a box-and-whisker diagram. Equation Transcription: Text Transcription: X (CaCO_3) 127, 128, . . . , 134

In the casino game roulette, if a player bets $1 on red (or on black or on odd or on even), the probability of winning $1 is \(18/38\) and the probability of losing $1 is \(20/38\). Suppose that a player begins with $5 and makes successive $1 bets. Let \(Y\) equal the player’s maximum capital before losing the $5. One hundred observations of \(Y\) were simulated on a computer, yielding the following data: 25 9 5 5 5 9 6 5 15 45 55 6 5 6 24 21 16 5 8 7 7 5 5 35 13 9 5 18 6 10 19 16 21 8 13 5 9 10 10 6 23 8 5 10 15 7 5 5 24 9 11 34 12 11 17 11 16 5 15 5 12 6 5 5 7 6 17 20 7 8 8 6 10 11 6 7 5 12 11 18 6 21 6 5 24 7 16 21 23 15 11 8 6 8 14 11 6 9 6 10 (a) Construct an ordered stem-and-leaf display. (b) Find the five-number summary of the data and draw a box-and-whisker diagram. (c) Calculate the IQR and the locations of the inner and outer fences. (d) Draw a box plot that shows the fences, suspected outliers, and outliers. (e) Find the 90th percentile. Equation Transcription: Text Transcription: 18/38 20/38 Y

In Exercise 6.1-4, the melting points of a firm’s alloy filaments are given for a sample of 50 filaments. (a) Construct a stem-and-leaf diagram of those melting points, using as stems \(30 f, 30 s, \ldots, 33 f\) (b) Find the five-number summary for these melting points. (c) Construct a box-and-whisker diagram. (d) Describe the symmetry of the data. Equation Transcription: Text Transcription: 30f, 30s, . . . , 33f

The weights (in grams) of 25 indicator housings used on gauges are as follows: 102.0 106.3 106.6 108.8 107.7 106.1 105.9 106.7 106.8 110.2 101.7 106.6 106.3 110.2 109.9 102.0 105.8 109.1 106.7 107.3 102.0 106.8 110.0 107.9 109.3 (a) Construct an ordered stem-and-leaf display, using integers as the stems and tenths as the leaves. (b) Find the five-number summary of the data and draw a box plot. (c) Are there any suspected outliers? Are there any outliers?

In Exercise 6.1-3, measurements for 96 plungers are given. Use those measurements to (a) Construct a stem-and-leaf diagram using integer stems. (b) Find the five-number summary of the data. (c) Construct a box-and-whisker diagram. Are there any outliers? Exercise 6.1-3 During the course of an internship at a company that manufactures diesel engine fuel injector pumps, a student had to measure the category “plungers that force the fuel out of the pumps.” This category is based on a relative scale, measuring the difference in diameter (in microns or micrometers) of a plunger from that of an absolute minimum acceptable diameter. For 96 plungers randomly taken from the production line, the data are as follows: (a) Calculate the sample mean and the sample standard deviation of these measurements. (b) Use the class boundaries 10.95, 11.95, . . . , 22.95 to construct a histogram of the data.

When you purchase 1-pound bags of carrots, you can buy either baby carrots or regular carrots. We shall compare the weights of 75 bags of each of these types of carrots. The following table gives the weights of the bags of baby carrots: 1.03 1.03 1.06 1.02 1.03 1.03 1.03 1.02 1.03 1.03 1.06 1.04 1.05 1.03 1.04 1.03 1.05 1.06 1.04 1.04 1.03 1.04 1.04 1.06 1.03 1.04 1.05 1.04 1.04 1.02 1.03 1.05 1.05 1.03 1.04 1.03 1.04 1.04 1.03 1.04 1.03 1.04 1.04 1.04 1.05 1.04 1.04 1.03 1.03 1.05 1.04 1.04 1.05 1.04 1.03 1.03 1.05 1.03 1.04 1.05 1.04 1.04 1.04 1.05 1.03 1.04 1.04 1.04 1.04 1.03 1.05 1.05 1.05 1.03 1.04 This table gives the weights of the regular-sized carrots: 1.29 1.10 1.28 1.29 1.23 1.20 1.31 1.25 1.13 1.26 1.19 1.33 1.24 1.20 1.26 1.24 1.11 1.14 1.15 1.15 1.19 1.26 1.14 1.20 1.20 1.20 1.24 1.25 1.28 1.24 1.26 1.20 1.30 1.23 1.26 1.16 1.34 1.10 1.22 1.27 1.21 1.09 1.23 1.03 1.32 1.21 1.23 1.34 1.19 1.18 1.20 1.20 1.13 1.43 1.19 1.05 1.16 1.19 1.07 1.21 1.36 1.21 1.00 1.23 1.22 1.13 1.24 1.10 1.18 1.26 1.12 1.10 1.19 1.10 1.24 (a) Calculate the five-number summary of each set of weights. (b) On the same graph, construct box plots for each set of weights. (c) If the carrots are the same price per package, which is the better buy? Which type of carrots would you select?

Here are underwater weights in kilograms for 82 male students: 3.7 3.6 4.0 4.3 3.8 3.4 4.1 4.0 3.7 3.4 3.5 3.8 3.7 4.9 3.5 3.8 3.3 4.8 3.4 4.6 3.5 5.3 4.4 4.2 2.5 3.1 5.2 3.8 3.3 3.4 4.1 4.6 4.0 1.4 4.3 3.8 4.7 4.4 5.0 3.2 3.1 4.2 4.9 4.5 3.8 4.2 2.7 3.8 3.8 2.0 3.4 4.9 3.3 4.3 5.6 3.2 4.7 4.5 5.2 5.0 5.0 4.0 3.8 5.3 4.5 3.8 3.8 3.4 3.6 3.3 4.2 5.1 4.0 4.7 6.5 4.4 3.6 4.7 4.5 2.3 4.0 3.7 Here are underwater weights in kilograms for 100 female students: 2.0 2.0 2.1 1.6 1.9 2.0 2.0 1.3 1.3 1.2 2.3 1.9 2.1 1.2 2.0 1.6 1.1 2.2 2.2 1.4 1.7 2.4 1.8 1.7 2.0 2.1 1.6 1.7 1.8 0.7 1.9 1.7 1.7 1.1 2.0 2.3 0.5 1.3 2.7 1.8 2.0 1.7 1.2 0.7 1.1 1.1 1.7 1.7 1.2 1.2 0.7 2.3 1.7 2.4 1.0 2.4 1.4 1.9 2.5 2.2 2.1 1.4 2.4 1.8 2.5 1.3 0.5 1.7 1.9 1.8 1.3 2.0 2.2 1.7 2.0 2.5 1.2 1.4 1.4 1.2 2.2 2.0 1.8 1.4 1.9 1.4 1.3 2.5 1.2 1.5 0.8 2.0 2.2 1.8 2.0 1.6 1.5 1.6 1.5 2.6 (a) Group each set of data into classes with a class width of 0.5 kilograms and in which the class marks are 0.5, 1.0, 1.5, ... . (b) Draw histograms of the grouped data. (c) Construct box-and-whisker diagrams of the data and draw them on the same graph. Describe what this graph shows.

An insurance company experienced the following mobile home losses in 10,000s of dollars for 50 catastrophic events: 1223344555 5 6 7 7 9 9 9 10 11 12 22 24 28 29 31 33 36 38 38 38 39 41 48 49 53 55 74 82 117 134 192 207 224 225 236 280 301 308 351 527 (a) Find the five-number summary of the data and draw a box-and-whisker diagram. (b) Calculate the IQR and the locations of the inner and outer fences. (c) Draw a box plot that shows the fences, suspected outliers, and outliers. (d) Describe the distribution of losses. (See Exercise 6.1-6.)

In Exercise 6.1-5, data are given for the number of $1 bets a player can make in roulette before losing $5. Use those data to respond to the following: (a) Determine the order statistics. (b) Find the five-number summary of the data. (c) Draw a box-and-whisker diagram. (d) Find the locations of the inner and outer fences, and draw a box plot that shows the fences, the suspected outliers, and the outliers. (e) In your opinion, does the median or sample mean give a better measure of the center of the data?

In the casino game roulette, if a player bets $1 on red (or on black or on odd or on even), the probability of winning $1 is 18/38 and the probability of losing $1 is 20/38. Suppose that a player begins with $5 and makes successive $1 bets. Let Y equal the players maximum capital before losing the $5. One hundred observations of Y were simulated on a computer, yielding the following data: 25 9 5 5 5 9 6 5 15 45 55 6 5 6 24 21 16 5 8 7 7 5 5 35 13 9 5 18 6 10 19 16 21 8 13 5 9 10 10 6 23 8 5 10 15 7 5 5 24 9 11 34 12 11 17 11 16 5 15 5 12 6 5 5 7 6 17 20 7 8 8 6 10 11 6 7 5 12 11 18 6 21 6 5 24 7 16 21 23 15 11 8 6 8 14 11 6 9 6 10 (a) Construct an ordered stem-and-leaf display. (b) Find the five-number summary of the data and draw a box-and-whisker diagram. (c) Calculate the IQR and the locations of the inner and outer fences. (d) Draw a box plot that shows the fences, suspected outliers, and outliers. (e) Find the 90th percentile.

Let X denote the concentration of calcium carbonate (CaCO3) in milligrams per liter. Following are 20 observations of X: 130.8 129.9 131.5 131.2 129.5 132.7 131.5 127.8 133.7 132.2 134.8 131.7 133.9 129.8 131.4 128.8 132.7 132.8 131.4 131.3 (a) Construct an ordered stem-and-leaf display, using stems of 127, 128, ..., 134. (b) Find the midrange, range, interquartile range, median, sample mean, and sample variance. (c) Draw a box-and-whisker diagram.

The weights (in grams) of 25 indicator housings used on gauges are as follows: 102.0 106.3 106.6 108.8 107.7 106.1 105.9 106.7 106.8 110.2 101.7 106.6 106.3 110.2 109.9 102.0 105.8 109.1 106.7 107.3 102.0 106.8 110.0 107.9 109.3 (a) Construct an ordered stem-and-leaf display, using integers as the stems and tenths as the leaves. (b) Find the five-number summary of the data and draw a box plot. (c) Are there any suspected outliers? Are there any outliers?

In Exercise 6.1-4, the melting points of a firms alloy filaments are given for a sample of 50 filaments. (a) Construct a stem-and-leaf diagram of those melting points, using as stems 30f, 30s, ... , 33f. (b) Find the five-number summary for these melting points. (c) Construct a box-and-whisker diagram. (d) Describe the symmetry of the data.

In Exercise 6.1-7, lead concentrations near the San Diego Freeway in 1976 are given. During the fall of 1977, the weekday afternoon lead concentrations (in g/m3) at the measurement station near the San Diego Freeway in Los Angeles were as follows: 9.5 10.7 8.3 9.8 9.1 9.4 9.6 11.9 9.5 12.6 10.5 8.9 11.4 12.0 12.4 9.9 10.9 12.3 11.0 9.2 9.3 9.3 10.5 9.4 9.4 8.2 10.4 9.3 8.7 9.8 9.1 2.9 9.8 5.7 8.2 8.1 8.8 9.7 8.1 8.8 10.3 8.6 10.2 9.4 14.8 9.9 9.3 8.2 9.9 11.6 8.7 5.0 9.9 6.3 6.5 10.2 8.8 8.0 8.7 8.9 6.8 6.6 7.3 16.7 (a) Construct a frequency distribution and display the results in the form of a histogram. Is this distribution symmetric? (b) Calculate the sample mean and sample standard deviation.(c) Locate x, x s on your histogram. How many observations lie within one standard deviation of the mean? How many lie within two standard deviations of the mean? (d) Using the data from Exercise 6.1-7 and the data from this exercise, construct a back-to-back stem-and-leaf diagram with integer stems in the center and the leaves for 1976 going to the left and those for 1977 going to the right. (e) Construct box-and-whisker displays of both sets of data on the same graph. (f) Use your numerical and graphical results to interpret what you see.