Solution Manual for Introductory Statistics, 9th Edition

Chapter 2 11 Chapter 2 Organizing and Graphing Data Section 2.1 2.1 Data in their original form are often too large and unmanageable. It is easier to make sense of grouped data than ungrouped data and easier to make decisions and draw conclusions using grouped data. 2.2 The relative frequency for a category is obtained by dividing the frequency of that category by the sum of the frequencies of all categories. The percentage for a category is obtained by multiplying the relative frequency of that category by 100. Example 22 in the text is an example which shows how relative frequencies and percentages are calculated. 2.3 a. and b. Category Frequency Y N D 23 13 4 Relative Frequency 23/40 = 0.575 13/40 = 0.325 4/40 = 0.100 c. 57.5% of the elements belong to category Y. d. 17/40 = 42.5% of the elements belong to categories N or D. e. D 10.0% N 32.5% Y 57.5% Percentage 57.5 32.5 10.0 Chapter 2 f. Pareto Chart of Categories 40 100 Counts 60 20 Percent 80 30 40 10 a. and b. 0 Categories Counts Percent Cum % Y 23 57.5 57.5 Category Frequency G B I 14 21 5 N 13 32.5 90.0 D 0 4 10.0 100.0 Relative Frequency 14/40 = 0.35 21/40 = 0.525 5/40 = 0.125 Percentage 35 52.5 12.5 c. Thirty-five percent of the adults in this sample said that building casinos is good. d. (21 + 5) / 40 = 65% of the adults in this sample either said that building casinos is bad or were indifferent. e. Chart of Counts 20 15 Counts 2.4 20 10 5 0 B G Categories I 12 Chapter 2 f. Pie Chart of Categories Category B G I I 12.5% G 35% B 52.5% g. Pareto Chart of Categories 40 100 Counts 60 20 Percent 80 30 40 10 0 Categories Counts Percent Cum % 2.5 a. and b. c. Category PI S V PO B C 20 G 21 52.5 52.5 B 14 35.0 87.5 Frequency 9 8 13 3 1 2 I 0 5 12.5 100.0 Relative Frequency 9/36 = 0.25 8/36 = 0.222 13/36 = 0.361 3/36 = 0.083 1/36 = 0.028 2/36 = 0.056 V + PO + C = 13 + 3 + 2 = 18; 18/36 = 0.5 = 50% 50% of the respondents mentioned vegetables and fruits, poultry, or cheese. Percentage 25 22.2 36.1 8.3 2.8 5.6 13 Chapter 2 Relative Frequency d. 0.4 0.3 0.2 0.1 0 PI S V PO B C Favorite Pizza Topping 2.6 a. and b. Category Frequency C CK CC D O 4 5 4 2 1 c. CC 25.0% D 12.5% O 6.3% C 25.0% CK 31.3% Relative Frequency 4/16 = 0.250 5/16 = 0.313 4/16 = 0.250 2/16 = 0.125 1/16 = 0.063 Percentage 25.0 31.3 25.0 12.5 6.3 14 Chapter 2 2.7 15 a. Let N = No financial stress, S = Some financial stress, H = High financial stress, and O = Overwhelming financial stress. Pie Chart of Financial Stress Level Category N S H O O 5% N 14% H 18% S 63% b. 100 100 80 80 60 60 40 40 20 20 0 Financial Stress Level Percentage Percent Cum % S 63 63.0 63.0 H 18 18.0 81.0 N 14 14.0 95.0 Other 5 5.0 100.0 Percent Percentage Pareto Chart of Financial Stress Level 0 Section 2.2 2.8 The three decisions that have to be made to group a data set in the form of a frequency distribution table are 1. The number of classes to be used to group the given data. 2. The width of each class. 3. The lower limit of the first class. 2.9 The relative frequency for a class is obtained by dividing the frequency of that class by the sum of frequencies of all classes. The percentage for a class is obtained by multiplying the relative frequency of that class by 100. Example 2-4 is an example that illustrates the calculation of relative frequencies and percentages. 2.10 A data set that does not contain fractional values is usually grouped by using classes with limits. Example 24 is an example of the writing classes using limits method. A data set that contains fractional values is grouped by using the less than method. Example 25 is an example of the less than method. Single-valued Chapter 2 16 classes are used to group a data set that contains only a few distinct (integer) values. Example 26 is an example of the single-valued classes method. 2.11 a. 31 + 78 + 49 + 81 + 117 + 13 = 369 customers were served. b. Each class has a width of 4. Gallons of Gas Class Width (Class Limits) 0 to less than 4 4 4 to less than 8 4 8 to less than 12 4 12 to less than 16 4 16 to less than 20 4 20 to less than 24 4 Gallons of Gas 0 to less than 4 4 to less than 8 8 to less than 12 12 to less than 16 16 to less than 20 20 to less than 24 c. Class Midpoint 0+4 =2 2 4+8 =6 2 8 + 12 = 10 2 12 + 16 = 14 2 16 + 20 = 18 2 20 + 24 = 22 2 Number of Customers 31 78 49 81 117 13 Relative Frequency 31/369 ≈ 0.084 78/369 ≈ 0.211 49/369 ≈ 0.133 81/369 ≈ 0.220 117/369 ≈ 0.317 13/369 ≈ 0.035 Percentage 8.4 21.1 13.3 22.0 31.7 3.5 d. 22.0 + 31.7 + 3.5 = 57.2% of the customers purchased 12 gallons or more. e. The number of customers who purchased 10 gallons or less cannot be determined exactly because 10 is not a boundary value. f. 2.12 Gallons of Gasoline Cumulative Frequency 0 to less than 4 0 to less than 8 0 to less than 12 0 to less than 16 0 to less than 20 0 to less than 24 31 31 + 78 = 109 31 + 78 + 49 = 158 31 + 78 + 49 + 81 = 239 31 + 78 + 49 + 81 + 117 = 356 31 + 78 + 49 + 81 + 117 + 13 = 369 a. and b. Class Limits $1 to $200 $201 to $400 $401 to $600 $601 to $800 $801 to $1000 $1001 to $1200 Cumulative Relative Frequency 31/369 = 0.084 109/369 = 0.295 158/369 = 0.428 239/369 = 0.648 356/369 = 0.965 1.000 Class Boundaries $0.5 to less than $200.5 $200.5 to less than $400.5 $400.5 to less than $600.5 $600.5 to less than $800.5 $800.5 to less than $1000.5 $1000.5 to less than $1200.5 Class Midpoints $100.5 $300.5 $500.5 $700.5 $ 900.5 $1100.5 Cumulative Percentage 8.4 29.5 42.8 64.8 96.5 100.0 Chapter 2 2.13 a. and b. Commuting Times Frequency 0 to 9 10 to 19 20 to 29 30 to 39 40 to 49 2 14 14 13 7 Relative Frequency 2/50 = 0.04 14/50 = 0.28 14/50 = 0.28 13/50 = 0.26 7/50 = 0.14 17 Percentage 4 28 28 26 14 c. Histogram for Commuting Times 30 25 Percentage 20 15 10 5 0 0 to 9 10 to 19 20 to 29 30 to 39 40 to 49 Commuting Times d. (13 + 7)/50 = 40% of the workers in the sample commute for 30 minutes or more. e. Commuting Times 0 to 9 10 to 19 20 to 29 30 to 39 40 to 49 2.14 a. and b. Cumulative Frequency 2 2 + 14 = 16 2 + 14 + 14 = 30 2 + 14 + 14 + 13 = 43 2 + 14 + 14 + 13 + 7 = 50 Age 20 to 29 30 to 39 40 to 49 50 to 59 60 to 69 Cumulative Relative Frequency 2/50 = 0.04 16/50 = 0.32 30/50 = 0.60 43/50 = 0.86 50/50 = 1.00 Frequency 6 9 6 8 1 Cumulative Percentage 4 32 60 86 100 Relative Frequency 6/30 = 0.200 9/30 = 0.300 6/30 = 0.200 8/30 = 0.267 1/30 = 0.033 Percentage 20.0 30.0 20.0 26.7 3.30 Chapter 2 c. Frequency Histogram for Age of Male Participants 9 8 Frequency 7 6 5 4 3 2 1 0 20 to 29 30 to 39 40 to 49 50 to 59 60 to 69 Age of Male Participants d. a. and b. Age 20 to 29 30 to 39 40 to 49 50 to 59 60 to 69 Frequency 8 9 6 6 1 Relative Frequency 8/30 = 0.267 9/30 = 0.300 6/30 = 0.200 6/30 = 0.200 1/30 = 0.033 Percentage 26.7 30.0 20.0 20.0 3.30 c. Frequency Histogram for Age of Female Participants 9 8 7 Frequency 2.15 (6 + 9)/30 = 50% of the male participants are younger than 40 years of age. 6 5 4 3 2 1 0 20 to 29 30 to 39 40 to 49 50 to 59 60 to 69 Age of Female Participants d. (8 + 9)/30 = 56.7% of female participants are younger than 40 years of age. e. The male and female age distributions are very similar, with only slight differences in the exact heights of the bars. 18 Chapter 2 2.16 a. and b. Weight 91 to 125 126 to 160 161 to 195 196 to 230 231 to 265 Frequency 2 7 5 10 6 Relative Frequency 2/30 = 0.067 7/30 = 0.233 5/30 = 0.167 10/30 = 0.333 6/30 = 0.200 Percentage 6.7 23.3 16.7 33.3 20.0 c. Relative Frequency Histogram for Weights of Male Participants 0.35 Relative Frequency 0.30 0.25 0.20 0.15 0.10 0.05 0.00 91 to 125 126 to 160 161 to 195 196 to 230 231 to 265 Weights of Male Participants d. a. and b. Weight 91 to 125 126 to 160 161 to 195 196 to 230 231 to 265 Frequency 5 7 3 6 9 Relative Frequency 5/30 = 0.167 7/30 = 0.233 3/30 = 0.100 6/30 = 0.200 9/30 = 0.300 c. Relative Frequency Histogram for Weights of Female Participants 0.30 0.25 Relative Frequency 2.17 (2 + 7)/30 = 30% of male participants weighed less than 161 pounds. 0.20 0.15 0.10 0.05 0.00 91 to 125 126 to 160 161 to 195 196 to 230 231 to 265 Weights of Female Participants d. (5 + 7)/30 = 40% of female participants weighed less than 161 pounds. Percentage 16.7 23.3 10.0 20.0 30.0 19 Chapter 2 e. 2.18 The weight distributions were similar, but 10% more of the females had a weight below 161 pounds than did the males. The percentage above 195 pounds was the same in both distributions, but of these more females fell in the 231 to 265 pounds range than did males. a. and b. Blood Glucose Level 75 to 89 90 to 104 105 to 119 120 to 134 135 to 149 Frequency 5 7 8 7 3 Relative Frequency 5/30 = 0.167 7/30 = 0.233 8/30 = 0.267 7/30 = 0.233 3/30 = 0.100 Percentage 16.7 23.3 26.7 23.3 10.0 c. Percentage Distribution Histogram for Male Blood Glucose Levels 30 25 Percentage 20 15 10 5 0 75 to 89 90 to 104 105 to 119 120 to 134 135 to 149 Blood Glucose Level of Males d. (7 + 3)/30 = 33.3% of male participants had a blood glucose level higher than 119. e. Blood Glucose Level 75 to 89 75 to 104 75 to 119 75 to 134 75 to 149 2.19 20 Cumulative Frequency Cumulative Relative Frequency Cumulative Percentage 5 5 + 7 = 12 5 + 7 + 8 = 20 5 + 7 + 8 + 7 = 27 5 + 7 + 8 + 7 + 3 = 30 5/30 = 0.167 12/30 = 0.400 20/30 = 0.667 27/30 = 0.900 30/30 = 1.000 16.7 40.0 66.7 90.0 100.0 Relative Frequency 6/30 = 0.200 4/30 = 0.133 7/30 = 0.233 7/30 = 0.233 6/30 = 0.200 Percentage 20.0 13.3 23.3 23.3 20.0 a. and b. Blood Glucose Level 75 to 89 90 to 104 105 to 119 120 to 134 135 to 149 Frequency 6 4 7 7 6 Chapter 2 c. Percentage Distribution Histogram for Female Blood Glucose Levels 25 Percentage 20 15 10 5 0 75 to 89 90 to 104 105 to 119 120 to 134 135 to 149 Blood Glucose Level of Females d. (7 + 6)/30 = 43.3% of female participants had a blood glucose level higher than 119. e. Taking the center of both distributions to be the class 105 to 119, the shape of the left and right tails between the two distribution is swapped, meaning there are more females with blood glucose levels less than 119 than there are males with such glucose levels, and there are more females with blood glucose level greater than 119 than there are males with such blood glucose levels. f. Blood Glucose Level 75 to 89 75 to 104 75 to 119 75 to 134 75 to 149 Cumulative Frequency 6 6 + 4 = 10 6 + 4 + 7 = 17 6 + 4 + 7 + 7 = 24 6 +4 + 7 + 7 + 6 = 30 Cumulative Relative Frequency 6/30 = 0.200 10/30 = 0.333 17/30 = 0.567 24/30 = 0.800 30/30 = 1.000 Cumulative Percentage 20.0 33.3 56.7 80.0 100.0 2.20 Strikeouts Per Game 6.30 to less than 6.85 6.85 to less than 7.40 7.40 to less than 7.95 7.95 to less than 8.50 8.50 to less than 9.05 Frequency 3 6 10 9 2 Relative Frequency 3/30 = 0.100 6/30 = 0.200 10/30 = 0.333 9/30 = 0.300 2/30 = 0.067 Percentage 10.0 20.0 33.3 30.0 6.7 21 Chapter 2 2.21 a. and b. Turnovers 1 2 3 4 5 6 7 8 Frequency 4 5 3 3 7 2 0 1 Relative Frequency 4/25 = 0.160 5/25 = 0.200 3/25 = 0.120 3/25 = 0.120 7/25 = 0.280 2/25 = 0.080 0/25 = 0.000 1/25 = 0.040 22 Percentage 16.0 20.0 12.0 12.0 28.0 8.0 0.0 4.0 c. 3 + 7 = 10 games had four or five turnovers. The relative frequency is 10/25 = 0.400. Frequency d. 7 6 5 4 3 2 1 0 1 2 3 4 5 6 Turnovers 7 8 2.22 65 Frequency Frequency 60 40 20 55 45 35 25 0 0 1 2 3 4 Number of Tickets 0 1 2 3 4 Number of Tickets The truncated graph exaggerates the difference in the number of students with different numbers of tickets. Section 2.3 2.23 To prepare a stem-and-leaf display for a data set, each value is divided into two parts; the first part is called the stem and the second part is called the leaf. The stems are written on the left side of a vertical line and the leaves for each stem are written on the right side of the vertical line next to the corresponding stem. Example 2-9 is an example of a stem-and-leaf display. 2.24 The advantage of a stem-and-leaf display over a frequency distribution is that by preparing a stem-and-leaf display we do not lose information on individual observations. From a stem-and-leaf display we can obtain the original data. However, we cannot obtain the original data from a frequency distribution table. Consider the stem-and-leaf display from Example 28: 5 2 0 7 6 5 9 1 8 4 7 5 9 1 2 6 9 7 1 2 8 0 7 1 6 3 4 7 9 6 3 5 2 2 8 Chapter 2 The data that were used to make this stem-and-leaf display are: 52, 50, 57, 65, 69, 61, 68, 64, 75, 79, 71, 72, 76, 79, 77, 71, 72, 80, 87, 81, 86, 83, 84, 87, 96, 93, 95, 92, 92, 98 2.25 The data that were used to make this stem-and-leaf display are: 218, 245, 256, 329, 367, 383, 397, 404, 427, 433, 471, 523, 537, 551, 563, 581, 592, 622, 636, 647, 655, 678, 689, 810, 841 23 Chapter 2 2.26 0 1 2 3 4 5 6 2.27 24 1 0 0 1 8 0 8 a. b. 3 2 2 4 3 3 4 3 6 5 3 7 6 4 6 5 8 6 9 6 9 7 9 7 9 0 1 2 3 4 7 1 1 0 0 9 2 2 0 2 4 2 1 2 5 3 1 4 5 3 2 6 6 4 2 6 7 4 3 8 7 5 4 8 6 6 8 6 7 8 6 7 8 8 9 0 0 1 1 2 2 3 3 4 4 7 1 5 1 5 0 6 0 6 9 2 5 2 6 0 7 2 6 4 6 2 6 1 7 2 8 7 3 6 1 9 4 7 3 8 2 9 8 4 9 2 8 4 9 3 8 8 9 9 2 3 0 1 5 3 5 5 5 6 8 8 8 9 1 2 2 2 3 4 4 5 5 6 7 8 8 9 2 8 8 0 0 1 1 2 2 3 3 3 5 0 5 1 8 3 5 1 5 2 5 8 5 3 9 7 6 5 2 6 6 2 7 9 6 9 . 0 1 2 3 4 5 6 9 9 4 a. 0 1 2 3 b. 2.29 9 9 9 Answers will vary, but the split stem-and-leaf display seems to better discern differences in the data in the range 10 – 30. c. 2.28 2 2 0 3 8 1 5 0 1 2 3 0 5 7 1 2 3 8 8 2 8 8 3 8 8 4 9 9 4 Chapter 2 2.30 a. b. 25 2 3 4 5 6 7 8 9 2-4 5-6 7-9 58 20 30 05 10 02 40 57 58 05 02 45 38 30 17 05 45 68 * 30 05 60 38 20 06 68 20 38 06 90 50 35 20 70 60 38 21 90 45 50 20 * 60 21 65 70 75 28 65 87 30 65 28 38 70 65 60 75 87 90 * * 10 40 17 45 20 68 35 70 38 90 * 57 68 Section 2.4 2.31 In order to prepare a dotplot, first we draw a horizontal line with numbers that cover the given data set. Then we place a dot above the value on the number line that represents each measurement in the data set. Example 2-12 illustrates this procedure. 2.32 The benefits of a dot plot is that it is quick to form and it can illustrate where data points in a set naturally cluster. 2.33 2.34 Dotplot of Vehicle Fatalities 0 9 18 27 36 Vehicle Fatalities 2.35 45 54 63 Chapter 2 26 2.36 Dotplot of Scores 2.37 35 42 49 56 63 70 77 Scores Supplementary Exercises 2.38 a. and b. Political Party D DR F R W Frequency 9 4 2 11 4 Relative Frequency 9/30 = 0.300 4/30 = 0.133 2/30 = 0.067 11/30 = 0.367 4/30 = 0.133 Percentage 30.0 13.3 6.7 36.7 13.3 c. Relative Frequency W 13.3% D 30.0% 0.4 0.3 0.2 0.1 0 R 36.7% D DR F R W DR 13.3% F 6.7% Political Party d. 13.3% of these presidents were Whigs. 2.39 a. and b. TV sets owned 0 1 2 3 4 Frequency 1 14 14 8 3 Relative Frequency 1/40 = 0.025 14/40 = 0.350 14/40 = 0.350 8/40 = 0.200 3/40 = 0.075 Percentage 2.5 35.0 35.0 20.0 7.5 Chapter 2 27 c. Frequency 15 10 5 0 0 1 2 3 4 TV Sets Owned d. (14 + 8 + 3)/40 = 62.5% of the households own two or more television sets. 2.40 a. and b. Number of Text Messages 32−37 38−43 44−49 50−55 56−61 Frequency 10 9 13 6 2 Relative Frequency 10/40 = 0.250 9/40 = 0.225 13/40 = 0.325 6/40 = 0.150 2/40 = 0.050 Percentage 25.0 22.5 32.5 15.0 5.0 Percentage c. 15 10 5 0 32-37 38-43 44-49 50-55 56-61 Number of Text Messages d. 2.41 On (13 + 6 + 2)/40 = 52.5% of the 40 days, the student sent more than 44 text messages. a. and b. Number of Orders 23 – 29 30 – 36 37 – 43 44 – 50 51 – 57 Frequency 4 9 6 8 3 Relative Frequency 4/30 = 0.133 9/30 = 0.300 6/30 = 0.200 8/30 = 0.267 3/30 = 0.100 Percentage 13.3 30.0 20.0 26.7 10.0 c. For (6 + 8 + 3)/30 = 56.7% of the hours in this sample, the number of orders was more than 36. 2.42 a. and b. Concession (dollars) 0 to less than 6 6 to less than 12 12 to less than 18 18 to less than 24 24 to less than 30 Frequency 9 10 5 4 2 Relative Frequency 9/30 = 0.300 10/30 = 0.333 5/30 = 0.167 4/30 = 0.133 2/30 = 0.067 Percentage 30.0 33.3 16.7 13.3 6.7 Chapter 2 28 c. Frequency 15 10 5 0 0-6 6 – 12 12 – 18 18 – 24 24 – 30 Concessions a. and b. 2.43 Commute Length (in minutes) 22 to less than 28 28 to less than 34 34 to less than 40 40 to less than 46 46 to less than 52 Frequency Relative Frequency Percentage 5 14 8 2 1 5/30 = 0.167 14/30 = 0.467 8/30 = 0.267 2/30 = 0.067 1/30 = 0.033 16.7 46.7 26.7 6.7 3.3 c. Frequency Histogram for Commute Length 14 12 Frequency 10 8 6 4 2 0 22 to less than 28 28 to less than 34 34 to less than 40 40 to less than 46 46 to less than 52 Commute Length (in minutes) 2.44 2.45 3 4 5 6 2 0 0 1 2 3 4 5 3 1 0 3 1 1 4 2 2 4 0 1 0 5 2 3 7 0 1 2 6 2 4 7 3 9 7 1 4 3 7 4 7 4 7 5 8 2 5 7 8 5 3 6 9 5 7 7 4 7 4 7 2.47 20 30 40 Number of Orders 50 7 60 7 7 5 9 8 8 6 9 7 8 8 9 Chapter 2 2.48 29 Age 18 to less than 20 20 to less than 25 25 to less than 30 30 to less than 40 40 to less than 50 50 to less than 60 60 and over a. Frequency 7 12 18 14 15 16 35 Relative Frequency 7/117 = 0.060 12/117 = 0.103 18/117 = 0.154 14/117 = 0.120 15/117 = 0.128 16/117 = 0.137 35/117 = 0.299 Relative Frequency .300 .250 .200 .150 .100 .050 60 and over 50 to < 60 40 to < 50 30 to < 40 25 to < 30 20 to < 25 18 to < 20 .000 b. and c. This histogram is misleading because the class widths differ. If you were to change the frequency distribution so that the class widths were equal, the resulting histogram would give a clearer picture. 2.49 a. Using Sturge’s formula: c = 1 + 3.3log n = 1 + 3.3log135 = 1 + 3.3(2.13033377) = 1 + 7.03 = 8.03 » 8 . b. Approximate class width Largest value – smallest value = Number of classes 53 – 20 = = 4.125 8 Use a class width of 5. 2.50 a. The top money winners on the men’s tour tend to make more money per tournament than those on the women’s tour. Earnings on the men’s tour begin at $2300, and more of the data points are toward the higher end of the scale. Earnings on the women’s tour begin at $800, and more of the data points are toward the lower end of the scale. b. Typical earnings per tournament played for the women’s tour would be around $2500; typical earnings per tournament played for the men’s tour would be around $3650. c. The data do not appear to have similar spreads for the two tours. Earnings on the men’s tour begin at $2300, the largest grouping is between $2300 and $4800, and go up to $9500. Earnings on the women’s tour begin at $800, the largest grouping is between $1100 and $2600, and only go up to $7500. Chapter 2 30 d. On the women’s tour, the $7500 earnings level appears to be an outlier; on the men’s tour, both the $8700 and $9500 earnings levels appear to be outliers. a. Answers will vary. 2.51 b. i. 9 10 11 12 13 14 15 16 17 18 19 20 9 2 0 3 2 6 5 1 4 0 3 2 8 4 3 3 7 9 2 4 2 3 4 8 5 3 8 7 5 5 6 8 9 8 9 9 8 4 5 3 5 8 9 9 ii. The display shows a bimodal distribution, due to the presence of both females and males in the sample. The males tend to be heavier, so their weights are concentrated in the larger values, while the females’ weights are found primarily in the smaller values. c. Females 9 8 6 8 5 5 Males 8 5 3 8 4 3 6 7 9 2 0 3 3 8 5 4 9 10 11 12 13 14 15 16 17 18 19 20 2 7 9 1 4 0 3 2 8 2 4 2 3 4 8 5 3 5 9 9 9 9 Self-Review Test 1. An ungrouped data set contains information on each member of a sample or population individually. The first part of Example 2-1 in the text, listing the responses of each of the 30 employees, is an example of ungrouped data. Data presented in the form of a frequency table are called grouped data. Table 2.4 in the solution of Example 2-1 is an example of grouped data. 2. a. 5 b. 7 c. 17 d. 6.5 e. 13.5 f. 90 g. .30 3. A histogram that is identical on both sides of its central point is called a symmetric histogram. A histogram that is skewed to the right has a longer tail on the right side, and a histogram that is skewed to the left has a longer tail on the left side. Figure 2.8 in the text provides graphs of symmetric histograms, Figure 2.9a displays a histogram skewed to the right, and Figure 2.9b displays a histogram that is skewed to the left. Chapter 2 a. and b. c. Net Worth vs. $200,000 M L N Frequency Relative Frequency Percentage 12 18 6 12/36 = 0.333 18/36 = 0.500 6/36 = 0.167 33.3 50.0 16.7 18/36 = 50% of senior citizens have net worth less than $200,000. d. Frequency Histogram for Networth Classification 20 Frequency 15 10 5 0 M L N Networth Classification e. Pareto Chart of Networth Classification 40 100 30 80 60 20 40 10 20 0 Networth Classification Frequency Percent Cum % L 18 50.0 50.0 M 12 33.3 83.3 N 6 16.7 100.0 0 Percent Frequency 4. 31 Chapter 2 f. Pie Chart of Networth Classification Category M L N N 16.7% M 33.3% L 50% 5. a. and b. Monthly Expense on Gas (in dollars) 50 to 149 150 to 249 250 to 349 350 to 449 450 to 549 Frequency Relative Frequency Percentage 9 13 11 9 6 9/48 = 0.188 13/48 = 0.271 11/48 = 0.229 9/48 = 0.188 6/48 = 0.125 18.8 27.1 22.9 18.8 12.5 c. Percentage Distribution Histogram for Monthly Expenses on Gas 30 25 Percentage 20 15 10 5 0 50 to 149 150 to 249 250 to 349 350 to 449 450 to 549 Monthly Expenses on Gas (in $) d. (9 + 6)/48 = 31.25% of car owners in this sample spent $350 or more on gas per month. e. Monthly Expense Cumulative on Gas Frequency 50 to 149 9 150 to 249 9 + 13 = 22 250 to 349 9 + 13 + 11 = 33 350 to 449 9 + 13 + 11 + 9 = 42 450 to 549 9 + 13 + 11 + 9 + 6 = 48 Shopping Expense Frequency Cumulative Relative Frequency 9/48 = 0.188 22/48 = 0.458 33/48 = 0.688 42/48 = 0.875 48/48 = 1.000 Relative Frequency Cumulative Percentage 18.8 45.8 68.8 87.5 100.0 Percentage 32 Chapter 2 6. a. and c. (in dollars) 20 to less than 60 60 to less than 100 100 to less than 140 140 to less than 180 180 to less than 220 6 8 7 5 4 6/30 = 0.200 8/30 = 0.267 7/30 = 0.233 5/30 = 0.167 4/30 = 0.133 20.0 26.7 23.3 16.7 13.3 b. The width of each class is 40 dollars. d. (6 + 8 + 7)/30 = 70% of these customers spent less than $140 at this grocery store. e. Frequency Histogram for Shopping Expenses 9 8 Frequency 7 6 5 4 3 2 1 0 2o to ss le an th 60 60 to ss le an th 0 10 0 10 to ss le an th 0 14 0 14 to ss le an th 0 18 0 18 to ss le an th 0 22 Shopping Expenses (in $) Shopping Expense (in dollars) 20 to less than 60 60 to less than 100 100 to less than 140 140 to less than 180 180 to less than 220 f. 7. 8. 9. 0 1 2 3 4 0 0 2 30 6 2 1 7 2 2 8 3 2 4 5 4 9 5 6 Cumulative Frequency 6 6 + 8 = 14 6 + 8 + 7 = 21 6 + 8 + 7 + 5 = 26 6 + 8 + 7 + 5 + 4 = 30 6 6 7 8 Cumulative Relative Frequency 6/30 = 0.200 14/30 = 0.467 21/30 = 0.700 26/30 = 0.867 30/30 = 1.000 9 33 37 42 44 46 47 49 51 53 53 56 60 67 67 71 79 Cumulative Percentage 20.0 46.7 70.0 86.7 100.0 33 Chapter 2 34