Chapter 02 - Tabular and Graphical Methods Chapter Tabular and Graphical Methods Solutions a Rating Total Frequency 12 36 Relative Frequency 12/36 = 0.333 9/36 = 0.250 7/36 = 0.194 5/36 = 0.139 3/36 = 0.083 1.000 b More than a third of the patrons are very satisfied with the entrees Overall more than half of the customers gave a top rating of either or Only 8.3% gave the lowest rating a Rating Excellent Good Fair Poor Total Frequency 12 24 Relative Frequency 5/24 = 0.208 12/24 = 0.500 4/24 = 0.167 3/24 = 0.125 1.000 b The most common response is Good which comprises 50% of total responses More than 70% of the patients reveal that they are in good or excellent health conditions a Expectation Better Same Worse Frequency 16 Relative Frequency 5/25 = 0.20 16/25 = 0.64 4/25 = 0.16 2-1 © 2014 by McGraw-Hill Education This is proprietary material solely for authorized instructor use Not authorized for sale or distribution in any manner This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part Chapter 02 - Tabular and Graphical Methods Total 25 1.00 Most of the chief executives (64%) believed that the economy would be the same in the next 12 months b Expectations of U.S economy Worse 16% Better 20% Better Same Worse Same 64% Relative Frequency Expectations of U.S economy 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00 Better Same Worse Expectation Type a Delays PM Delays All Day Delays AM Delays None Frequency Relative Frequency 1/18 = 0.056 6/18 = 0.333 4/18 = 0.222 7/18 = 0.389 2-2 © 2014 by McGraw-Hill Education This is proprietary material solely for authorized instructor use Not authorized for sale or distribution in any manner This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part Chapter 02 - Tabular and Graphical Methods Total 18 1.000 The most common type of delays was ‘None’, comprising 38.9% of all types The second most common type was ‘All Day Delays’, comprising 33.3% b Air Travel Delays PM Delays 6% PM Delays None 39% All Day Delays 33% All Day Delays AM Delays None AM Delays 22% Relative Frequency Air Travel Delays 0.50 0.40 0.30 0.20 0.10 0.00 PM Delays All Day Delays AM Delays None Delay Type a 22 (18 + 4) out of 50 rookies received a rating of or better; 14 (10 + 4) out of 50 rookies received a rating of or worse 2-3 © 2014 by McGraw-Hill Education This is proprietary material solely for authorized instructor use Not authorized for sale or distribution in any manner This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part Chapter 02 - Tabular and Graphical Methods b Rating Total Relative Frequency 4/50 = 0.08 10/50 = 0.20 14/50 = 0.28 18/50 = 0.36 4/50 = 0.08 1.00 8% of the rookies received a rating of c Relative Frequency Ratings of Pro-football Rookies 0.4 0.3 0.2 0.1 Ratings a Response Good Jobs Affordable homes Top schools Low crimes Things to Total Frequency 0.37×5,324 = 1,970 0.15×5,324 = 799 0.11×5,324 = 586 0.23×5,324 = 1225 0.14×5,324 = 745 5,324 1225 respondents considered ‘Low crimes’ as the most important criterion b 2-4 © 2014 by McGraw-Hill Education This is proprietary material solely for authorized instructor use Not authorized for sale or distribution in any manner This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part Chapter 02 - Tabular and Graphical Methods Survey Responses 2500 Frequency 2000 1500 1000 500 Good Jobs Affordable Top schools Low crimes Things to homes Responses a Top Vacation Choice Cruises Beaches Amusement Parks Big Cities Lakes Summer Camp Total Relative Frequency 140/316 = 0.443 68/316 = 0.215 68/316 = 0.215 20/316 = 0.063 12/316 = 0.038 8/316 = 0.025 1.000 44.3% of the children cited ‘Cruises’ as the perfect summer trip b Top Vacation Choice Survey 160 Frequency 140 120 100 80 60 40 20 Cruises Beaches Amusement Big Cities Parks Lakes Summer Camp Vacation Choice 2-5 © 2014 by McGraw-Hill Education This is proprietary material solely for authorized instructor use Not authorized for sale or distribution in any manner This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part Chapter 02 - Tabular and Graphical Methods a Car-Rental Company Enterprise Hertz Avis Budget Dollar Thrifty Other Total Relative Frequency (Market Share) 10.7/21.9 = 0.489 4.7/21.9 = 0.215 4/21.9 = 0.183 1.5/21.9 = 0.068 1/21.9 = 0.046 1.000 b Hertz accounted for 21.5% of sales c Car-Rental Company Revenues Other 5% Dollar Thrifty 7% Enterprise Hertz Avis Budget 18% Enterprise 49% Avis Budget Dollar Thrifty Hertz 21% Other a 2-6 © 2014 by McGraw-Hill Education This is proprietary material solely for authorized instructor use Not authorized for sale or distribution in any manner This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part Chapter 02 - Tabular and Graphical Methods CBS News Survey Relative Frequency 0.5 0.4 0.3 0.2 0.1 Cure for End of Signs of life Peace in cancer dependence in outer Middle East found on oil space Other None will happen Events CBS News Survey None will happen 7% Other 6% Peace in Middle East 8% Cure for cancer found Cure for cancer found 40% End of Signs of life dependence on oil in outer space 27% 12% b End of dependence on oil Signs of life in outer space Peace in Middle East Other None will happen (0.4 * 829) = 332 respondents believe that a cure for cancer will be found 10 a The number of responses for “Others” is the difference between the total number of responses and the sum of responses in the table That is, 5 5 b The proportion of respondents that felt that the Green Bay Packers would win Super Bowl XLV is 1,076/20,825 = 0.052 c Team Falcons Saints Texans Relative Frequency 4,040/20,825 = 0.194 1,880/20,825 = 0.090 1,791/20,825 = 0.086 2-7 © 2014 by McGraw-Hill Education This is proprietary material solely for authorized instructor use Not authorized for sale or distribution in any manner This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part Chapter 02 - Tabular and Graphical Methods Cowboys Vikings Colts Steelers Patriots Packers Others Total 1,631/20,825 = 0.078 1,438/20,825 = 0.069 1,149/20,825 = 0.055 1,141/20,825 = 0.055 1,095/20,825 = 0.053 1,076/20,825 = 0.052 5,584/20,825 = 0.268 1.000 Super Bowl XLV Poll Relative Frequency 0.3 0.25 0.2 0.15 0.1 0.05 Falcons Saints Texans Cowboys Vikings Colts Steelers Patriots Packers Others Team 11 a Since 60% favored Obama and 30% favored Romney in terms of likeability, then 10% favored neither Obama nor Romney b Of the 500 respondents, 300 (=500×0.60) favored Obama and 150 (=500×0.30) favored Romney So Obama was favored by 150 more respondents 12 a According to this survey, an athlete in football was most likely to sustain an injury with lifelong consequences An athlete in martial arts was least likely to sustain an injury with lifelong consequences b Approximately 79 respondents (=992×0.08) believed that professional hockey players were most likely to sustain an injury with lifelong consequences 2-8 © 2014 by McGraw-Hill Education This is proprietary material solely for authorized instructor use Not authorized for sale or distribution in any manner This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part Chapter 02 - Tabular and Graphical Methods 13 This graph does not correctly depict what has happened to Caterpillar’s stock price over this period The graph has been given a relatively high value of $500 on the vertical axis This compresses the data so that the increase of the stock price is not as apparent as it should be 14 This graph does not correctly depict what has happened to sales over the most recent five-year period The vertical axis has been stretched so that the increase in sales appears more pronounced than warranted 15 a Class up to 5 up to 7 up to 9 up to 11 11 up to 13 13 up to 15 Frequency 5 Total = 30 b Classes up to 5 up to 7 up to 9 up to 11 11 up to 13 13 up to 15 Relative Frequency 5/30 = 0.17 5/30 = 0.17 8/30 = 0.27 4/30 = 0.13 5/30 = 0.17 Cumulative Frequency 5 + = 10 + + = 18 + + + = 22 + + + + = 27 3/30 = 0.10 Total = 1.00 + + + + + = 30 Cumulative Relative Frequency 0.17 0.17 + 0.17 = 0.34 0.34 + 0.27 = 0.61 0.61 + 0.13 = 0.74 0.74 + 0.17 = 0.91 0.91 + 0.10 ≈ 1.00 c observations are at least but less than 9; 18 observations are less than d 27% of the observations are at least but less than 9; 61% are less than e 2-9 © 2014 by McGraw-Hill Education This is proprietary material solely for authorized instructor use Not authorized for sale or distribution in any manner This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part Chapter 02 - Tabular and Graphical Methods Histogram Relative Frequency 0.3 0.25 0.2 0.15 0.1 0.05 up to 5 up to 7 up to 9 up to 11 11 up to 13 13 up to 15 Class f Ogive Relative Frequency 0.8 0.6 0.4 0.2 0 10 Data 15 20 16 a Classes -10 up to 0 up to 10 10 up to 20 20 up to 30 30 up to 40 Frequency 31 19 Total = 70 19 observations are at least 10 but less than 20 b Classes -10 up to Relative Frequency 9/70 = 0.129 Cumulative Relative Frequency 0.129 2-10 © 2014 by McGraw-Hill Education This is proprietary material solely for authorized instructor use Not authorized for sale or distribution in any manner This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part Chapter 02 - Tabular and Graphical Methods -20 up to -10 -10 up to 0 up 10 10 up 20 20 up to 30 Total = 24 b Classes (in %) -20 up to -10 -10 up to 0 up 10 10 up 20 20 up to 30 Relative Frequency 4/24 = 0.167 4/24 = 0.292 9/24 = 0.375 3/24 = 0.125 1/24 = 0.042 Total ≈ 1.000 Cumulative Frequency 4 + = 11 11 + = 20 20 + = 23 23 + = 24 Cumulative Relative Frequency 4/24 = 0.167 11/24 = 0.458 20/24 = 0.833 23/24 = 0.958 24/24 = 1.000 c Nine funds had returns of at least 0% but less than 10%; there were funds with returns of 10% or more d 12.5% of the funds had a return of at least 10% but not greater than 20%; 95.8% of the funds had returns less than 20% 54 a Region Northeast Midwest South West Relative Frequency 6,166/37,276 = 0.165 7,237/37,276 = 0.194 15,501/37,276 = 0.416 8,372/37,276 = 0.225 Total = 1.000 19.4% of people living below the poverty level live in the Midwest region b 2-35 © 2014 by McGraw-Hill Education This is proprietary material solely for authorized instructor use Not authorized for sale or distribution in any manner This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part Chapter 02 - Tabular and Graphical Methods West 22% Northeast 17% Northeast Midwest Midwest 19% South West South 42% People Below Poverty Level Relative Frequency 0.5 0.4 0.3 0.2 0.1 Northeast Midwest South West Region These charts show that the highest percentage of people who live below the poverty level live in the South, and the lowest percentage live in the Northeast 55 a Resolution Saving more Paying down debt Making more income Spending less Investing more Saving for large purchase Don’t know Relative Frequency 328/1026 = 0.32 257/1026 = 0.25 154/1026 = 0.15 133/1026 = 0.13 103/1026 = 0.10 41/1026 = 0.04 10/1026 = 0.01 Total = 1.00 2-36 © 2014 by McGraw-Hill Education This is proprietary material solely for authorized instructor use Not authorized for sale or distribution in any manner This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part Chapter 02 - Tabular and Graphical Methods 25% of the respondents said paying down debt was their top financial resolution b Financial Resolution Relative Frequency 0.35 0.3 0.25 0.2 0.15 0.1 0.05 Saving more Paying Making down debt more income Spending Investing Saving for less more large purchase Don’t know Resolution The bar chart shows that “Saving more” is the top financial resolution, followed by “Paying down debt” Only a small portion of the respondents didn’t know their financial resolution 56 a Response A few days A few long weekends One week Two weeks Frequency 0.21(3057) = 642 0.18(3057) = 550 0.36(3057) = 1101 0.25(3057) = 764 Total = 3057 Approximately 1101 people are going to take a one week vacation b 2-37 © 2014 by McGraw-Hill Education This is proprietary material solely for authorized instructor use Not authorized for sale or distribution in any manner This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part Chapter 02 - Tabular and Graphical Methods Vacation Plan Two weeks 25% A few days 21% A few days A few long weekends One week Two weeks One week 36% A few long weekends 18% 57 a Use of an unexpected tax refund Relative Frequency 0.5 0.4 0.3 0.2 0.1 Pay off debts Put it in the Spend it bank I never get a refund Other Tax Redund Notice that the most frequent responses were regards to paying off debts or putting it in the bank b Since 11% of 1026 respondents said they would spend the refund, we find Therefore, approximately 113 of the respondents would spend the tax refund 58 a The pie chart is below 2-38 © 2014 by McGraw-Hill Education This is proprietary material solely for authorized instructor use Not authorized for sale or distribution in any manner This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part Chapter 02 - Tabular and Graphical Methods The chart shows the highest percentage of people live in the South and the lowest percentage live in the Northeast b The chart shows the highest percentage of people living in poverty are in the South and the lowest percentage of people living in poverty are living in the Northeast The percentage of people living in poverty in the South is higher than the percentage of people that live in South, and the percentage of people living in poverty in the Northeast is less than the percentage of people that live in the Northeast 59 a 2-39 © 2014 by McGraw-Hill Education This is proprietary material solely for authorized instructor use Not authorized for sale or distribution in any manner This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part Chapter 02 - Tabular and Graphical Methods Relative Frequency Attendance 1000 up to 1250 1250 up to 1500 1500 up to 1750 1750 up to 2000 2000 up to 2250 2250 up to 2500 Cumulative Frequency 5/60 = 0.083 6/60 = 0.100 10/60 = 0.167 20/60 = 0.333 15/60 = 0.250 4/60 = 0.067 Total = 1.000 Cumulative Relative Frequency 5+6 = 11 11+10 = 21 21+20 = 41 41+15 = 56 56+4 = 60 0.083 0.083+0.100 = 0.183 0.183+0.167 = 0.350 0.350+0.333 = 0.683 0.683+0.250 = 0.933 0.933+0.067 = 1.000 b The most likely attendance range is from 1,750 up to 2,000 with a 33% frequency; there were 41 times out of 60 that attendance was less than 2,000 c Attendance was at least 1,750 but less than 2,000 33.3% of the time; Attendance was less than 1,750 people 35% of the time; therefore, attendance was 1,750 or more 65% of the time d Histogram of Attendance in July and August Relative Frequency 0.35 0.3 0.25 0.2 0.15 0.1 0.05 1000 up to 1250 1250 up to 1500 1500 up to 1750 1750 up to 2000 2000 up to 2250 2250 up to 2500 Attendance The distribution is not symmetric; it is negatively skewed 60 a Average MPG Relative frequency 15 up to 20 20 up to 25 25 up to 30 15/80 = 0.1875 30/80 = 0.3750 15/80 = 0.1875 Cumulative Frequency 15 15 + 30 = 45 45 + 15 = 60 Cumulative Relative Frequency 0.1875 45/80 = 0.5625 60/80 = 0.7500 2-40 © 2014 by McGraw-Hill Education This is proprietary material solely for authorized instructor use Not authorized for sale or distribution in any manner This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part Chapter 02 - Tabular and Graphical Methods 30 up to 35 35 up to 40 40 up to 45 10/80 = 0.1250 7/80 = 0.0875 3/80 = 0.0375 Total = 1.0000 60 + 10 = 70 70 + = 77 77 + = 80 70/80 = 0.8750 77/80 = 0.9625 80/80 = 1.0000 b 60 cars got less than 30 mpg; 37.5% of the cars got at least 20 but less than 25 mpg; 87.5% of the cars got less than 35 mpg; Since 87.5% got less than 35 mpg, 12.5% of the cars got 35 mpg or more c Mileage Economy Test 0.4 Relative frequency 0.35 0.3 0.25 0.2 0.15 0.1 0.05 Average MPG The distribution is not symmetric; it is positively skewed 61 Days Working From Home 19% 12% 18% 7% 15% 29% 2-41 © 2014 by McGraw-Hill Education This is proprietary material solely for authorized instructor use Not authorized for sale or distribution in any manner This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part Chapter 02 - Tabular and Graphical Methods Days Working From Home Relative frequency 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00 Days 62 a There were people out of 25 with a net worth greater than $20 billion Since 4/25 = 0.16, 16% of the wealthiest people had net worth greater than $20 billion b Two people had a net worth less than $10 billion, which is 2/25 = 0.08, or 8% From the previous question, we know that 16% had a net worth greater than $20 billion Therefore, 16% + 8% = 24% did not have a net worth between $10 and $20 billion Consequently, 76% had net worth between $10 billion and $20 billion c Stem Leaf 66 47 3346 01556779 013337899 The distribution is not symmetric; it is negatively skewed The majority of ages range from the 60s to 70s Table 2.16 shows the majority of ages to be in the 50s and 60s Further, this diagram shows ages ranging from 36 to 79, whereas Table 2.16 has ages ranging from 36 to 90 63 Stem Leaf 8899 00112222334456688999 2-42 © 2014 by McGraw-Hill Education This is proprietary material solely for authorized instructor use Not authorized for sale or distribution in any manner This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part Chapter 02 - Tabular and Graphical Methods 0099 07 The vast majority of the PEG ratios fall in the range The diagram represents somewhat positively skewed distribution; there are a few firms with relatively high PEG ratios 64 a Types of Houses sold in New Jersey Other 20% Colonial Colonial 30% Contemporary Ranch Ranch 30% Contemporary 20% Other Types of Houses sold in New Jersey Frequency Colonial Contemporary Ranch Other Houses These charts show that the majority (60%) of houses were either Ranch or Colonial, but also 40% were either Contemporary or some other type b To figure out how wide to make the classes, find the highest price and subtract the lowest price to get the range That is $568,000 - $300,000 = $268,000 Then, since we want classes, divide the range by 7; 268,000/7 = $38,386 However, for ease of interpretation, round to the 2-43 © 2014 by McGraw-Hill Education This is proprietary material solely for authorized instructor use Not authorized for sale or distribution in any manner This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part Chapter 02 - Tabular and Graphical Methods most sensible number: $50,000 Therefore, our classes will have a width of $50,000, with a lower bound of the first class of $300,000 Classes 300,000 up to 350,000 350,000 up to 400,000 400,000 up to 450,000 450,000 up to 500,000 500,000 up to 550,000 550,000 up to 600,000 Frequency Total = 20 c Types of Houses sold in New Jersey Frequency 300,000 up to 350,000 up to 400,000 up to 450,000 up to 500,000 up to 550,000 up to 350,000 400,000 450,000 500,000 550,000 600,000 Houses 2-44 © 2014 by McGraw-Hill Education This is proprietary material solely for authorized instructor use Not authorized for sale or distribution in any manner This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part Chapter 02 - Tabular and Graphical Methods Ogive for House Price 25 Frequency 20 15 10 0 100 200 300 400 500 House Price (in $1000s) 600 700 The histogram shows that the most frequent house price is in the $350,000 up to $400,000 range The ogive shows that the middle price (with a frequency of 10/20 or 50%) is about $400,000 65 25 Sales (in $1000s) 20 15 10 0 10 20 30 40 Advertising (in $100s) The scatter plot shows that the relation between Advertising and Sales is positive The positive trend demonstrates that an increase in advertising will tend to increase sales 66 2-45 © 2014 by McGraw-Hill Education This is proprietary material solely for authorized instructor use Not authorized for sale or distribution in any manner This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part Chapter 02 - Tabular and Graphical Methods 35 30 25 PPG 20 15 10 34 35 36 37 38 39 40 MPG The scatterplot reveals no clear relationship between PPG and MPG Case Study 2.1: Frequency Distribution and Relative Frequency Distribution Sector Consumer Energy Finance Health Manufacturing Technology Total Frequency 5 30 Relative Frequency 0.233 0.067 0.167 0.133 0.167 0.233 1.000 The pie chart is below 2-46 © 2014 by McGraw-Hill Education This is proprietary material solely for authorized instructor use Not authorized for sale or distribution in any manner This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part Chapter 02 - Tabular and Graphical Methods The sectors with the largest representations are the technology, manufacturing and finance sectors The sector with the lowest representation is the energy sector Case Study 2.2 The net profit margin is a firm’s net profit after taxes to revenue It is measured in percentage, showing the percentage of net income per dollar in sales or other operating income Net Profit Margin -10% up to -5% -5 up to 0 up to 5 up to 10 10 up to 15 15 up to 20 Frequency 10 11 2 Total = 32 Relative Frequency 1/32 = 0.031 6/32 = 0.188 10/32 = 0.313 11/32 = 0.344 2/32 = 0.063 2/32 = 0.063 Total ≈ Cumulative Frequency 17 28 30 32 Cumulative Relative Frequency 1/32 = 0.031 7/32 = 0.219 17/32 = 0.531 28/32 = 0.875 30/32 = 0.938 32/32 = 1.000 2-47 © 2014 by McGraw-Hill Education This is proprietary material solely for authorized instructor use Not authorized for sale or distribution in any manner This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part Chapter 02 - Tabular and Graphical Methods Histogram for Net Profic Margin 12 Frequency 10 -10 up to -5 -5 up to 0 up to 5 up to 10 10 up to 15 15 up to 20 Net Profit Margin Ogive Relative Frequency 0.8 0.6 0.4 0.2 -20 -10 10 Net Profit Margin 20 30 The data tends to cluster between 0% and 10%, as shown in the histogram The net profit margins range from -5.19% to 19.95% Approximately 53% of the firms have a net profit margin below 5% Case Study 2.3 Life Expectancy Frequency 73.5 up to 75 75 up to 76.5 76.5 up to 78 78 up to 79.5 79.5 up to 81 81 up to 82.5 16 16 Relative Frequency 1/50=0.02 7/50=0.14 9/50=0.18 16/50=0.32 16/50=0.32 1/50=0.02 Cumulative Frequency 17 33 49 50 Cumulative Relative Frequency 1/50=0.02 8/50=0.16 17/50=0.34 33/50=0.66 49/50=0.98 50/50=1.00 2-48 © 2014 by McGraw-Hill Education This is proprietary material solely for authorized instructor use Not authorized for sale or distribution in any manner This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part Chapter 02 - Tabular and Graphical Methods Histogram for Life Expectancy 20 Frequency 15 10 73.5 up to 75 75 up to 76.5 76.5 up to 78 78 up to 79.5 79.5 up to 81 81 up to 82.5 Life Expectancy The data tends to cluster between 78 and 81, as shown in the histogram The distribution is negatively skewed 2-49 © 2014 by McGraw-Hill Education This is proprietary material solely for authorized instructor use Not authorized for sale or distribution in any manner This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part ... found 10 a The number of responses for “Others” is the difference between the total number of responses and the sum of responses in the table That is, 5 5 b The proportion of respondents that felt... 1.00 b 45 cities had a vacancy rate of less than 12%; 40% of the cities had a vacancy rate of at least 6% but less than 9%; 70% of the cities had a vacancy rate of less than 9% c Histogram for Vacancy... point of about 0.70 Thus, about 70% of the salaries were less than $18,000,000 b Draw a vertical line through Salary of 14 It intercepts the ogive at the point of about 0.15 Thus, about 15% of the