Test bank and solution of business statistics ch03 tabular and graphical method (1)

Chapter 02 - Tabular and Graphical Methods Chapter Tabular and Graphical Methods Solutions a Rating Frequency 12 Relative Frequency 12/36 = 0.333 9/36 = 0.250 7/36 = 0.194 2-1 Chapter 02 - Tabular and Graphical Methods Total 36 5/36 = 0.139 3/36 = 0.083 0.999 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 2-2 Chapter 02 - Tabular and Graphical Methods a Rating Excellent Good Fair Frequency 12 Relative Frequency 5/24 = 0.208 12/24 = 0.500 4/24 = 0.167 2-3 Chapter 02 - Tabular and Graphical Methods Poor Total 24 3/24 = 0.125 b The most common response is Good which comprises 50% of total responses More than half of the patients reveal that they are in good or excellent health conditions 2-4 Chapter 02 - Tabular and Graphical Methods a Expectation Better Same Worse Frequency 16 Relative Frequency 5/25 = 0.20 16/25 = 0.64 4/25 = 0.16 2-5 Chapter 02 - Tabular and Graphical Methods Total 25 b Most of the chief executives (64%) believed that the economy would be the same in the next 12 months b a Delays PM Delays All Day Delays AM Delays Frequency Relative Frequency 1/18 = 0.056 6/18 = 0.333 4/18 = 0.222 2-6 Chapter 02 - Tabular and Graphical Methods None Total 18 7/18 = 0.389 The most common delays were None, comprising 38.9% of all delays The second most common were All Day Delays, comprising 33.3% of all delays b 2-7 Chapter 02 - Tabular and Graphical Methods 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 2-8 Chapter 02 - Tabular and Graphical Methods b Rating Total Relative Frequency 4/50 = 0.08 10/50 = 0.2 14/50 = 0.28 18/50 = 0.36 4/50 = 0.08 2-9 Chapter 02 - Tabular and Graphical Methods 8% of the rookies received a rating of c 2-10 Chapter 02 - Tabular and Graphical Methods The charts reveal parent preferences Sixty-five percent of parents want their children to have a profession such as a doctor, lawyer, banker or president Less preferable are other professions such humanitarian-aid worker or a movie star b Since 9% of parents want their children to become an athlete, 50 Therefore, among 550 parents approximately 50 parents want their kids to become an athlete 43 a Classes Frequency 2-41 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 ≈ 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 = 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% 44 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 = 19.4% of people living below the poverty level live in the Midwest region b 2-42 Chapter 02 - Tabular and Graphical Methods These charts show that the region with the highest percentage of people who live below the poverty level live in the South, and the lowest percentage is in the Northeast 45 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 = 0.320 257/1026 = 0.250 154/1026 = 0.150 133/1026 = 0.130 103/1026 = 0.100 41/1026 = 0.040 10/1026 = 0.010 Total = 2-43 Chapter 02 - Tabular and Graphical Methods 25% of the sample said paying down debt was the top financial resolution b The bar chart shows that saving more in general is the top financial resolution, followed by paying down debt Only a small portion of the sample didn’t know their financial resolution 46 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 2-44 Chapter 02 - Tabular and Graphical Methods 47 a 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, Therefore, approximately 113 of the respondents would spend the tax refund 48 a Drug Relative Frequency 2-45 Chapter 02 - Tabular and Graphical Methods Topomax Lamictal Depakote Lyrica Keppra 1825.4/5718.4 = 0.319 1684.3/5718.4 = 0.295 770.4/5718.4 = 0.135 727.8/5718.4 = 0.127 710.5/5718.4 = 0.124 Total = b Lamictal accounted for 29.5% of the sales c 49 a 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 Relative Frequency 5/60 = 0.083 6/60 = 0.10 10/60 = 0.167 20/60 = 0.333 15/60 = 0.25 4/60 = 0.067 Total = Cumulative Frequency 5+6 = 11 11+10 = 21 21+20 = 41 41+15 = 56 56+4 = 60 Cumulative Relative Frequency 0.083 0.083+0.10 = 0.183 0.183 + 0.167 = 0.35 0.35 + 0.333 = 0.683 0.683 + 0.25 = 0.933 0.933 + 0.067 = 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 2-46 Chapter 02 - Tabular and Graphical Methods 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 (1 – 0.35 = 0.65), 65% of the time d The histogram is not symmetric; it is negatively skewed 50 a Average MPG 15 up to 20 20 up to 25 25 up to 30 30 up to 35 35 up to 40 40 up to 45 Relative frequency 15/80 = 0.1875 30/80 = 0.375 15/80 = 0.1875 10/80 = 0.125 7/80 = 0.0875 3/80 = 0.0375 Total = Cumulative Frequency 15 15 + 30 = 45 45 + 15 = 60 60 + 10 = 70 70 + = 77 77 + = 80 2-47 Cumulative Relative Frequency 0.1875 45/80 = 0.5625 60/80 = 0.75 70/80 = 0.875 77/80 = 0.9625 80/80 = Chapter 02 - Tabular and Graphical Methods 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, (1 - 0.875 = 0.125), 12.5% of the cars got 35 mpg or more c The histogram is not symmetric; it is positively skewed 51 52 2-48 Chapter 02 - Tabular and Graphical Methods d There were people out of 25 with a net worth greater than $20 billion Therefore, 4/25 = 0.16, so 16% of the wealthiest people had net worth greater than $20 billion e 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 Therefore, (1 – 0.24) = 0.76, so 76% had net worth between $10 billion and $20 billion f Steam 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 51 Steam Leaf 8899 00112222334456688999 0099 07 The vast majority of the PEG ratios fall in the range The diagram is somewhat positively skewed; there are a few firms with relatively high PEG ratios 52 a 2-49 Chapter 02 - Tabular and Graphical Methods 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 most sensible number: $50,000 Therefore, our classes will have a width of $50,000, starting at $300,000 Classes 300,000 up to 350,000 Frequency 2-50 Chapter 02 - Tabular and Graphical Methods 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 Total = 20 c 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 2-51 Chapter 02 - Tabular and Graphical Methods 53 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 54 The scatterplot reveals no clear relationship between PPG and MPG Case Study 2.1 Proportion of Nike’s Net Sales by Region: US Region 2000 4732.1/8588.3 = 0.551 2-52 2009 6542.9/16661.8 = 0.392 Chapter 02 - Tabular and Graphical Methods EMEA Region Asia Pacific Region Americas Region 2350.9/8588.3 = 0.274 955.1/8588.3 = 0.111 550.2/8588.3 = 0.064 Total = 5512.2/16661.8 = 0.331 3322/16661.8 = 0.199 1284.7/16661.8 = 0.077 Total ≈ Proportion of Adidas’ Net Sales by Region (From Table 2.6): 2000 Europe North America Asia Latin America 2009 0.492 0.328 0.151 0.029 Total = 0.423 0.228 0.252 0.097 Total = 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 ≈ 2-53 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 = Chapter 02 - Tabular and Graphical Methods  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 Median Housing Price (in $1000s) $0 up to $100 Frequency Relative Frequency 0.12 Cumulative Frequency Cumulative Relative Frequency 0.12 $100 up to $200 29 0.58 35 0.7 $200 up to $300 11 0.22 46 0.92 $300 up to $400 0.04 48 0.96 $400 up to $500 0.04 50 Total = 50 Total =1 2-54 Chapter 02 - Tabular and Graphical Methods  The majority of median housing prices (70%) are below $200,000 The prices range from $82,700 up to $477,700 The distribution is positively skewed with only states having a median housing price above $400,000 2-55 ... Hertz accounted for 21.5% of sales c 2-13 Chapter 02 - Tabular and Graphical Methods 2-14 Chapter 02 - Tabular and Graphical Methods a 2-15 Chapter 02 - Tabular and Graphical Methods b (0.4 * 829)... 02 - Tabular and Graphical Methods 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 2-8 Chapter 02 - Tabular and Graphical. .. 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 2-30 Chapter 02 - Tabular and Graphical Methods