Final HW 2.1

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Jun 12, 2024

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2.3(a) Both the circle graph in figure 2.1 and the bar graph in figure 2.2 display the Type of operation with corresponding number of operations of each type. (b) The circle graph displays the relative proportion of each type of operation as a whole. All portions of circle sum to 100%. Bar graph does not display the relative proportion of each type of operation as a whole. (c) Bar graph is better than circle graph because bar graph gives information about each type of operation individually along with relative proportion. Circle graph does not give answer about individual type of operations. 2.6 a) Here the variable of interest is ‘How young Americans feel about paying for an environmentally friendly vehicle’. (b) The type of the variable is categorical. This variable can has one of the four categories: A lot more, somewhat more, slightly more, would not pay more. (c) Following is the pie chart showing “How young Americans feel about paying for an environmentally friendly vehicle.” A lot more Somewhat more Slightly more Would not pay more. 0 5 10 15 20 25 30 35 40 11 36 33 20 How young Americans feel about paying for an en- vironmentally friendly vehicle Percentage d: Following is the bar chart showing “How young Americans feel about paying for an environmentally friendly vehicle.”

11% 36% 33% 20% How young Americans feel about paying for an environmentally friendly vehicle A lot more Somewhat more Slightly more Would not pay more. e) The information is given as the relative percentage of each category so pie chart is a better representation of the information. 2.7 a) Following is the bar graph of these scores using a vertical scale ranging from 80 to 110: Boston Chicago LA Lakers 80 85 90 95 100 105 110 90 108 96 Points scored by the winning teams on October 28, 2008 Opening night of the 2008–2009 NBA season Teams Score

(b) Following is the bar graph of these scores using a vertical scale ranging from 50 to 110: Boston Chicago LA Lakers 50 60 70 80 90 100 110 90 108 96 Points scored by the winning teams on October 28, 2008 Opening night of the 2008–2009 NBA season Teams Score (c) Graph in part (a) shows more variation in NBA score. Because the vertical scale of this graph has small range, 30. (d) To create an accurate representation of the relative size and variation between NBA scores use a vertical scale ranging from 0 to 110. Following is the bar graph of these scores using a vertical scale ranging from 0 to 110:

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Boston Chicago LA Lakers 0 10 20 30 40 50 60 70 80 90 100 110 90 108 96 Points scored by the winning teams on October 28, 2008 Opening night of the 2008–2009 NBA season Teams Score 2.10 a) The entry $64.02 shows that in the month of July, credit card had total transactions of $64.04 in Auto category. The entry $100.55 shows that in month of February, credit card had total transactions of $100.55 in Services category. b) The entry $1,159.19 shows in whole year the credit card had total transactions of $1,159.19 in Merchandise category. The entry $298.4 shows that credit cards had total transactions of $298.4 in month of June (including all categories).

c) Following is the required pie chart. Each part displays one category with relative percentage as a whole. Travel 125 $0.05 Restau rant 326.34 $0.13 Mer- chandise 1159.19 $0.46 Auto 240.92 $0.10 Services 615.46 $0.25 Utilities 35.4 $0.01 Year-end category totals using both dollar amounts and percentages. d) Following is the required bar chart. Each bar displays one month total in dollars. Janu ary Februa ry March April May June Jul y Augus t September October November December $- $50.00 $100.00 $150.00 $200.00 $250.00 $300.00 $350.00 $400.00 $450.00 $500.00 $101.18 $126.20 $84.96 $420.78 $175.27 $298.42 $447.08 $127.42 $78.03 $124.56 $101.51 $416.90 Credit card transactions

2.12 a) Following table shows the percentages in descending order. Countries Percentage US 19.6 EU 17.9 CHINA 8.4 S KOREA 6.5 POLAND 4.8 GERMANY 4.2 BRAZIL 4.1 FRANCE 3.3 RUSSIA 3.1 TURKEY 2.9 ITLAY 2.8 UK 2.8 INDIA 2.5 TOTAL 82.9 And following is the bar graph showing the percentages in declining order. US EU Chin a S Korea Poland German y Bra zil Fran ce Russia Turkey Italy UK Indi a 0 5 10 15 20 25 19.6 17.9 8.4 6.5 4.8 4.2 4.1 3.3 3.1 2.9 2.8 2.8 2.5 E-mail spam relayed by each country in 2007. Country Percentage (b) Total of the percentage (82.9%) of e-mail spam relayed by each country in 2007 is not 100% so Pareto graph of this information cannot be constructed.

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2.15 A) Total defect count in the report is 56+45+23+12+8+6 = 150 Hence, the total defect count in the report is 150. b) Total defect count is 150 and out of this 45 are Scratch. So the percentage for scratch is 45 / 150 * 100 = 30% Hence, the percentage of scratch is 30%. (c) Cumulative percentage for bend is obtained by adding defects count of blem, scratch, chip and bend and divide the sum by the number of defects. So 56 +45+23+12 / 150 = 0.907 Hence, cumulative percentage for bend is 90.7%. (d) Defects Blem and scratch are together 67.3% so management should give special attention on these defects. 2.18 A) cumulative percentage of data. Complaint category Number Percentage Cumulative count Cumulative Percentage Flight problems 2031 21.90% 2031 21.90% Customer service 1715 18.49% 3746 40.38% Baggage 1421 15.32% 5167 55.70% Reservations/ticketing/boarding 1159 12.49% 6326 68.20% Refunds 1106 11.92% 7432 80.12% Fares 523 5.64% 7955 85.76% Disabilities 477 5.14% 8432 90.90% Over sales 454 4.89% 8886 95.80% Others 322 3.47% 9208 99.27% Advertising 68 0.73% 9276 100.00%

The Pareto Graph using the above information. Following is the Pareto graph showing the consumer complaints against top U.S. airlines. (b) Airlines should pay most attention to correcting complaints about flight problems, customer services, baggage, reservations/ticketing/boarding, and refunds. Line graph shows that these problems cover 80% of overall problems. 2.21 Height Frequency 72 1 72 2 73 1 74 1 74 2 74 3 74 4 74 5 75 1 75 2 76 1 76 2 77 1 77 2 77 3 77 4 78 1 78 2 80 1

80 2 80 3 81 1 81 2 81 3 81 4 82 1 82 2 82 3 84 1 86 1 the dot plot of data from the above information. 70 75 80 85 90 0 1 2 3 4 5 6 THe Height of Basketball Players Height in Inches Frequency b) The shortest height of the player is 72 inches and there are 2 players with this height. And the tallest height of the player is 86 inches. c) The most common height is 74 inches. There are 5 players with this height. (d) There are 5 dots corresponding to 74 inches. So it is the most common height. 2.24 (a) There are 15 dots in the dot plots so number of data values is 15. (b) Five smallest values of data approximately are 11.2, 11.2, 11.3, 11.4 and 11.7. (c) The value of largest data item is approximately 15.6. (d) Value 13.8 is occurred greatest number of time. It occurs three times.

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2.29 (a) Place value of leaf is hundredths. It means 59|7 means 5.97. And 63|5 means 6.35 (b) Here N is 16. So number of data values are 16. Or number of leaves is 16 so number of data values is 16. (c) The first four data values are 5.97, 6.01, 6.04, 6.08. (d) The left hand side of the figure shows the cumulative frequencies of values. First stem at top has 1 value and second stem has 3 values so second value at the left hand side column is 4. Likewise cumulative frequencies start at the bottom.

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