ec 203 p1

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Boston University *

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203

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Statistics

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Feb 20, 2024

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Problem Set #1 Exercises (10 th edition): #6,23,33,39,41,43. 6) TVNetworks. Nielsen Media Research tracks the top-rated television shows. The following data show the television network that produced each of the 25 top-rated shows in the history of television. a) Construct a frequency distribution, percent frequency distribution, and bar chart for the data. . tabulate Network Network | Freq. Percent Cum. ------------+----------------------------------- ABC | 6 24.00 24.00 CBS | 9 36.00 60.00 FOX | 1 4.00 64.00 NBC | 9 36.00 100.00 ------------+----------------------------------- Total | 25 100.00 0 2 4 6 8 10 ABC CBS FOX NBC b) Which networks have done the best in terms of presenting top-rated television shows? Compare the performance of ABC, CBS, and NBC. NBC and CBS did the best, ABC is the next and FOX Is the last. 23) MarketIndexes. The data show the year-to-date percent change (YTD % Change) for 30 stock-market indexes from around the world (The Wall Street Journal). a) Using a class width of 5 beginning with −20 and going to 40, develop a frequency distribution for the data. % Change | Freq. Percent Cum. ------------+----------------------------------- -16.3 | 1 3.33 3.33 -14.4 | 1 3.33 6.67 -9.3 | 1 3.33 10.00 -6.4 | 2 6.67 16.67

-4.7 | 1 3.33 20.00 -3.5 | 1 3.33 23.33 -2.5 | 1 3.33 26.67 1.3 | 1 3.33 30.00 2.3 | 1 3.33 33.33 2.6 | 1 3.33 36.67 4.2 | 1 3.33 40.00 6.4 | 1 3.33 43.33 6.6 | 2 6.67 50.00 9.3 | 1 3.33 53.33 9.9 | 1 3.33 56.67 10 | 1 3.33 60.00 10.1 | 1 3.33 63.33 10.2 | 1 3.33 66.67 10.6 | 1 3.33 70.00 11.8 | 1 3.33 73.33 12.6 | 1 3.33 76.67 13.8 | 1 3.33 80.00 14.5 | 1 3.33 83.33 16.6 | 1 3.33 86.67 17.4 | 2 6.67 93.33 21.1 | 1 3.33 96.67 31.4 | 1 3.33 100.00 ------------+----------------------------------- Total | 30 100.00 b) Prepare a histogram. Interpret the histogram, including a discussion of the general shape of the histogram. 0 .01 .02 .03 .04 -20 -10 0 10 20 30 YTD % Change 33) BrandValue. Each year Forbes ranks the world’s most valuable brands. A portion of the data for 82 of the brands in the 2013 Forbes list is shown in Table 2.12. The data set includes the variables listed below. Brand: The name of the brand.

Industry: The type of industry associated with the brand, labeled Automotive & Luxury, Consumer Packaged Goods, Financial Services, Other, Technology. Brand Value ($ billion): A measure of the brand’s value in billions of dollars developed by Forbes based on a variety of financial information about the brand. 1-Yr Value Change (%): The percentage change in the value of the brand over the previous year. Brand Revenue ($ billion): The total revenue in billions of dollars for the brand. a) Prepare a crosstabulation of the data on Industry (rows) and Brand Value ($ billion). Use classes of 0–10, 10–20, 20–30, 30–40, 40–50, and 50–60 for Brand Value ($ billion). tabulate BrandValuebillions Industry Brand | Value ($ | Industry billions) | Automot.. Consume.. Financi.. Other Technol.. | Total -----------+-------------------------------------------------------+---------- 5.4 | 0 1 0 0 0 | 1 5.5 | 1 0 0 0 0 | 1 5.6 | 0 1 1 1 0 | 3 5.7 | 1 0 2 1 0 | 4 5.8 | 0 0 0 1 0 | 1 5.9 | 0 0 0 0 1 | 1 6 | 0 0 1 0 0 | 1 6.2 | 0 1 0 0 0 | 1 6.3 | 0 0 1 0 0 | 1 6.4 | 0 0 0 3 1 | 4 6.5 | 1 0 0 0 0 | 1 6.6 | 0 0 0 0 1 | 1 6.8 | 0 0 1 0 0 | 1 6.9 | 1 0 1 1 0 | 3 7 | 2 0 0 1 1 | 4 7.1 | 1 0 0 1 0 | 2 7.4 | 1 0 1 0 0 | 2 7.7 | 0 0 1 0 0 | 1 7.9 | 0 1 0 0 0 | 1 8 | 0 0 0 0 1 | 1 8.1 | 1 0 0 0 0 | 1 8.4 | 0 0 0 1 0 | 1 8.5 | 0 0 0 1 1 | 2 8.7 | 0 1 0 0 1 | 2 9 | 0 0 1 0 0 | 1 9.1 | 0 1 1 0 0 | 2 9.3 | 1 0 0 0 0 | 1 9.4 | 0 0 0 1 0 | 1 9.6 | 0 1 0 1 0 | 2

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9.7 | 0 0 0 1 0 | 1 10.1 | 0 0 0 1 0 | 1 10.2 | 0 0 0 2 0 | 2 10.5 | 1 0 0 0 0 | 1 10.6 | 1 0 0 0 0 | 1 10.9 | 1 0 0 0 0 | 1 11.1 | 0 1 0 0 0 | 1 11.5 | 0 0 0 1 0 | 1 11.6 | 0 1 0 0 0 | 1 11.8 | 0 1 0 0 0 | 1 12.1 | 1 0 0 0 0 | 1 12.9 | 0 0 0 1 0 | 1 13.7 | 0 0 0 1 1 | 2 14.2 | 0 0 1 0 0 | 1 14.7 | 0 0 0 0 1 | 1 15.2 | 0 0 1 0 0 | 1 15.3 | 0 0 0 0 1 | 1 16.1 | 0 0 0 1 0 | 1 16.6 | 0 0 0 1 0 | 1 16.9 | 0 1 0 0 0 | 1 18 | 0 0 1 0 0 | 1 18.2 | 0 0 0 1 0 | 1 18.3 | 0 1 0 0 0 | 1 19.3 | 0 0 0 1 0 | 1 19.6 | 0 0 0 0 1 | 1 28.4 | 1 0 0 0 0 | 1 30.9 | 0 0 0 0 1 | 1 34.2 | 0 0 0 1 0 | 1 39.4 | 0 0 0 1 0 | 1 47.3 | 0 0 0 0 1 | 1 50.7 | 0 0 0 0 1 | 1 56.7 | 0 0 0 0 1 | 1 -----------+-------------------------------------------------------+---------- Total | 15 12 14 26 15 | 82 b) Prepare a frequency distribution for the data on Industry. tabulate Industry Industry | Freq. Percent Cum. ------------------------+----------------------------------- Automotive & Luxury | 15 18.29 18.29 Consumer Packaged Goods | 12 14.63 32.93 Financial Services | 14 17.07 50.00 Other | 26 31.71 81.71

Technology | 15 18.29 100.00 ------------------------+----------------------------------- Total | 82 100.00 c) Prepare a frequency distribution for the data on Brand Value ($ billion). tabulate BrandValuebillions Brand Value | ($ | billions) | Freq. Percent Cum. ------------+----------------------------------- 5.4 | 1 1.22 1.22 5.5 | 1 1.22 2.44 5.6 | 3 3.66 6.10 5.7 | 4 4.88 10.98 5.8 | 1 1.22 12.20 5.9 | 1 1.22 13.41 6 | 1 1.22 14.63 6.2 | 1 1.22 15.85 6.3 | 1 1.22 17.07 6.4 | 4 4.88 21.95 6.5 | 1 1.22 23.17 6.6 | 1 1.22 24.39 6.8 | 1 1.22 25.61 6.9 | 3 3.66 29.27 7 | 4 4.88 34.15 7.1 | 2 2.44 36.59 7.4 | 2 2.44 39.02 7.7 | 1 1.22 40.24 7.9 | 1 1.22 41.46 8 | 1 1.22 42.68 8.1 | 1 1.22 43.90 8.4 | 1 1.22 45.12 8.5 | 2 2.44 47.56 8.7 | 2 2.44 50.00 9 | 1 1.22 51.22 9.1 | 2 2.44 53.66 9.3 | 1 1.22 54.88 9.4 | 1 1.22 56.10 9.6 | 2 2.44 58.54 9.7 | 1 1.22 59.76 10.1 | 1 1.22 60.98 10.2 | 2 2.44 63.41 10.5 | 1 1.22 64.63 10.6 | 1 1.22 65.85 10.9 | 1 1.22 67.07 11.1 | 1 1.22 68.29

11.5 | 1 1.22 69.51 11.6 | 1 1.22 70.73 11.8 | 1 1.22 71.95 12.1 | 1 1.22 73.17 12.9 | 1 1.22 74.39 13.7 | 2 2.44 76.83 14.2 | 1 1.22 78.05 14.7 | 1 1.22 79.27 15.2 | 1 1.22 80.49 15.3 | 1 1.22 81.71 16.1 | 1 1.22 82.93 16.6 | 1 1.22 84.15 16.9 | 1 1.22 85.37 18 | 1 1.22 86.59 18.2 | 1 1.22 87.80 18.3 | 1 1.22 89.02 19.3 | 1 1.22 90.24 19.6 | 1 1.22 91.46 28.4 | 1 1.22 92.68 30.9 | 1 1.22 93.90 34.2 | 1 1.22 95.12 39.4 | 1 1.22 96.34 47.3 | 1 1.22 97.56 50.7 | 1 1.22 98.78 56.7 | 1 1.22 100.00 ------------+----------------------------------- Total | 82 100.00 . d) How has the crosstabulation helped in preparing the frequency distributions in parts (b) and (c)? By showing the joint distribution of categorical variables. It identifies relationships, provides frequency tables, summary statistics, and visualizations. e) A) What conclusions can you draw about the type of industry and the brand value? The dataset shows a diverse range of industries, with a largest percent in "Other" category. Most brands have values between 5.6 and 7.1 billion dollars. Higher brand values (e.g., 14.7 billion and above) are less common. Overall, the dataset indicates a concentration of brands in the mid-range of brand values. 39) MPG. A study on driving speed (miles per hour) and fuel efficiency (miles per gallon) for midsize automobiles resulted in the data given in the file. a) Construct a scatter diagram with driving speed on the horizontal axis and fuel efficiency on the vertical axis.

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0 20 40 60 mean of SpeedMilesHour 35 32 30 28 26 25 23 21 b)Comment on any apparent relationship between these two variables. Higher the speed, the more efficient the fuel efficiency 41) Hypertension. People often wait until middle age to worry about having a healthy heart. However, many studies have shown that earlier monitoring of risk factors such as blood pressure can be very beneficial (The Wall Street Journal). Having higher than normal blood pressure, a condition known as hypertension, is a major risk factor for heart disease. Suppose a large sample of individuals of various ages and gender was selected and that each individual’s blood pressure was measured to determine if they have hypertension. The sample data shows the percentage of individuals with hypertension. a) Develop a side-by-side bar chart with age on the horizontal axis, the percentage of individuals with hypertension on the vertical axis, and side-by-side bars based on gender. 0 .2 .4 .6 .8 20-34 35-44 45-54 55-64 65-74 75+ mean of Male mean of Female b) What does the display you developed in part (a) indicate about hypertension and age? As ages, hypertension increases in both male and female. c) Comment on differences by gender. Before the age of 64, male tend to have more hypertension but after that, female tend to have more hypertension along with the increase in age.

43) ManagerTime. The Northwest regional manager of an outdoor equipment retailer conducted a study to determine how managers at three store locations are using their time. A summary of the results are given in the data file. a) Create a stacked bar chart with store location on the horizontal axis and percentage of time spent on each task on the vertical axis. 0 .2 .4 .6 .8 1 Seattle Portland Bend mean of Meetings mean of Reports mean of Customers mean of Idle b) Create a side-by-side bar chart with store location on the horizontal axis and side-by-side bars of the percentage of time spent on each task. 0 .1 .2 .3 .4 .5 Bend Portland Seattle mean of Meetings mean of Reports mean of Customers mean of Idle c) Which type of bar chart (stacked or side-by-side) do you prefer for these data? Why? I prefer side by side chart. I is easy to see and easier to compare the value with other graphs.

ec 203 p1

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