8.2 relative frequency homework answers

Assignment 2

For this assignment, you will use graphics and numerical methods to illustrate the statistical concepts you have learned. You will construct frequency tables, histograms, bar graphs, and box plots, as examples of how to grasp meaningful information from a numerical or graphical examination of a set of data.

Download Data File 2 Attachment and complete the questions and answers as presented. Unless otherwise requested, submit all assignments with the problems/questions and answers in Word file format.

1. Disgruntled shareholders who put pressure on corporate management to make certain financial decisions may be referred to as shareholder activists. A survey of 240 large investors was conducted to determine how widespread shareholder activism is. One question asked was “If the chief executive officer and the board of directors differed on company strategy, what action would you, as a large investor of the firm, take?

Response

Number of Investors

Seek formal explanation

154

Seek CEO performance review

49

Dismiss CEO

20

Seek no action

17

Total

240

a. Construct a relative frequency table for the data.

b. Display the relative frequencies in a graph.

c. Discuss the findings.

2. More than 20 years ago, a survey of 2,016 small businesses (defined as having fewer than 100 employees) were surveyed regarding their weekly Internet usage to advertise and sell their products. The survey found 1,855 small business did not use the Internet, 121 used the Internet from one to five hours per week, and 40 that used the Internet six or more hours per week.

a. Identify the variable measured in the survey.

b. Summarize the survey results with a graph.

c. What portion of the 2,016 businesses used the Internet on a weekly basis?

d. If the same survey were conducted today, show the results you would expect in a frequency table. Explain your projected findings.

3. Consider the following set of data, which represents the reported company percentage of revenue spent for research and development.

Percentage of Revenues Spent on Research and Development

Company

Percentage

Company

Percentage

Company

Percentage

Company

Percentage

1

13.5

14

9.5

27

8.2

40

7.5

2

8.4

15

8.1

28

6.9

41

7.1

3

10.5

16

13.5

29

7.2

42

13.2

4

9.0

17

9.9

30

8.2

43

7.7

5

9.3

18

6.9

31

9.6

44

5.9

6

9.7

19

7.5

32

7.2

45

5.2

7

6.6

20

11.1

33

8.8

46

5.6

8

10.6

21

8.2

34

11.3

47

11.7

9

10.1

22

8.0

35

8.5

48

6.0

10

7.1

23

7.7

36

9.4

49

7.8

11

8.0

24

7.4

37

10.5

50

6.5

12

7.9

25

6.5

38

6.9

13

6.8

26

9.5

39

6.5

a. Create a stem-and-leaf display for these data.

b. Generate a histogram for these data. Use a bin width of 1.1.

c. Calculate the mean, median, and mode for these data.

d. Calculate the range and standard deviation for the percentages.

SOURCE: MBS, Figure 2.7, p. 37 – 58.

4. Construct a frequency table for the weight (in pounds) given below of 36 cans of regular Coke. Start the first bin at 0.7900 pound and use a bin width of 0.0050 pound. Discuss your findings.

0.8192

0.8194

0.8211

0.8176

0.8062

0.8143

0.8110

0.8152

0.7901

0.8152

0.8079

0.8161

0.8161

0.8163

0.8194

0.8247

0.8165

0.8172

0.8150

0.8264

0.8207

0.8073

0.8295

0.8170

0.8150

0.8189

0.8181

0.8284

0.8128

0.8229

0.8251

0.8244

0.8244

0.8126

0.8044

0.8192

5. Construct a frequency table for the weight (in pounds) given below of 36 cans of diet Coke. Start the first bin at 0.7750 pound and use a bin width of 0.0050 pound. Discuss your findings.

0.7773

0.7874

0.7868

0.7802

0.7806

0.7907

0.7879

0.7833

0.7923

0.7910

0.7813

0.7859

0.7822

0.7896

0.7839

0.7861

0.7874

0.7852

0.7870

0.7826

0.7837

0.7872

0.7923

0.7760

0.7758

0.7822

0.7844

0.7892

0.7830

0.7771

0.7881

0.7822

0.7852

0.7879

0.7885

0.7811

6. Use the data in Problem 4 to construct a histogram.

7. Use the data in Problem 5 to construct a histogram.

8. Suppose a friend drilled a hole in a die, filled it with a lead weight, and then proceeded to roll it. The results she obtained are given in the following frequency table:

Outcome

Frequency

1

27

2

31

3

42

4

40

5

28

6

32

a. According to the data, how many times was the die rolled?

b. How many times was the outcome greater than 2?

c. What percentage of outcomes were 6?

d. List the relative frequencies that correspond to the given frequencies.

e. List the cumulative frequencies that correspond to the given frequencies.

9. The following table lists the number of persons killed in fatal car crashes for three different categories of blood alcohol content (BAC) of drivers. Display the data using the graph you think most appropriate for the data.

Year

BAC of 0.0

(No alcohol)

BAC of 0.01 to 0.07

BAC of 0.08 and higher

1990

24,083

2,810

17,572

1995

25,968

2,300

13,423

2000

26,300

2,349

13,171

2005

27,542

2,350

13,532

2010

21.787

1,988

11,242

10. The following data shows the ages of the first seven presidents of an East Coast university founded in the early 1800’s and the ages of the seven most recent presidents of that same university at the time each became President.

First seven: 57 61 57 57 58 57 61

Last seven: 61 52 69 64 46 54 47

a. Find the mean, median, and range for each of the two data sets.

b. Give the five-number summary and draw a boxplot for each of the two data sets.

c. Find the standard deviation for each of the two data sets.