University of North Carolina, Greensboro

ECO 25

PROBLEM1 

1)Thirty students in the School of Business were asked what their majors were. The following represents their responses (M ? Management; A ? Accounting; E ? Economics; O ? Others).

 

A	M	M	A	M	M	E	M	O	A
E	E	M	A	O	E	M	A	M	A
M	A	O	A	M	E	E	M	A	M

 

1. 1. Construct a frequency distribution and a bar chart.
   2. Construct a relative frequency distribution and a pie chart.

 

 

 

 

 

2. Twenty employees of ABC Corporation were asked if they liked or disliked the new district manager. Below are their responses. Let L represent liked and D represent disliked.

 

L	L	D	L	D
D	D	L	L	D
D	L	D	D	L
D	D	D	D	L

 

1. 1. Construct a frequency distribution and a bar chart.
   2. Construct a relative frequency distribution and a pie chart.

 

 

 

 

 

 

3. A student has completed 20 courses in the School of Arts and Sciences. Her grades in the 20 courses are shown below.

 

A	B	A	B	C
C	C	B	B	B
B	A	B	B	B
C	B	C	B	A

 

1. 1. Develop a frequency distribution and a bar chart for her grades.
   2. Develop a relative frequency distribution for her grades and construct a pie chart.

 

 

 

 

 

 

4. A sample of 50 TV viewers were asked, "Should TV sponsors pull their sponsorship from programs that draw numerous viewer complaints?" Below are the results of the survey. (Y ? Yes; N ? No; W ? Without Opinion)

 

N	W	N	N	Y	N	N	N	Y	N
N	Y	N	N	N	N	N	Y	N	N
Y	N	Y	W	N	Y	W	W	N	Y
W	W	N	W	Y	W	N	W	Y	W
N	Y	N	Y	N	W	Y	Y	N	Y

 

1. 1. Construct a frequency distribution and a bar chart.

1. 2. Construct a relative frequency distribution and a pie chart.

 

 

 

 

 

 

5. Forty shoppers were asked if they preferred the weight of a can of soup to be 6 ounces, 8 ounces, or 10 ounces. Below are their responses.

 

6	6	6	10	8	8	8	10	6	6
10	10	8	8	6	6	6	8	6	6
8	8	8	10	8	8	6	10	8	6
6	8	8	8	10	10	8	10	8	6

 

1. 1. Construct a frequency distribution and graphically represent the frequency distribution.
   2. Construct a relative frequency distribution and graphically represent the relative frequency distribution.

 

 

 

 

 

6. There are 800 students in the School of Business Administration. There are four majors in the School: Accounting, Finance, Management, and Marketing. The following shows the number of students in each major.

 

Major                              Number of Students    

 

Accounting	240
Finance	160
Management	320
Marketing	80

 

Develop a percent frequency distribution and construct a bar chart and a pie chart.

 

 

 

7. Below you are given the examination scores of 20 students.

 

52	99	92	86	84
63	72	76	95	88
92	58	65	79	80
90	75	74	56	99

 

1. 1. Construct a frequency distribution for this data. Let the first class be 50 - 59 and draw a histogram.
   2. Construct a cumulative frequency distribution.
   3. Construct a relative frequency distribution.
   4. Construct a cumulative relative frequency distribution.

 

 

                            2                       5                    0.10                           0.25

 

 

 

 

8. Two hundred members of a fitness center were surveyed. One survey item stated, "The facilities are always clean." The members' responses to the item are summarized below. Fill in the missing value for the frequency distribution.

 

Opinion                            Frequency    

 

Strongly Agree	63
Agree	92
Disagree Strongly Disagree	15
No Opinion	14

 

9. Fill in the missing value for the following relative frequency distribution.

 

Opinion                                     Relative Frequency     

 

Strongly Agree	0.315
Agree	0.460
Disagree Strongly Disagree	0.075
No Opinion	0.070

 

10. Fill in the missing value for the following percent frequency distribution.

 

         Annual Salaries                Percent Frequency                        Under $30,000                                         10

$30,000 ? 49,999                               35

$50,000 ? 69,999                               40

$70,000 ? 89,999

$90,000 and over                             5

 

 

 

 

11. The following is a summary of the number of hours spent per day watching television for a sample of 100 people. What is wrong with the frequency distribution?

 

       Hours/Day            Frequency    

 

0 ? 1	10
1 ? 3	45
3 ? 5	20
5 ? 7	20
7 ? 9	5

 

 

 

 

12. A summary of the results of a job satisfaction survey follows. What is wrong with the relative frequency distribution?

 

Rating                    Relative Frequency     

 

Poor	.15
Fair	.45
Good	.25
Excellent	.30

 

 

13. The frequency distribution below was constructed from data collected from a group of 25 students.

 

        Height in Inches             Frequency     

 

58 ? 63	3
64 ? 69	5
70 ? 75	2
76 ? 81	6
82 ? 87	4
88 ? 93	3
94 ? 99	2

 

1. 1. Construct a relative frequency distribution.
   2. Construct a cumulative frequency distribution.
   3. Construct a cumulative relative frequency distribution.

 

 

 

 

 

 

 

14. The frequency distribution below was constructed from data collected on the quarts of soft drinks consumed per week by 20 students.

 

      Quarts of Sof t Drink          Frequency     

 

0 ? 3	4
4 ? 7	5
8 ? 11	6
12 ? 15	3
16 ? 19	2

 

1. 1. Construct a relative frequency distribution.
   2. Construct a cumulative frequency distribution.

1. 3. Construct a cumulative relative frequency distribution.

 

 

 

 

 

 

15. The grades of 10 students on their first management test are shown below.

 

94	61	96	66	92
68	75	85	84	78

 

1. 1. Construct a frequency distribution. Let the first class be 60 ? 69.
   2. Construct a cumulative frequency distribution.
   3. Construct a relative frequency distribution.

 

 

 

 

 

 

16. You are given the following data on the ages of employees at a company. Construct a stem-and- leaf display. Specify the leaf unit for the display.

 

26	32	28	45	58
52	44	36	42	27
41	53	55	48	32
42	44	40	36	37

 

 

 

17. Construct a stem-and-leaf display for the following data. Specify the leaf unit for the display.

 

12	52	51	37	47	40	38	26	57	31
49	43	45	19	36	32	44	48	22	18

 

 

 

18. You are given the following data on the earnings per share for ten companies. Construct a stem- and-leaf display. Specify the leaf unit for the display.

 

2.6	1.4	1.3	0.5	2.2
1.1	1.1	0.7	0.9	2.0

 

 

 

19. You are given the following data on the annual salaries for eight employees. Construct a stem- and-leaf display. Specify the leaf unit for the display.

 

$26,500	$27,850	$25,000	$27,460
$26,890	$25,400	$26,150	$30,000

 

 

 

 

 

 

20. You are given the following data on the price/earnings (P/E) ratios for twelve companies. Construct a stem-and-leaf display. Specify the leaf unit for the display.

 

23	25	39	47	22	37
8	36	48	28	37	26

 

 

 

 

 

 

21. You are given the following data on times (in minutes) to complete a race. Construct a stem- and-leaf display. Specify the leaf unit for the display.

 

15.2	15.8	12.4	11.9	15.2
14.7	14.8	11.8	12.0	12.1

 

 

 

22. The SAT math scores of a sample of business school students and their genders are shown below.

 

                              SAT Math Scores                             

 

Gender	Less than 400	400 up to 600	600 and more	Total
Female	24	168	48	240
Male	40	96	24	160
Total	64	264	72	400

 

1. 1. How many students scored less than 400?
   2. How many students were female?
   3. Of the male students, how many scored 600 or more?
   4. Compute row percentages and comment on any relationship that may exist between SAT math scores and gender of the individuals.
   5. Compute column percentages.

 

 

 

 

 

 

23. A market research firm has conducted a study to determine consumer preference for a new package design for a particular product. The consumers, ages were also noted.

 

                        Package Design                      

 

Age	A	B	C	Total
Under 25	18	18	29	65
25 – 40	18	12	5	35
Total	36	30	34	100

 

1. 1. Which package design was most preferred overall?
   2. What percent of those participating in the study preferred package A?
   3. What percent of those under 25 years of age preferred package A?
   4. What percent of those aged 25 ? 40 preferred package A?
   5. Is the preference for package A the same for both age groups?

 

 

 

 

 

 

24. Partial results of a study follow in a crosstabulation of column percentages.

 

Gender	Cash	Method of Payment Credit Card	Check
Female	18%	50%	90%
Male	82%	50%	10%
Total	100%	100%	100%

 

1. 1. Interpret the 18% found in the first row and first column of the crosstabulation.
   2. If 50 of those in the study paid by check, how many of the males paid by check?

 

 

 

 

 

25. For the following observations, plot a scatter diagram and indicate what kind of relationship (if any) exist between x and y.

 

         x                 y        

 

2	7
6	19
3	9
5	17
4	11

 

 

26. For the following observations, plot a scatter diagram and indicate what kind of relationship (if any) exists between women's height (inches) and annual starting salary ($1000).

 

       Height              Salary      

 

64	45
63	40
68	39
65	38
67	42
66	45
65	43
64	35
66	33

 

 

27. For the following observations, plot a scatter diagram and indicate what kind of relationship (if any) exists between the amount of sugar in one serving of cereal (grams) and the amount of fiber in one serving of cereal (grams).

 

        Sugar               Fiber       

 

1.2	3.2
1.3	3.1
1.5	2.8
1.8	2.4
2.2	1.1
2.8	1.3
3.0	1.0

 

 

28. What type of graph is depicted below?

 

 

 

 

29. What type of relationship is depicted in the following scatter diagram?

 

 

 

 

 

30. What type of relationship is depicted in the following scatter diagram?

 

 

 

 

 

 

 

 

31. What type of relationship is depicted in the following scatter diagram?

 

 

 

 

 

32. It is time for Roger Hall, manager of new car sales at the Maxwell Ford dealership, to submit his order for new Mustang coupes. These cars will be parked in the lot, available for immediate sale to buyers who are not special-ordering a car. Roger must decide how many Mustangs of each color he should order. The new color options are very similar to the past year’s options.

 

Roger believes the colors chosen by customers who special-order their cars best reflect most customers’ true color preferences. He has taken a random sample of 40 special orders for Mustang coupes placed in the past year. The color preferences found in the sample are listed below.

 

Blue	Black	Green	White	Black	Red	Red	White
Black	Red	White	Blue	Blue	Green	Red	Black
Red	White	Blue	White	Red	Red	Black	Black
Green	Black	Red	Black	Blue	Black	White	Green
Blue	Red	Black	White	Black	Red	Black	Blue

 

1. 1. Prepare a frequency distribution, relative frequency distribution, and percent frequency distribution for the data set.
   2. Construct a bar chart showing the frequency distribution of the car colors.
   3. Construct a pie chart showing the percent frequency distribution of the car colors.

 

 

 

 

 

 

 

33. Missy Walters owns a mail-order business specializing in clothing, linens, and furniture for children. She is considering offering her customers a discount on shipping charges for furniture based on the dollar-amount of the furniture order. Before Missy decides the discount policy, she needs a better understanding of the dollar-amount distribution of the furniture orders she receives.

Missy had an assistant randomly select 50 recent orders that included furniture. The assistant recorded the value, to the nearest dollar, of the furniture portion of each order. The data collected is listed below.

 

136	281	226	123	178	445	231	389	196	175
211	162	212	241	182	290	434	167	246	338
194	242	368	258	323	196	183	209	198	212
277	348	173	409	264	237	490	222	472	248
231	154	166	214	311	141	159	362	189	260

 

1. 1. Prepare a frequency distribution, relative frequency distribution, and percent frequency distribution for the data set using a class width of $50.
   2. Construct a histogram showing the percent frequency distribution of the furniture-order values in the sample.
   3. Develop a cumulative frequency distribution and a cumulative percent frequency distribution for this data.