Business statistics., Summaries of Statistics

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K. Black,

Business statistics

CHAPTER 2—DESCRIPTIVE STATISTICS: TABULAR AND GRAPHICAL

PRESENTATIONS

MULTIPLE CHOICE

1. A frequency distribution is a tabular summary of data showing the a. fraction of items in several classes b. percentage of items in several classes c. relative percentage of items in several classes d. number of items in several classes ANS: D
2. A frequency distribution is a. a tabular summary of a set of data showing the relative frequency b. a graphical form of representing data c. a tabular summary of a set of data showing the frequency of items in each of several nonoverlapping classes d. a graphical device for presenting qualitative data ANS: C
3. A tabular summary of a set of data showing the fraction of the total number of items in several classes is a a. frequency distribution b. relative frequency distribution c. frequency d. cumulative frequency distribution ANS: B
4. Qualitative data can be graphically represented by using a(n) a. histogram b. frequency polygon c. ogive d. bar graph ANS: D
5. The relative frequency of a class is computed by a. dividing the midpoint of the class by the sample size b. dividing the frequency of the class by the midpoint c. dividing the sample size by the frequency of the class d. dividing the frequency of the class by the sample size ANS: D
6. The percent frequency of a class is computed by a. multiplying the relative frequency by 10 b. dividing the relative frequency by 100 c. multiplying the relative frequency by 100 d. adding 100 to the relative frequency ANS: C

b. the number of classes c. one d. any value larger than one ANS: C

14. The sum of the percent frequencies for all classes will always equal a. one b. the number of classes c. the number of items in the study d. 100 ANS: D
15. The most common graphical presentation of quantitative data is a a. histogram b. bar graph c. relative frequency d. pie chart ANS: A
16. The total number of data items with a value less than the upper limit for the class is given by the a. frequency distribution b. relative frequency distribution c. cumulative frequency distribution d. cumulative relative frequency distribution ANS: C
17. The relative frequency of a class is computed by a. dividing the cumulative frequency of the class by n b. dividing n by cumulative frequency of the class c. dividing the frequency of the class by n d. dividing the frequency of the class by the number of classes ANS: C
18. In constructing a frequency distribution, the approximate class width is computed as a. (largest data value - smallest data value)/number of classes b. (largest data value - smallest data value)/sample size c. (smallest data value - largest data value)/sample size d. largest data value/number of classes ANS: A
19. In constructing a frequency distribution, as the number of classes are decreased, the class width a. decreases b. remains unchanged c. increases d. can increase or decrease depending on the data values ANS: C
20. The difference between the lower class limits of adjacent classes provides the a. number of classes

b. class limits c. class midpoint d. class width ANS: D

21. In a cumulative frequency distribution, the last class will always have a cumulative frequency equal to a. one b. 100% c. the total number of elements in the data set ANS: C
22. In a cumulative relative frequency distribution, the last class will have a cumulative relative frequency equal to a. one b. zero c. the total number of elements in the data set ANS: A
23. In a cumulative percent frequency distribution, the last class will have a cumulative percent frequency equal to a. one b. 100 c. the total number of elements in the data set ANS: B
24. Data that provide labels or names for categories of like items are known as a. qualitative data b. quantitative data c. label data d. category data ANS: A
25. A tabular method that can be used to summarize the data on two variables simultaneously is called a. simultaneous equations b. crosstabulation c. a histogram d. an ogive ANS: B
26. A graphical presentation of the relationship between two variables is a. an ogive b. a histogram c. either an ogive or a histogram, depending on the type of data d. a scatter diagram ANS: D
27. A histogram is said to be skewed to the left if it has a a. longer tail to the right b. shorter tail to the right

33. Refer to Exhibit 2 - 1. The relative frequency of students working 9 hours or less a. is 20 b. is 100 c. is 0. d. 0. ANS: D
34. Refer to Exhibit 2 - 1. The percentage of students working 19 hours or less is a. 20% b. 25% c. 75% d. 80% ANS: B
35. Refer to Exhibit 2-1. The cumulative relative frequency for the class of 20 - 29 a. is 300 b. is 0. c. is 0. d. is 0. ANS: C
36. Refer to Exhibit 2 - 1. The cumulative percent frequency for the class of 30 - 39 is a. 100% b. 75% c. 50% d. 25% ANS: A
37. Refer to Exhibit 2-1. The cumulative frequency for the class of 20 - 29 a. is 200 b. is 300 c. is 0. d. is 0. ANS: B
38. Refer to Exhibit 2 - 1. If a cumulative frequency distribution is developed for the above data, the last class will have a cumulative frequency of a. 100 b. 1 c. 30 - 39 d. 400 ANS: D
39. Refer to Exhibit 2-1. The percentage of students who work at least 10 hours per week is a. 50% b. 5% c. 95% d. 100% ANS: C

40. Refer to Exhibit 2 - 1. The number of students who work 19 hours or less is a. 80 b. 100 c. 200 d. 400 ANS: B
41. Refer to Exhibit 2 - 1. The midpoint of the last class is a. 50 b. 34 c. 35 d. 34. ANS: D Exhibit 2 - 2 A survey of 800 college seniors resulted in the following crosstabulation regarding their undergraduate major and whether or not they plan to go to graduate school. Undergraduate Major Graduate School Business Engineering Others Total Yes 70 84 126 280 No 182 208 130 520 Total 252 292 256 800
42. Refer to Exhibit 2-2. What percentage of the students does not plan to go to graduate school? a. 280 b. 520 c. 65 d. 32 ANS: C
43. Refer to Exhibit 2 - 2. What percentage of the students' undergraduate major is engineering? a. 292 b. 520 c. 65 d. 36. ANS: D
44. Refer to Exhibit 2 - 2. Of those students who are majoring in business, what percentage plans to go to graduate school? a. 27. b. 8. c. 70 d. 72. ANS: A
45. Refer to Exhibit 2-2. Among the students who plan to go to graduate school, what percentage indicated "Other" majors? a. 15.

d. 60 ANS: C PROBLEM

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 a. Construct a frequency distribution and a bar graph. b. Construct a relative frequency distribution and a pie chart. ANS: (a) (b) Relative Major Frequency Frequency M 12 0. A 9 0. E 6 0. O 3 0. Total 30 1.
2. Twenty employees of ABC Corporation were asked if they liked or disliked the new district manager. Below you are given 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 L D L

a. Construct a frequency distribution and a bar graph. b. Construct a relative frequency distribution and a pie chart. ANS: a and b Preferences Frequency Relative Frequency L 9 0. D 11 0. Total 20 1.

3. Forty shoppers were asked if they preferred the weight of a can of soup to be 6 ounces, 8 ounces, or 10 ounces. Below you are given 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 a. Construct a frequency distribution and graphically represent the frequency distribution. b. Construct a relative frequency distribution and graphically represent the relative frequency

Grade Frequency Frequency A 4 0. B 11 0. C 5 0. Total 20 1.

5. 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 a. Construct a frequency distribution and a bar graph. b. Construct a relative frequency distribution and a pie chart. ANS: a and b Frequency Relative Frequency No 24 0. Yes 15 0. Without Opinion 11 0. Total 50 1.

6. 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 a. Construct a frequency distribution for this data. Let the first class be 50 - 59 and draw a histogram. b. Construct a cumulative frequency distribution. c. Construct a relative frequency distribution. d. Construct a cumulative relative frequency distribution. ANS: a. b. c. d. Cumulative Cumulative Relative Relative Score Frequency Frequency Frequency Frequency 50 - 59 3 3 0.15 0. 60 - 69 2 5 0.10 0. 70 - 79 5 10 0.25 0. 80 - 89 4 14 0.20 0. 90 - 99 6 20 0.30 1. Total 20 1.
7. The frequency distribution below was constructed from data collected from a group of 25 students.

Total 20 1.

9. The grades of 10 students on their first management test are shown below. 94 61 96 66 92 68 75 85 84 78 a. Construct a frequency distribution. Let the first class be 60 - 69. b. Construct a cumulative frequency distribution. c. Construct a relative frequency distribution. ANS: a. b. c. Cumulative Relative Class Frequency Frequency Frequency 60 - 69 3 3 0. 70 - 79 2 5 0. 80 - 89 2 7 0. 90 - 99 3 10 0. Total 10 1.
10. 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. ANS: Major Percent Frequency Accounting 30% Finance 20% Management 40% Marketing 10%

11. You are given the following data on the ages of employees at a company. Construct a stem-and-leaf display. 26 32 28 45 58 52 44 36 42 27 41 53 55 48 32 42 44 40 36 37 ANS: 2 | 6 7 8 3 | 2 2 6 6 7 4 | 0 1 2 2 4 4 5 8 5 | 2 3 5 8
12. Construct a stem-and-leaf display for the following data. 12 52 51 37 47 40 38 26 57 31 49 43 45 19 36 32 44 48 22 18 ANS: 1 | 2 8 9 2 | 2 6 3 | 1 2 6 7 8 4 | 0 3 4 5 7 8 9 5 | 1 2 7
13. The SAT scores of a sample of business school students and their genders are shown below. SAT Scores Gender Less than 20 20 up to 25 25 and more Total Female 24 168 48 240 Male 40 96 24 160 Total 64 264 72 400 a. How many students scored less than 20? b. How many students were female? c. Of the male students, how many scored 25 or more? d. Compute row percentages and comment on any relationship that may exist between SAT

15. For the following observations, plot a scatter diagram and indicate what kind of relationship (if any) exist between x and y. x y 8 4 5 5 3 9 2 12 1 14 ANS: A negative relationship between x and y appears to exist.
16. Five hundred recent graduates indicated their majors as follows. Major Frequency Accounting 60 Finance 100 Economics 40 Management 120 Marketing 80 Engineering 60 Computer Science 40 Total 500 a. Construct a relative frequency distribution. b. Construct a percent frequency distribution. ANS: a. b. Relative Percent Major Frequency Frequency Frequency Accounting 60 0.12 12 Finance 100 0.20 20 Economics 40 0.08 8 Management 120 0.24 24

Marketing 80 0.16 16 Engineering 60 0.12 12 Computer Science 40 0.08 8 Total 500 1.00 100

17. A sample of the ages of 10 employees of a company is shown below. 20 30 40 30 50 30 Construct a dot plot for the above data.

ANS:

18. The following data set shows the number of hours of sick leave that some of the employees of Bastien's, Inc. have taken during the first quarter of the year (rounded to the nearest hour). 19 22 27 24 28 12 23 47 11 55 25 42 36 25 34 16 45 49 12 20 28 29 21 10 59 39 48 32 40 31 a. Develop a frequency distribution for the above data. (Let the width of your classes be 10 units and start your first class as 10 - 19.) b. Develop a relative frequency distribution and a percent frequency distribution for the data. c. Develop a cumulative frequency distribution. d. How many employees have taken less than 40 hours of sick leave? ANS: Hours of Sick Leave Taken a. Freq. b. Relative Freq. b. Percent Freq. c. Cum. Freq. 10 - 19 6 0.20 20 6 20 - 29 11 0.37 37 17 30 - 39 5 0.16 16 22 40 - 49 6 0.20 20 28 50 - 59 2 0.07 7 30 d. 22
19. The sales record of a real estate company for the month of May shows the following house prices (rounded to the nearest $1,000). Values are in thousands of dollars. 105 55 45 85 75 30 60 75 79 95 a. Develop a frequency distribution and a percent frequency distribution for the house prices.