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CHAPTER 2—DESCRIPTIVE STATISTICS: TABULAR AND GRAPHICAL DISPLAYS

MULTIPLE CHOICE

1. The minimum number of variables represented in a bar chart is
a.|1|
b.|2|
c.|3|
d.|4|

ANS: A PTS: 1

2. The minimum number of variables represented in a histogram is
a.|1|
b.|2|
c.|3|
d.|4|

ANS: A PTS: 1

3. Which of the following graphical methods is most appropriate for categorical data?
a.|ogive|
b.|pie chart|
c.|histogram|
d.|scatter diagram|

ANS: B PTS: 1

4. In a stem-and-leaf display,
a.|a single digit is used to define each stem, and a single digit is used to define each leaf|
b.|a single digit is used to define each stem, and one or more digits are used to define each leaf|
c.|one or more digits are used to define each stem, and a single digit is used to define each leaf|
d.|one or more digits are used to define each stem, and one or more digits are used to define each leaf|

ANS: C PTS: 1

5. A graphical method that can be used to show both the rank order and shape of a data set simultaneously is a
a.|relative frequency distribution|
b.|pie chart|
c.|stem-and-leaf display|
d.|pivot table|

ANS: C PTS: 1

6. The proper way to construct a stem-and-leaf display for the data set {62, 67, 68, 73, 73, 79, 91, 94, 95, 97} is to
a.|exclude a stem labeled ‘8’|
b.|include a stem labeled ‘8’ and enter no leaves on the stem|
c.|include a stem labeled ‘(8)’ and enter no leaves on the stem|
d.|include a stem labeled ‘8’ and enter one leaf value of ‘0’ on the stem|

ANS: B PTS: 1

7. Data that provide labels or names for groupings of like items are known as
a.|categorical data|
b.|quantitative data|
c.|label data|
d.|generic data|

ANS: A PTS: 1

8. A researcher is gathering data from four geographical areas designated: South = 1; North = 2; East = 3; West = 4. The designated geographical regions represent
a.|categorical data|
b.|quantitative data|
c.|directional data|
d.|either quantitative or categorical data|

ANS: A PTS: 1

9. Data that indicate how much or how many are known as
a.|categorical data|
b.|quantitative data|
c.|label data|
d.|category data|

ANS: B PTS: 1

10. The ages of employees at a company represent
a.|categorical data|
b.|quantitative data|
c.|label data|
d.|time series data|

ANS: B PTS: 1

11. A frequency distribution is
a.|a tabular summary of a set of data showing the fraction of items in each of several nonoverlapping classes|
b.|a graphical form of representing data|
c.|a tabular summary of a set of data showing the number of items in each of several nonoverlapping classes|
d.|a graphical device for presenting categorical data|

ANS: C PTS: 1

12. The sum of frequencies for all classes will always equal
a.|1|
b.|the number of elements in a data set|
c.|the number of classes|
d.|a value between 0 and 1|

ANS: B PTS: 1

13. 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 PTS: 1

14. If several frequency distributions are constructed from the same data set, the distribution with the widest class width will have the
a.|fewest classes|
b.|most classes|
c.|same number of classes as the other distributions since all are constructed from the same data|
d.|None of the other answers are correct.|

ANS: A PTS: 1

15. Excel's __________ can be used to construct a frequency distribution for categorical data.
a.|DISTRIBUTION function|
b.|SUM function|
c.|FREQUENCY function|
d.|COUNTIF function|

ANS: D PTS: 1

16. The cumulative relative frequency for the class of 11
a.|frequency distribution.|
b.|relative frequency distribution.|
c.|frequency.|
d.|cumulative frequency distribution.|

ANS: B PTS: 1

17. 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 PTS: 1

18. The sum of the relative frequencies for all classes will always equal
a.|the sample size|
b.|the number of classes|
c.|one|
d.|100|

ANS: C PTS: 1

19. A tabular summary of data showing the percentage of items in each of several nonoverlapping classes is a
a.|frequency distribution|
b.|relative frequency distribution|
c.|percent frequency distribution|
d.|cumulative percent frequency distribution|

ANS: C PTS: 1

20. 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 PTS: 1

21. 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 PTS: 1

22. 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|
d.|None of the other answers are correct.|

ANS: C PTS: 1

23. In a cumulative relative frequency distribution, the last class will have a cumulative relative frequency equal to
a.|one|
b.|zero|
c.|100|
d.|None of the other answers are correct.|

ANS: A PTS: 1

24. 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|
d.|None of the other answers are correct.|

ANS: B PTS: 1

25. 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 PTS: 1

26. A graphical device for depicting categorical data that have been summarized in a frequency distribution, relative frequency distribution, or percent frequency distribution is a(n)
a.|histogram|
b.|stem-and-leaf display|
c.|ogive|
d.|bar chart|

ANS: D PTS: 1

27. A graphical device for presenting categorical data summaries based on subdivision of a circle into sectors that correspond to the relative frequency for each class is a
a.|histogram|
b.|stem-and-leaf display|
c.|pie chart|
d.|bar chart|

ANS: C PTS: 1

28. Categorical data can be graphically represented by using a(n)
a.|histogram|
b.|frequency polygon|
c.|ogive|
d.|bar chart|

ANS: D PTS: 1

29. Fifteen percent of the students in a School of Business Administration are majoring in Economics, 20% in Finance, 35% in Management, and 30% in Accounting. The graphical device(s) that can be used to present these data is (are)
a.|a line graph|
b.|only a bar chart|
c.|only a pie chart|
d.|both a bar chart and a pie chart|

ANS: D PTS: 1

30. Methods that use simple arithmetic and easy-to-draw graphs to summarize data quickly are called
a.|exploratory data analysis|
b.|relative frequency distributions|
c.|bar charts|
d.|pie charts|

ANS: A PTS: 1

31. The total number of data items with a value less than or equal to 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 PTS: 1

32. Excel's __________ can be used to construct a frequency distribution for quantitative data.
a.|COUNTIF function|
b.|SUM function|
c.|PivotTable Report|
d.|AVERAGE function|

ANS: C PTS: 1

33. A graphical display of a frequency distribution, relative frequency distribution, or percent frequency distribution of quantitative data constructed by placing the class intervals on the horizontal axis and the frequencies on the vertical axis is a
a.|histogram|
b.|bar chart|
c.|stem-and-leaf display|
d.|pie chart|

ANS: A PTS: 1

34. A common graphical display of quantitative data is a
a.|histogram|
b.|bar chart|
c.|relative frequency|
d.|pie chart|

ANS: A PTS: 1

35. When using Excel to create a __________ one must edit the chart to remove the gaps between rectangles.
a.|scatter diagram|
b.|bar chart|
c.|histogram|
d.|pie chart|

ANS: C PTS: 1

36. A __________ can be used to graphically present quantitative data.
a.|histogram|
b.|pie chart|
c.|stem-and-leaf display|
d.|both a histogram and a stem-and-leaf display are correct|

ANS: D PTS: 1

37. A(n) __________ is a graph of a cumulative distribution.
a.|histogram|
b.|pie chart|
c.|stem-and-leaf display|
d.|ogive|

ANS: D PTS: 1

38. Excel's Chart Tools can be used to construct a
a.|bar chart|
b.|pie chart|
c.|histogram|
d.|All of these can be constructed using Excel's Chart Tools.|

ANS: D PTS: 1

39. To construct a bar chart using Excel's Chart Tools, choose __________ as the chart type.
a.|column|
b.|pie|
c.|scatter|
d.|line|

ANS: A PTS: 1

40. To construct a pie chart using Excel's Chart Tools, choose __________ as the chart type.
a.|column|
b.|pie|
c.|scatter|
d.|line|

ANS: B PTS: 1

41. To construct a histogram using Excel's Chart Tools, choose __________ as the chart type.
a.|column|
b.|pie|
c.|scatter|
d.|line|

ANS: A PTS: 1

42. Excel's Chart Tools does not have a chart type for constructing a
a.|bar chart|
b.|pie chart|
c.|histogram|
d.|stem-and-leaf display|

ANS: D PTS: 1

43. A tabular method that can be used to summarize the data on two variables simultaneously is called
a.|simultaneous equations|
b.|a crosstabulation|
c.|a histogram|
d.|a dot plot|

ANS: B PTS: 1

44. Excel's __________ can be used to construct a crosstabulation.
a.|Chart Tools|
b.|SUM function|
c.|PivotTable Report|
d.|COUNTIF function|

ANS: C PTS: 1

45. In a crosstabulation
a.|both variables must be categorical|
b.|both variables must be quantitative|
c.|one variable must be categorical and the other must be quantitative|
d.|either or both variables can be categorical or quantitative|

ANS: D PTS: 1

46. A graphical display of the relationship between two quantitative variables is
a.|a pie chart|
b.|a histogram|
c.|a crosstabulation|
d.|a scatter diagram|

ANS: D PTS: 1

47. Excel's __________ can be used to construct a scatter diagram.
a.|Chart Tools|
b.|SUM function|
c.|CROSSTAB function|
d.|RAND function|

ANS: A PTS: 1

48. When the conclusions based upon the aggregated crosstabulation can be completely reversed if we look at the unaggregated data, the occurrence is known as
a.|reverse correlation|
b.|inferential statistics|
d.|disaggregation|

ANS: C PTS: 1

49. Before drawing any conclusions about the relationship between two variables shown in a crosstabulation, you should
a.|investigate whether any hidden variables could affect the conclusions|
b.|construct a scatter diagram and find the trendline|
c.|develop a relative frequency distribution|
d.|construct an ogive for each of the variables|

ANS: A PTS: 1

50. A histogram is not appropriate for displaying which of the following types of information?

a.|frequency|
b.|relative frequency|
c.|cumulative frequency|
d.|percent frequency|

ANS: C PTS: 1

51. For stem-and-leaf displays where the leaf unit is not stated, the leaf unit is assumed to equal
a.|0|
b.|.1|
c.|1|
d.|10|

ANS: C PTS: 1

52. Which of the following graphical methods is not intended for quantitative data?
a.|ogive|
b.|dot plot|
c.|scatter diagram|
d.|pie chart|

ANS: D PTS: 1

53. Which of the following is least useful in studying the relationship between two variables?
a.|trendline|
b.|stem-and-leaf display|
c.|crosstabulation|
d.|scatter diagram|

ANS: B PTS: 1

54. The sum of the relative frequencies in any relative frequency distribution always equals
a.|the number of observations|
b.|1.00|
c.|100|
d.|the number of variables|

ANS: B PTS: 1

55. The sum of the frequencies in any frequency distribution always equals
a.|the number of observations|
b.|1.00|
c.|100|
d.|the number of variables|

ANS: A PTS: 1

Exhibit 2-1
The numbers of hours worked (per week) by 400 statistics students are shown below.

|Number of hours|Frequency|
| 0 - 9| 20|
|10 - 19| 80|
|20 - 29|200|
|30 - 39|100|

56. Refer to Exhibit 2-1. The class width for this distribution
a.|is 9|
b.|is 10|
c.|is 39, which is: the largest value minus the smallest value or 39 - 0 = 39|
d.|varies from class to class|

ANS: B PTS: 1

57. Refer to Exhibit 2-1. The midpoint of the last class is
a.|50|
b.|34|
c.|35|
d.|34.5|

ANS: D PTS: 1

58. Refer to Exhibit 2-1. The number of students working 19 hours or less
a.|is 80|
b.|is 100|
c.|is 180|
d.|is 300|

ANS: B PTS: 1

59. Refer to Exhibit 2-1. The relative frequency of students working 9 hours or less
a.|is 20|
b.|is 100|
c.|is 0.95|
d.|0.05|

ANS: D PTS: 1

60. Refer to Exhibit 2-1. The cumulative relative frequency for the class of 20 - 29
a.|is 300|
b.|is 0.25|
c.|is 0.75|
d.|is 0.5|

ANS: C PTS: 1

61. Refer to Exhibit 2-1. The percentage of students working 10 - 19 hours is
a.|20%|
b.|25%|
c.|75%|
d.|80%|

ANS: A PTS: 1

62. 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 PTS: 1

63. 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 PTS: 1

64. Refer to Exhibit 2-1. The cumulative frequency for the class of 20 - 29
a.|is 200|
b.|is 300|
c.|is 0.75|
d.|is 0.50|

ANS: B PTS: 1

65. 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 PTS: 1

66. 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 PTS: 1

Exhibit 2-2
Information on the type of industry is provided for a sample of 50 Fortune 500 companies.

|Industry Type|Frequency|
|Banking| 7|
|Consumer Products|15|
|Electronics|10|
|Retail|18|

67. Refer to Exhibit 2-2. The number of industries that are classified as retail is
a.|32|
b.|18|
c.|0.36|
d.|36%|

ANS: B PTS: 1

68. Refer to Exhibit 2-2. The relative frequency of industries that are classified as banking is
a.|7|
b.|0.07|
c.|0.70|
d.|0.14|

ANS: D PTS: 1

69. Refer to Exhibit 2-2. The percent frequency of industries that are classified as electronics is
a.|10|
b.|20|
c.|0.10|
d.|0.20|

ANS: B PTS: 1

Exhibit 2-3
The number of sick days taken (per month) by 200 factory workers is summarized below.

|Number of Days|Frequency|
| 0 - 5|120|
| 6 - 10| 65|
|11 - 15| 14|
|16 - 20| 1|

70. Refer to Exhibit 2-3. The class width for this distribution
a.|is 5|
b.|is 6|
c.|is 20, which is: the largest value minus the smallest value or 20 - 0 = 20|
d.|varies from class to class|

ANS: B PTS: 1

71. Refer to Exhibit 2-3. The midpoint of the first class is
a.|10|
b.|2|
c.|2.5|
d.|3|

ANS: C PTS: 1

72. Refer to Exhibit 2-3. The number of workers who took less than 11 sick days per month
a.|was 15|
b.|was 200|
c.|was 185|
d.|was 65|

ANS: C PTS: 1

73. Refer to Exhibit 2-3. The number of workers who took at most 10 sick days per month
a.|was 15|
b.|was 200|
c.|was 185|
d.|was 65|

ANS: C PTS: 1

74. Refer to Exhibit 2-3. The number of workers who took more than 10 sick days per month
a.|was 15|
b.|was 200|
c.|was 185|
d.|was 65|

ANS: A PTS: 1

75. Refer to Exhibit 2-3. The number of workers who took at least 11 sick days per month
a.|was 15|
b.|was 200|
c.|was 185|
d.|was 65|

ANS: A PTS: 1

76. Refer to Exhibit 2-3. The relative frequency of workers who took 10 or fewer sick days
a.|was 185|
b.|was 0.925|
c.|was 93|
d.|was 15|

ANS: B PTS: 1

77. Refer to Exhibit 2-3. The cumulative relative frequency for the class of 11 - 15
a.|is 199|
b.|is 0.07|
c.|is 1|
d.|is 0.995|

ANS: D PTS: 1

78. Refer to Exhibit 2-3. The percentage of workers who took 0 - 5 sick days per month was
a.| 20%|
b.|120%|
c.| 75%|
d.| 60%|

ANS: D PTS: 1

79. Refer to Exhibit 2-3. The cumulative percent frequency for the class of 16 - 20 is
a.| 100%|
b.| 65%|
c.|92.5%|
d.| 0.5%|

ANS: A PTS: 1

80. Refer to Exhibit 2-3. The cumulative frequency for the class of 11 - 15
a.|is 200|
b.|is 14|
c.|is 199|
d.|is 1|

ANS: C PTS: 1

Exhibit 2-4
A survey of 400 college seniors resulted in the following crosstabulation regarding their undergraduate major and whether or not they plan to go to graduate school.

|Yes| 35| 42| 63|140|
|No| 91|104| 65|260|
|Total|126|146|128|400|

81. Refer to Exhibit 2-4. What percentage of the students does not plan to go to graduate school?
a.|280|
b.|520|
c.| 65|
d.| 32|

ANS: C PTS: 1

82. Refer to Exhibit 2-4. What percentage of the students' undergraduate major is engineering?
a.|292|
b.|520|
c.|65|
d.|36.5|

ANS: D PTS: 1

83. Refer to Exhibit 2-4. Of those students who are majoring in business, what percentage plans to go to graduate school?
a.|27.78|
b.|8.75|
c.|70|
d.|72.22|

ANS: A PTS: 1

84. Refer to Exhibit 2-4. Among the students who plan to go to graduate school, what percentage indicated "Other" majors?
a.|15.75|
b.|45|
c.|54|
d.|35|

ANS: B PTS: 1

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 chart.|
b.|Construct a relative frequency distribution and a pie chart.|

ANS:

|a. and b.|
||
|Major|Frequency|Relative Frequency||
|M|12|0.4||
|A| 9|0.3||
|E| 6|0.2||
|O| 3|0.1||
|Total|30|1.0||

PTS: 1

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||

a.|Construct a frequency distribution and a bar chart.|
b.|Construct a relative frequency distribution and a pie chart.|

ANS:

|a. and b.|
||
|Preferences|Frequency|Relative Frequency||
|L| 8|0.4||
|D|12|0.6||
|Total|20|1.0||

PTS: 1

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||

a.|Develop a frequency distribution and a bar chart for her grades.|
b.|Develop a relative frequency distribution for her grades and construct a pie chart.|

ANS:

|a. and b.|
||
|A| 4|0.20||
|B|11|0.55||
|C| 5|0.25||
|Total|20|1.00||

PTS: 1

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|

a.|Construct a frequency distribution and a bar chart.|
b.|Construct a relative frequency distribution and a pie chart.|

ANS:

|a. and b.|
||
|Response|Frequency|Relative Frequency||
|No|24|0.48||
|Yes|15|0.30||
|Without Opinion|11|0.22||
|Total|50|1.00||

PTS: 1

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|

a.|Construct a frequency distribution and graphically represent the frequency distribution.|
b.|Construct a relative frequency distribution and graphically represent the relative frequency distribution.|

ANS:

|a. and b.|
||
|Preferences|Frequency|Relative Frequency||
|6 ounces|14|0.350||
|8 ounces|17|0.425||
|10 ounces| 9|0.225||
|Total|40|1.000||

PTS: 1

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.

ANS:

|Major|Percent Frequency|
|Accounting|30%|
|Finance|20%|
|Management|40%|
|Marketing|10%|

PTS: 1

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||

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.|
|||Relative|Cumulative|Cumulative|
|Score|Frequency|Frequency|Frequency|Relative Frequency|
|50 - 59| 3| 3|0.15|0.15|
|60 - 69| 2| 5|0.10|0.25|
|70 - 79| 5|10|0.25|0.50|
|80 - 89| 4|14|0.20|0.70|
|90 - 99| 6|20|0.30|1.00|
|Total|20||1.00||

PTS: 1

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|

ANS:
16

PTS: 1

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|

ANS:
0.080

PTS: 1

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|

ANS:
10

PTS: 1

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|

ANS:
The classes overlap.

PTS: 1

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|

ANS:
The relative frequencies do not sum to 1.

PTS: 1

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||

a.|Construct a relative frequency distribution.|
b.|Construct a cumulative frequency distribution.|
c.|Construct a cumulative relative frequency distribution.|

ANS:

||a.|b.|c.|
||Relative|Cumulative|Cumulative|
Height (inches)|Frequency|Frequency|Frequency|Relative Frequency|
58 - 63|3|0.12| 3|0.12|
64 - 69|5|0.20| 8|0.32|
70 - 75|2|0.08|10|0.40|
76 - 81|6|0.24|16|0.64|
82 - 87|4|0.16|20|0.80|
88 - 93|3|0.12|23|0.92|
94 - 99|2|0.08|25|1.00|
||1.00|||

PTS: 1

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

|Quarts of Soft Drink|Frequency||
|0 - 3|4||
|4 - 7|5||
|8 - 11|6||
|12 - 15|3||
|16 - 19|2||

a.|Construct a relative frequency distribution.|
b.|Construct a cumulative frequency distribution.|
c.|Construct a cumulative relative frequency distribution.|

ANS:

|a.|b.|c.|
|Relative|Cumulative|Cumulative|
Quarts of Soft Drinks|Frequency|Frequency|Relative Frequency|
0 - 3|0.20| 4|0.20|
4 - 7|0.25| 9|0.45|
8 - 11|0.30|15|0.75|
12 - 15|0.15|18|0.90|
16 - 19|0.10|20|1.00|
Total|1.00|||

PTS: 1

15. 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|0.3|
70 - 79| 2| 5|0.2|
80 - 89| 2| 7|0.2|
90 - 99| 3|10|0.3|
Total|10||1.0|

PTS: 1

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||

ANS:

Leaf Unit = 1|
2 | 6|7|8|||||
3 | 2|2|6|6|7|||
4 | 0|1|2|4|4|5|8|
5 | 2|3|5|8||||

PTS: 1

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|

ANS:

Leaf Unit = 1|
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|||||

PTS: 1

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|

ANS:

Leaf Unit = 0.1|
0 | 5|7|9||
1 | 1|1|3|4|
2 | 0|2|6||

PTS: 1

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|

ANS:

Leaf Unit = 100|
25 | 0|4||
26 | 1|5|8|
27 | 4|8||
28 ||||
29 ||||
30 | 0|||

PTS: 1

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|

ANS:

Leaf Unit = 1|
0 | 8|||||
1 ||||||
2 | 2|3|5|6|8|
3 | 6|7|7|9||
4 | 7|8||||

PTS: 1

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|

ANS:

Leaf Unit = 0.1|
11 | 8|9||
12 | 0|1|4|
13 ||||
14 | 7|8||
15 | 2|2|8|

PTS: 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|

a.|How many students scored less than 400?|
b.|How many students were female?|
c.|Of the male students, how many scored 600 or more?|
d.|Compute row percentages and comment on any relationship that may exist between SAT math scores and gender of the individuals.|
e.|Compute column percentages.|

ANS:

a.|64|
b.|240|
c.|24|
d.||
||
||SAT Math Scores||
|Gender|Less than 400|400 up to 600|600 and more|Total|
|Female|10%|70%|20%|100%|
|Male|25%|60%|15%|100%|
||
|From the above percentages it can be noted that the largest percentages of both genders' SAT scores are in the 400 to 600 range. However, 70% of females and only 60% of males have SAT scores in this range. Also it can be noted that 10% of females' SAT scores are under 400, whereas, 25% of males' SAT scores fall in this category.|
e.||
||SAT Math Scores||
|Gender|Less than 400|400 up to 600|600 and more||
|Female|37.5%|63.6%|66.7%||
|Male|62.5%|36.4%|33.3%||
|Total|100%|100%|100%||

PTS: 1

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|

a.|Which package design was most preferred overall?|
b.|What percent of those participating in the study preferred package A?|
c.|What percent of those less than 25 years of age preferred package A?|
d.|What percent of those aged 25 - 40 preferred package A?|
e.|Is the preference for package A the same for both age groups?|

ANS:
a.|Design A|
b.|36%|
c.|27.7%|
d.|51.4%|
e.|No, although both groups have the 18 people who prefer Design A, the percentage of those in the "Under 25" age group who prefer Design A is smaller than that of the "25 - 40" age group (27.7% vs. 51.4%).|

PTS: 1

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

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

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

ANS:
a.|Of those who pay with cash, 18% are female.|
b.|5|

PTS: 1

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|

ANS:
A positive relationship between x and y appears to exist.

PTS: 1

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|

ANS:
No relationship between women's heights and salaries appears to exist.

PTS: 1

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|

ANS:
A negative relationship between amount of sugar and amount of fiber appears to exist.

PTS: 1

28. What type of graph is depicted below?

ANS:
A scatter diagram

PTS: 1

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

ANS:
A positive relationship

PTS: 1

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

ANS:
A negative relationship

PTS: 1

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

ANS:
No apparent relationship

PTS: 1

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 |

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

ANS:
a.
Colorof Car|Frequency|Relative Frequency|Percent Frequency|
Black|12|0.300| 30.0|
Blue| 7|0.175| 17.5|
Green| 4|0.100| 10.0|
Red|10|0.250| 25.0|
White| 7|0.175| 17.5|
Total|40|1.000|100.0|
b.

c.

PTS: 1

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|

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

ANS:
a.
FurnitureOrder|Frequency|Relative Frequency|Percent Frequency|
100-149|3|0.06|6|
150-199|15|0.30|30|
200-249|14|0.28|28|
250-299|6|0.12|12|
300-349|4|0.08|8|
350-399|3|0.06|6|
400-449|3|0.06|6|
450-499|2|0.04|4|
b.

c.
FurnitureOrder|Frequency|Cumulative Frequency|Cumulative % Frequency|
100-149|3|3|6|
150-199|15|18|36|
200-249|14|32|64|
250-299|6|38|76|
300-349|4|42|84|
350-399|3|45|90|
400-449|3|48|96|
450-499|2|50|100|

PTS: 1

34. Develop a stretched stem-and-leaf display for the data set below, using a leaf unit of 10.

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|

ANS:
|Leaf Unit = 10|
1| 2|3|4|||||||||||||
1| 5|5|6|6|6|7|7|7|8|8|8|9|9|9|9|
2| 0|1|1|1|1|2|2|3|3|3|4|4|4|4||
2| 5|6|6|7|8|9||||||||||
3| 1|2|3|4||||||||||||
3| 6|6|8|||||||||||||
4| 0|3|4|||||||||||||
4| 7|9||||||||||||||

PTS: 1

35. Guests staying at Marada Inn were asked to rate the quality of their accommodations as being excellent, above average, average, below average, or poor. The ratings provided by a sample of 20 quests are shown below.

Below Average Average Above Average Above Average Above Average Above Average Above Average Below Average Below Average Average Poor Poor Above Average Average Above Average Average Excellent Above Average Average Above Average

a. Provide a frequency distribution showing the number of occurrences of each rating level in the sample.
b. Construct relative frequency and percent frequency distributions for the data.
c. Display the frequencies graphically with a bar graph.
d. Display the percent frequencies graphically with a pie chart.

ANS:
a.
Quality Rating|Frequency|
Poor|2|
Below Average|3|
Average|5|
Above Average|9|
Excellent|1|
Total|20|
b.
Quality Rating|Relative Frequency|Percent Frequency|
Poor|0.10|10|
Below Average|0.15|15|
Average|0.25|25|
Above Average|0.45|45|
Excellent|0.05|5|
Total|1.00|100|

c.

d.

PTS: 1

36. The manager of Hudson Auto Repair would like to get a better picture of the distribution of costs for new parts used in the engine tune-up jobs done in the garage. A sample of 50 customer invoices for tune-ups has been taken and the costs of parts, rounded to the nearest dollar, are listed below.

Develop a frequency distribution for these cost data. Use your own judgment to determine the number of classes and class width that provide a distribution that will be meaningful and helpful to the manager.

a. Develop a stem-and-leaf display showing both the rank order and shape of the data set.
b. Develop a stretched stem-and-leaf display using two stems for each leading digit(s).
c. Which display is better at revealing the natural grouping and variation in the data?

ANS:
a. Stem-and-leaf

5| |2|7| | | | | | | | | | | | | | | |
6| |2|2|2|2|5|6|7|8|8|8|9|9|9| | | | |
7| |1|1|2|2|3|3|4|4|5|5|5|6|7|8|9|9|9|
8| |0|0|2|3|5|8|9| | | | | | | | | | |
9| |1|3|7|7|8|9| | | | | | | | | | | |
10| |1|4|5|5|9| | | | | | | | | | | | |
b. Stretched stem-and-leaf
5| |2| | | | | | | | |
5| |7| | | | | | | | |
6| |2|2|2|2| | | | | |
6| |5|6|7|8|8|8|9|9|9|
7| |1|1|2|2|3|3|4|4| |
7| |5|5|5|6|7|8|9|9|9|
8| |0|0|2|3| | | | | |
8| |5|8|9| | | | | | |
9| |1|3| | | | | | | |
9| |7|7|8|9| | | | | |
10| |1|4| | | | | | | |
10| |5|5|9| | | | | | |
c. The stretched stem-and-leaf display in (b) does a better job of revealing the dispersion of the data. 37. Ithaca Log Homes manufactures four styles of log houses that are sold in kits. The price (in \$000) and style of homes the company has sold in the past year are shown below.

Price| | Style|Price| | Style|Price| | Style|
100||A-Frame|>100||Colonial|
100||Split-Level|100||Split-Level|100||Ranch|>100||Split-Level|
100||Colonial|>100||Ranch|

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...Dear Mr. President, As you know, civic and political participation is important. It allows any citizen to be active in the government. Some people in the world are more active than others. One of those people happens to have been Dorothea Dix. I am writing you to see if there is any way we could acknowledge what Dix did for the people of our country. Dorothea Dix was born in Hampden Maine in 1802. Her journey began when she witnessed the horrible conditions of a women’s prison in Massachusetts. She saw how the prisoners, especially the mentally ill, were being treated, and knew she had to make a change. She spent the next 40 years of her life trying to improve conditions. Dix began traveling throughout the state to research the conditions of other prisons. She gathered information that she then presented to the Massachusetts legislature. By doing this, she managed to get more money for the expansion of the State Mental Hospital. Although this itself was a major accomplishment, she wasn’t satisfied. She then traveled all over the country doing more research such as the conditions of the prisons, and the treatment of the patients. She started campaigning to create humane asylums and succeeded in quite a few states. Next, Dix decided to go to congress. She wanted them to grant her more than 12 million acres of land to use for the benefit of the mentally ill. Both houses of congress approved the bill, but it was vetoes by President Franklin Pierce in 1854. Dix was less than...

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...in other wards people come to the United States with the hope of getting a better life and achieving the ultimate “American Dream”. Indeed the United States being a developed country and having one of the best economy has favourable living conditions in comparison to other parts of the world. This was not the basic reason back in the 17thand 18th century where America was more so a dump place for the poor or people trying to escape harsh governments. Immigration into America is still going on to this very day and it has become an issue amongst many who claim that it is impacting the country in a negative way. Is immigration really having a negative impact in the United States? Perhaps Immigration does have its pros and cons. All together I do agree that there are a lot of effects of a large movement of people into the United States. One of them largely being the variety of races that has made America a uniquely diversified nation that it is today. One of the races being Iranian American that’s purely an immigration group considering that they all came from the Iranian Republic....

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...Task 1: 1.1 Define the following terms: A. Population – The collection of all individuals or items under consideration in a statistical study. B. Sample- That part of the population from which information is obtained (pg. 4) 1.7 Descriptive or inferential TV Viewing Times. The Nielsen Company collect sand publishes information on the television viewing habits of Americans. Data from a sample of Americans yielded the following estimates of average TV viewing time per month for all Americans 2 years old and older. The times are in hours and minutes (NA, not avail- able). [SOURCE: Nielsen’s Three Screen Report, May 2008] Answer: This is an example of a descriptive form of data, because of the summary of the number of Americans 2 years old and older watching TV. 1.14 Offshore Drilling. A CNN/Opinion Research Corporation poll of more than 500 U.S adults, taken in July 2008, revealed that a majority of Americans favor offshore drilling for oil and natural gas; specifically, of those sampled, about 69% were in favor. Answer: a. Identify the population and sample for this study. 1. Population is 500 U.S adults 2. Sample- 69% b. Is the percentage provided a descriptive statistic or an inferential statistic> Explain your answer. 1. Inferential because it is measuring the reliability of conclusions about a population based on information obtained. 1.17 The Salk Vaccine. In the 1940s and early 1950s, the public was greatly concerned......

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...VATE INSIDE STORIES 2014—THE THING AROUND YOUR NECK Inside Stories The Thing Around Your Neck By Chimamanda Ngozi Adichie Teaching notes prepared by Yasmine McCafferty Edited by Tony Thompson CONTENTS INTRODUCTION .........................................................................................................3   WAYS INTO THE TEXT ..............................................................................................5   RUNNING SHEET AND THE STRUCTURE OF THE TEXT ......................................6   CHARACTERS..........................................................................................................17   ISSUES AND THEMES.............................................................................................20   LANGUAGE AND STYLE..........................................................................................26   FURTHER ACTIVITIES.............................................................................................28   KEY QUOTES ...........................................................................................................31   TEXT RESPONSE TOPICS ......................................................................................33   REFERENCES, RESOURCES AND SUPPLEMENTARY TEXTS ...........................34   Cover design by Viveka de Costa Formatted by Maria Anagnostou © VATE 2013 May be used for educational purposes within the institution that......

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