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	PTS:	1	TOP:	Descriptive Statistics	

	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 categorical data	

ANS:	C	PTS:	1	TOP:	Descriptive Statistics	

	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	PTS:	1	TOP:	Descriptive Statistics	

	4.	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	TOP:	Descriptive Statistics	

	5.	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	TOP:	Descriptive Statistics	

	6.	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	TOP:	Descriptive Statistics	

	7.	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) which can be used to present these data is (are)
a.	a line chart	
b.	only a bar chart	
c.	only a pie chart	
d.	both a bar chart and a pie chart	

ANS:	D	PTS:	1	TOP:	Descriptive Statistics	

	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.	label data	
d.	either quantitative or categorical data	

ANS:	A	PTS:	1	TOP:	Descriptive Statistics	

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

ANS:	D	PTS:	1	TOP:	Descriptive Statistics	

	10.	A cumulative relative frequency distribution shows
a.	the proportion of data items with values less than or equal to the upper limit of each class	
b.	the proportion of data items with values less than or equal to the lower limit of each class	
c.	the percentage of data items with values less than or equal to the upper limit of each class	
d.	the percentage of data items with values less than or equal to the lower limit of each class	

ANS:	A	PTS:	1	TOP:	Descriptive Statistics	

	11.	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	

ANS:	A	PTS:	1	TOP:	Descriptive Statistics	

	12.	The sum of the relative frequencies for all classes will always equal
a.	the sample size	
b.	the number of classes	
c.	one	
d.	any value larger than one	

ANS:	C	PTS:	1	TOP:	Descriptive Statistics	

	13.	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	TOP:	Descriptive Statistics	

	14.	The most common graphical presentation of quantitative data is a
a.	histogram	
b.	bar chart	
c.	relative frequency	
d.	pie chart	

ANS:	A	PTS:	1	TOP:	Descriptive Statistics	

	15.	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	PTS:	1	TOP:	Descriptive Statistics	

	16.	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	PTS:	1	TOP:	Descriptive Statistics	

	17.	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	PTS:	1	TOP:	Descriptive Statistics	

	18.	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	TOP:	Descriptive Statistics	

	19.	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	TOP:	Descriptive Statistics	

	20.	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 these alternatives is correct.	

ANS:	C	PTS:	1	TOP:	Descriptive Statistics	

	21.	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	
d.	None of these alternatives is correct.	

ANS:	A	PTS:	1	TOP:	Descriptive Statistics	

	22.	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 these alternatives is correct.	

ANS:	B	PTS:	1	TOP:	Descriptive Statistics	

	23.	Data that provide labels or names for categories of like items are known as
a.	categorical data	
b.	quantitative data	
c.	label data	
d.	category data	

ANS:	A	PTS:	1	TOP:	Descriptive Statistics	

	24.	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	PTS:	1	TOP:	Descriptive Statistics	

	25.	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	PTS:	1	TOP:	Descriptive Statistics	

	26.	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	
c.	shorter tail to the left	
d.	longer tail to the left	

ANS:	D	PTS:	1	TOP:	Descriptive Statistics	

	27.	When a histogram has a longer tail to the right, it is said to be
a.	symmetrical	
b.	skewed to the left	
c.	skewed to the right	
d.	none of these alternatives is correct	

ANS:	C	PTS:	1	TOP:	Descriptive Statistics	

	28.	In a scatter diagram, a line that provides an approximation of the relationship between the variables is known as
a.	approximation line	
b.	trend line	
c.	line of zero intercept	
d.	line of zero slope	

ANS:	B	PTS:	1	TOP:	Descriptive Statistics	

	29.	A histogram is
a.	a graphical presentation of a frequency or relative frequency distribution	
b.	a graphical method of presenting a cumulative frequency or a cumulative relative frequency distribution	
c.	the history of data elements	
d.	the same as a pie chart	

ANS:	A	PTS:	1	TOP:	Descriptive Statistics	

	30.	A situation in which conclusions based upon aggregated crosstabulation are different from unaggregated crosstabulation is known as
a.	wrong crosstabulation	
b.	Simpson's rule	
c.	Simpson's paradox	
d.	aggregated crosstabulation	

ANS:	C	PTS:	1	TOP:	Descriptive Statistics	

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	

	31.	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	TOP:	Descriptive Statistics	

	32.	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	TOP:	Descriptive Statistics	

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

ANS:	D	PTS:	1	TOP:	Descriptive Statistics	

	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	PTS:	1	TOP:	Descriptive Statistics	

	35.	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	TOP:	Descriptive Statistics	

	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	PTS:	1	TOP:	Descriptive Statistics	

	37.	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 0.5	

ANS:	B	PTS:	1	TOP:	Descriptive Statistics	

	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	PTS:	1	TOP:	Descriptive Statistics	

	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	PTS:	1	TOP:	Descriptive Statistics	

	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	PTS:	1	TOP:	Descriptive Statistics	

	41.	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	TOP:	Descriptive Statistics	

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	PTS:	1	TOP:	Descriptive Statistics	

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

ANS:	D	PTS:	1	TOP:	Descriptive Statistics	

	44.	Refer to Exhibit 2-2. 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	TOP:	Descriptive Statistics	

	45.	Refer to Exhibit 2-2. 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	TOP:	Descriptive Statistics	

Exhibit 2-3
Michael's Compute-All, a national computer retailer, has kept a record of the number of laptop computers they have sold for a period of 80 days.  Their sales records are shown below:

		Number of Laptops Sold	Number of Days

	0 - 19	5
	20 - 39	15
	40 - 59	30
	60 - 79	20
	80 - 99	10
	Total	80

	46.	Refer to Exhibit 2-3.  The class width of the above distribution is
a.	0 to 100	
b.	20	
c.	80	
d.	5	

ANS:	B	PTS:	1	TOP:	Descriptive Statistics	

	47.	Refer to Exhibit 2-3.  The lower limit of the first class is
a.	5	
b.	80	
c.	0	
d.	20	

ANS:	C	PTS:	1	TOP:	Descriptive Statistics	

	48.	Refer to Exhibit 2-3.  If one develops a cumulative frequency distribution for the above data, the last class will have a frequency of
a.	10	
b.	100	
c.	0 to 100	
d.	80	

ANS:	D	PTS:	1	TOP:	Descriptive Statistics	

	49.	Refer to Exhibit 2-3.  The percentage of days in which the company sold at least 40 laptops is
a.	37.5%	
b.	62.5%	
c.	90.0%	
d.	75.0%	

ANS:	D	PTS:	1	TOP:	Descriptive Statistics	

	50.	Refer to Exhibit 2-3.  The number of days in which the company sold less than 60 laptops is
a.	20	
b.	30	
c.	50	
d.	60	

ANS:	C	PTS:	1	TOP:	Descriptive Statistics	

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)	(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	TOP:	Descriptive Statistics	

	2.	Twenty employees of the Ahmadi 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 chart.	
b.	Construct a relative frequency distribution and a pie chart.	

ANS:	
a and b

Preferences	
Frequency	Relative
Frequency	
L	  9	0.45	
D	11	0.55	
Total	20	1.00	

PTS:	1	TOP:	Descriptive Statistics	

	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 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	TOP:	Descriptive Statistics	

	4.	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

Grade	
Frequency	Relative
Frequency	
A	  4	0.20	
B	11	0.55	
C	  5	0.25	
Total	20	1.00	

PTS:	1	TOP:	Descriptive Statistics	

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

ANS:	
a and b

Frequency	Relative
Frequency	
No	24	0.48	
Yes	15	0.30	
Without Opinion	11	0.22	
Total	50	1.00	

PTS:	1	TOP:	Descriptive Statistics	

	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	0.15	
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	TOP:	Descriptive Statistics	

	7.	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.	
				Cumulative	
Height		Relative	Cumulative	Relative	
(In Inches)	Frequency	Frequency	Frequency	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	TOP:	Descriptive Statistics	

	8.	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.	
				Cumulative	
Quarts of		Relative	Cumulative	Relative	
Soft Drinks	Frequency	Frequency	Frequency	Frequency	
  0 -   4	  4	0.20	  4	0.20	
  4 -   8	  5	0.25	  9	0.45	
  8 - 12	  6	0.30	15	0.75	
12 - 16	  3	0.15	18	0.90	
16 - 20	  2	0.10	20	1.00	
Total	20	1.00			

PTS:	1	TOP:	Descriptive Statistics	

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

PTS:	1	TOP:	Descriptive Statistics	

	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%	

PTS:	1	TOP:	Descriptive Statistics	

	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					

PTS:	1	TOP:	Descriptive Statistics	

	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					

PTS:	1	TOP:	Descriptive Statistics	

	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 scores and gender of the individuals.	
e.	Compute column percentages.	

ANS:	

a.	64	
b.	240	
c.	24	
		
d.	SAT Scores	
	Gender	Less than 20	20 up to 25	25 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 20 to 25 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 20, whereas, 25% of males' SAT scores fall in this category.	
			
e.	SAT Scores		
	Gender	Less than 20	20 up to 25	25 and more		
	Female	37.5%	63.6%	66.7%		
	Male	62.5%	36.4%	33.3%		
	Total	100%	100%	100%		

PTS:	1	TOP:	Descriptive Statistics	

	14.	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	TOP:	Descriptive Statistics	

	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.

PTS:	1	TOP:	Descriptive Statistics	

	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	

PTS:	1	TOP:	Descriptive Statistics	

	17.	A sample of the ages of 10 employees of a company is shown below.

20	30	40	30	50	
30	20	30	20	40	

Construct a dot plot for the above data.

ANS:	
		•				
	•	•				
	•	•	•			
	•	•	•	•		
10	20	30	40	50	60	

PTS:	1	TOP:	Descriptive Statistics	

	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:	

	a.	b.	b.	c.	
Hours of		Relative	Percent	Cum.	
Sick Leave Taken	Freq.	Freq.	Freq.	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

PTS:	1	TOP:	Descriptive Statistics	

	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.  (Use 5 classes and have your first class be 20 - 39.)	
b.	Develop a cumulative frequency and a cumulative percent frequency distribution for the above data.	
c.	What percentage of the houses sold at a price below $80,000?	

ANS:	

	a.	a.	b.	b.	
				Cum.	
Sales Price		Percent	Cum.	Percent	
(In Thousands of Dollars)	Freq.	Freq.	Freq.	Freq.	
20 - 39	1	10	1	10	
40 - 59	2	20	3	30	
60 - 79	4	40	7	70	
80 - 99	2	20	9	90	
100 - 119	1	10	10	100	
c.    70%

PTS:	1	TOP:	Descriptive Statistics	

	20.	The test scores of 14 individuals on their first statistics examination are shown below.

95	87	52	43	77	84	78	
75	63	92	81	83	91	88	

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

ANS:	
4	3					
5	2					
6	3					
7	5	7	8			
8	1	3	4	7	8	
9	1	2	5			

PTS:	1	TOP:	Descriptive Statistics	

	21.	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.

Undergraduate Major	
Graduate School	Business	Engineering	Others	Total	
Yes	35	42	63	140	
No	91	104	65	260	
Total	126	146	128	400	

a.	Are a majority of the seniors in the survey planning to attend graduate school?	
b.	Which discipline constitutes the majority of the individuals in the survey?	
c.	Compute row percentages and comment on the relationship between the students' undergraduate major and their intention of attending graduate school.	
d.	Compute the column percentages and comment on the relationship between the students' intention of going to graduate school and their undergraduate major.	

ANS:	
a.	No, majority (260) will not attend graduate school	
b.	Majority (146) are engineering majors	
c.
Undergraduate Major	
Graduate School	Business	Engineering	Others	Total	
Yes	25%	30%	45%	100%	
No	35%	40%	25%	100%	
      
Majority who plan to go to graduate school are from "Other" majors.  Majority of those who will not go to graduate school are engineering majors.
d.
Undergraduate Major	
Graduate School	Business	Engineering	Others	
Yes	27.8%	28.8%	49.2%	
No	72.2%	71.2%	50.8%	
Total	100%	100%	100%	

Approximately the same percentages of Business and engineering majors plan to attend graduate school (27.8% and 28.8% respectively).  Of the "Other" majors approximately half (49.2%) plan to go to graduate school.

PTS:	1	TOP:	Descriptive Statistics