Math 227 – Elementary Statistics: A Brief Version, 5/e Bluman
Section 2-1 #’s 3, 7, 8, 11
3)
Find the class boundaries, midpoints, and widths for each class.
a) 12 – 18
7)
b) 56 – 74
c) 695 – 705
Class Limits
12 – 18
Class Boundaries
11.5 – 18.5
56 – 74
55.5 – 74.5
695 – 705
694.5 – 705.5
13.6 – 14.7
13.55 – 14.75
2.15 – 3.93
2.145 – 3.935
d) 13.6 – 14.7
e) 2.15 – 3.93
Midpoints
12 + 18
=
2
56 + 74
=
2
695 + 705
=
2
13.6 + 14.7
=
2
2.15 + 3.93
=
2
30
= 15
2
130
= 65
2
1400
= 700
2
28.3
= 14.15
2
6.08
= 3.04
2
Class Width
7
19
11
1.2
1.79
Trust in Internet Information A survey was taken on how much trust people place in the
information they read on the Internet. Construct a categorical frequency distribution for the
data. A = trust in everything they read, M = trust in most of what they read, H = trust in about
one-half of what they read, S = trust in a small portion of what they read.
M M M A H M S M H M
S M M M M A M M A M
M M H M M M H M H M
A M M M H M M M M M
Class Limit
A
Frequency f
4
M
28
H
6
S
2
Total
40
Percent %
4
= 0.10
= 10%
40
28
= 0.70
= 70%
40
6
= 0.15
= 15%
40
2
= 0.05
= 5%
40
100 %
8)
State Gasoline Tax The state gas tax in cents per gallon for 25 states is given below. Construct a
grouped frequency distribution and a cumulative frequency distribution with 5 classes.
7.5
21.5
22
23
14.5
16
19
20.7
18.5
25.9
23.5
20
17
25.3
18
17
27.1
28
24
30
22
20
20
31
31.5
Range = 31.5-7.5 = 24 ; # of classes = 5; class width=
Class
Limits
Boundaries
Frequency f
Cf
7.5 - 12.4
12.5 - 17.4
17.5 - 22.4
22.5 - 27.4
27.5 - 32.4
7.45 - 12.45
12.45 - 17.45
17.45 - 22.45
22.45 - 27.45
27.45 - 32.45
1
4
10
6
4
25
1
5
15
21
25
Total
11)
24
= 4.8 or 5
5
GRE Scores at Top-Ranked Engineering Schools The average quantitative GRE scores for the top
30 graduate schools of engineering are listed. Construct a frequency distribution with 6 classes.
767 770 761 760 771 768 776 771 756 770
763 760 747 766 754 771 771 778 766 762
780 750 746 764 769 759 757 753 758 746
H = 780 ; L = 746 ; Range = 780 – 746 = 34 ; # of classes = 6 ; class width = Round up (
34
)=
6
Round up ( 5.6 ) = 6
Class Limits
746 – 751
752 – 757
758 – 763
764 – 769
770 – 775
776 – 781
Frequency f
4
4
7
6
6
3
Boundaries
745.5 – 751.5
751.5 – 757.5
757.5 – 763.5
763.5 – 769.5
769.5 – 775.5
775.5 – 781.5
Cf
4
8
15
21
27
30
Mid-point
748.5
754.5
760.5
766.5
772.5
778.8
Section 2-2 #’s 4, 5, 15, 16
4)
NFL Salaries The salaries (in millions of dollars) for 31 NFL teams for a specific season are given
in this frequency distribution.
Class limits
Frequency
Cf
Mid-point
39.9–42.8
2
2
41.35
42.9–45.8
2
4
44.35
45.9–48.8
5
9
47.35
48.9–51.8
5
14
50.35
51.9–54.8
12
26
53.35
54.9–57.8
5
31
56.35
Construct a histogram, a frequency polygon, and an ogive for the data; and comment on the
shape of the distribution.
a) Histogram:
b) Frequency Polygon:
c) Ogive:
The distribution is left skewed or negatively skewed.
5)
Automobile Fuel Efficiency Thirty automobiles were tested for fuel efficiency, in miles per
gallon (mpg). The following frequency distribution was obtained. Construct a histogram,
frequency polygon, and ogive for the data.
Class boundaries
Frequency
Cf
Midpoint
7.5 – 12.5
3
3
10
12.5 – 17.5
5
8
15
17.5 – 22.5
15
23
20
22.5 – 27.5
5
28
25
27.5 – 32.5
2
30
30
a) Histogram:
b) Frequency Polygon:
c) Ogive:
15)
Cereal Calories The number of calories per serving for selected ready-to-eat cereals is listed
here. Construct a frequency distribution using 7 classes. Draw a histogram, frequency polygon,
and ogive for the data, using relative frequencies. Describe the shape of the histogram.
130 190 140 80 100 120 220 220 110 100
210 130 100 90 210 120 200 120 180 120
190 210 120 200 130 180 260 270 100 160
190 240
80 120 90 190 200 210 190 180
115 210 110 225 190 130
L = 80 ; H = 270 ; Range = 270 – 80 = 190 ; # of classes = 7 ; Class width = Roundup (
Roundup ( 27.14) = 28
Class Limits
80 – 107
108 – 135
136 – 163
164 – 191
192 – 219
220 – 249
248 - 275
Total
a) Histogram:
Frequency
8
13
2
9
8
4
2
46
Boundaries
79.5 – 107.5
107.5 -135.5
135.5 – 163.5
163.5 – 191.5
191.5 – 219.5
219.5 – 247.5
247.5 -275.5
Cf
8
21
23
32
40
44
46
Rf %
17%
28%
4%
20%
17%
8%
4%
190
)=
7
The Histogram has 2 peaks.
b) Frequency Polygon:
c) Ogive:
16)
Protein Grams in Fast Food The amount of protein (in grams) for a variety of fast-food
sandwiches is reported here. Construct a frequency distribution using 6 classes. Draw a
histogram, frequency polygon, and ogive for the data, using relative frequencies. Describe the
shape of the histogram.
23 30 20 27 44 26 35 20 29 29
25 15 18 27 19 22 12 26 34 15
27 35 26 43 35 14 24 12 23 31
40 35 38 57 22 42 24 21 27 33
L = 12 ; H = 57 ; Range = 57 – 12 = 45 ; # of classes = 6 ; Class width = Roundup (
Class Limits
12 – 19
Frequency
7
Boundaries
11.5 – 19.5
Mid-point
15.5
Cf
7
20 – 27
17
19.5 – 27.5
23.5
24
28 – 35
10
27.5 – 35.5
31.5
34
36 – 43
4
35.5 – 43.5
39.5
38
44 – 51
1
43.5 – 51.5
47.5
39
52 – 59
1
51.5 – 59.5
55.5
40
Total
40
a) Histogram:
45
) = Roundup ( 7.5) = 8
6
Rf %
7
= 0.175
= 18%
40
17
= 0.425
= 43%
40
10
= 0.25
= 25%
40
4
= 0.1
= 10%
40
1
= 0.025
= 3%
40
1
= 0.025
= 3%
40
b) Frequency Polygon:
c) Ogive:
Section 2-3 #’s 3, 5, 6, 10, 14, 15, 16
3)
Internet Connections The following data represent the estimated number (in millions) of
computers connected to the Internet worldwide. Construct a Pareto chart for the data. Based on
the data, suggest the best place to market appropriate Internet products.
Location
Homes
Small companies
Large companies
Government agencies
Schools
Number of computers
240
102
148
33
47
The best place to market products would be to the home viewers.
5)
World Energy Use The following percentages indicate the source of energy used worldwide.
Construct a Pareto chart for the energy used.
Petroleum
Coal
Dry natural gas
Hydroelectric
Nuclear
Other (wind, solar,
etc.)
39.8%
23.2%
22.4%
7.0%
6.4%
1.2%
6)
Airline Departures draw a time series graph to represent the data for the number of
airline departures (in millions) for the given years. Over the years, is the number of departures
increasing, decreasing, or about the same?
Year
1996
1997
1998
1999
2000
2001
2002
Number of
departures
7.9
9.9
10.5
10.9
11.0
9.8
10.1
There was an increase in the number of departures until 2000, then a decrease in 2001, and
then an increase.
7)
Tobacco Consumption the data represent the personal consumption (in billions of dollars) for
tobacco in the United States. Draw a time series graph for the data and explain the trend.
Year
Amount
1995
8.5
1996
8.7
1997
9.0
1998
9.3
1999
9.6
2000
9.9
2001
10.2
2002
10.4
There is a steady increase in consumption of tobacco products.
10)
Reasons We Travel The following data are based on a survey from American Travel Survey on
why people travel. Construct a pie graph for the data and analyze the results.
Purpose
Personal business
(PB)
Number
146
Percent
146
= 14.6%
1000
14)
Visit friends or
relatives (VF)
330
Work-related
(WR)
225
Leisure
(L)
299
Total
1000
330
= 33.0%
1000
225
= 22.5%
1000
299
= 29.9%
1000
State which graph (Pareto chart, time series graph, or pie graph) would most appropriately
represent the given situation.
a) The number of students enrolled at a local college for each year during the last 5 years.
Answer: Time series graph
b) The budget for the student activities department at a certain college for each year
during the last 5 years.
Answer: Pie graph
c) The means of transportation the students use to get to school.
Answer: Pareto chart
d) The percentage of votes each of the four candidates received in the last election.
Answer: Pie graph
e) The record temperature of a city for the last 30 years.
Answer: Time series graph
f) The frequency of each type of crime committed in a city during the year.
Answer: Pareto chart
15)
President’s Ages at Inauguration The age at inauguration for each U.S. President is shown.
Construct a stem and leaf plot and analyze the data.
57 54 52 55 51 56
61 68 56 55 54 61
57 51 46 54 51 52
57 49 54 42 60 69
58 64 49 51 62 64
57 48 50 56 43 46
61 65 47 55 55 54
Double Stem and Leaf Plot
The distribution is somewhat symmetric and unimodal. The majority of the Presidents
were in their 50’s when inaugurated.
16)
Calories in Salad Dressings A listing of calories per one ounce of selected salad dressings (not
fat-free) is given below. Construct a stem and leaf plot for the data.
Section 2-4 #’s 6, 7, 13
6)
Hours Spent Jogging A researcher wishes to determine whether the number of hours a person
jogs per week is related to the person’s age. Draw a scatter plot and comment on the nature of
the relationship.
Age, x
34
22
48
56
62
Hours, y
5.5
7
3.5
3
1
Stem
Leaf
4
4
5
5
6
6
23
667899
011112244444
555566677778
0111244
589
7)
Recreational Expenditures A study was conducted to determine if the amount a person spends
per month on recreation is related to the person’s income. Draw a scatter plot and comment on
the nature of the relationship.
Income, x
Amount, y
$800
$60
$1200
$200
$1000
$160
$900
$135
$850
$45
$907
$90
$1100
$150
There appears to be a positive linear relationship between a person’s monthly income and the
amount a person spends on recreation each month.
13)
Absences and Final Grades An educator wants to see if there is a relationship between the
number of absences a student has and his or her final grade in a course. Draw a scatter plot and
comment on the nature of the relationship.
Number of
absences, x
10
12
2
0
8
5
Final Grade
70
65
96
94
75
82
There appears to be a negative linear relationship between the number of absences a
student has and his or her final grade in a course.