blueman 5th_chapter 2 hw soln
TRANSCRIPT
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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 b) 56 74 c) 695 705 d) 13.6 14.7 e) 2.15 3.93
Class Limits Class Boundaries Midpoints Class Width
12 18 11.5 18.5 12 18 3015
2 2
+= =
7
56 74 55.5 74.5 56 74 13065
2 2
+= =
19
695 705 694.5 705.5 695 705 1400700
2 2
+= =
11
13.6 14.7 13.55 14.75 13.6 14.7 28.314.15
2 2
+= =
1.2
2.15 3.93 2.145 3.935 2.15 3.93 6.083.04
2 2
+= =
1.79
7) Trust in Internet InformationA 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 Frequencyf Percent %
A 4 40.10 10%
40= =
M 28 280.70 70%
40
= =
H 6 60.15 15%
40= =
S 2 20.05 5%
40= =
Total 40 100 %
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8) State Gasoline TaxThe 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 16 23.5 17 22
21.5 19 20 27.1 20
22 20.7 17 28 20
23 18.5 25.3 24 3114.5 25.9 18 30 31.5
Range = 31.5-7.5 = 24 ; # of classes = 5; class width=24
4.8 or 55=
Class
Limits
Boundaries Frequencyf Cf
7.5 - 12.4 7.45 - 12.45 1 112.5 - 17.4 12.45 - 17.45 4 5
17.5 - 22.4 17.45 - 22.45 10 1522.5 - 27.4 22.45 - 27.45 6 2127.5 - 32.4 27.45 - 32.45 4 25
Total 25
11) 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 Frequencyf Boundaries Cf Mid-point
746 751 4 745.5 751.5 4 748.5
752 757 4 751.5 757.5 8 754.5
758 763 7 757.5 763.5 15 760.5764 769 6 763.5 769.5 21 766.5
770 775 6 769.5 775.5 27 772.5
776 781 3 775.5 781.5 30 778.8
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Section 2-2 #s 4, 5, 15, 16
4) NFL SalariesThe 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
39.942.8 2 2 41.35
42.945.8 2 4 44.35
45.948.8 5 9 47.35
48.951.8 5 14 50.35
51.954.8 12 26 53.35
54.957.8 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.
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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:
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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 (190
7) =
Roundup ( 27.14) = 28
Class Limits Frequency Boundaries Cf Rf %
80 107 8 79.5 107.5 8 17%
108 135 13 107.5 -135.5 21 28%
136 163 2 135.5 163.5 23 4%
164 191 9 163.5 191.5 32 20%
192 219 8 191.5 219.5 40 17%
220 249 4 219.5 247.5 44 8%
248 - 275 2 247.5 -275.5 46 4%
Total 46
a) Histogram:
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The Histogram has 2 peaks.
b) Frequency Polygon:
c) Ogive:
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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 (45
6) = Roundup ( 7.5) = 8
Class Limits Frequency Boundaries Mid-point Cf Rf %
12 19 7 11.5 19.5 15.5 7 70.175 18%
40= =
20 27 17 19.5 27.5 23.5 24 170.425 43%
40= =
28 35 10 27.5 35.5 31.5 34 100.25 25%
40= =
36 43 4 35.5 43.5 39.5 38 40.1 10%
40= =
44 51 1 43.5 51.5 47.5 39 10.025 3%
40= =
52 59 1 51.5 59.5 55.5 40 1 0.025 3%40
= =
Total 40
a) Histogram:
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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 Number of computers
Homes 240
Small companies 102
Large companies 148
Government agencies 33
Schools 47
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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 39.8%
Coal 23.2%
Dry natural gas 22.4%
Hydroelectric 7.0%
Nuclear 6.4%
Other (wind, solar,
etc.)
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
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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 1995 1996 1997 1998 1999 2000 2001 2002
Amount 8.5 8.7 9.0 9.3 9.6 9.9 10.2 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 onwhy people travel. Construct a pie graph for the data and analyze the results.
Purpose Number Percent
Personal business
(PB)
146 14614.6%
1000=
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Visit friends or
relatives (VF)
330 33033.0%
1000=
Work-related
(WR)
225 22522.5%
1000=
Leisure
(L)
299 299
29.9%1000=
Total 1000
14) 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 yearduring 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) Presidents 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
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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 50s when inaugurated.
16) Calories in Salad DressingsA 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 persons 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 23
4 667899
5 011112244444
5 5555666777786 0111244
6 589
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7) Recreational Expenditures A study was conducted to determine if the amount a person spends
per month on recreation is related to the persons income. Draw a scatter plot and comment on
the nature of the relationship.
Income, x $800 $1200 $1000 $900 $850 $907 $1100Amount, y $60 $200 $160 $135 $45 $90 $150
There appears to be a positive linear relationship between a persons 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
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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.