Blueman 5th_Chapter 2 HW Soln

8/13/2019 Blueman 5th_Chapter 2 HW Soln

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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:


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.


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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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.

Blueman 5th_Chapter 2 HW Soln

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