Solution Manual for Elementary Statistics A Step by Step Approach 9th Edition 0073534986 by Bluman

Chapter 2 - Frequency Distributions and Graphs 12.

Class width is not uniform.

EXERCISE SET 2-1 1. Frequency distributions are used to organize data in a meaningful way, to determine the shape of the distribution, to facilitate computational procedures for statistics, to make it easier to draw charts and graphs, and to make comparisons among different sets of data.

13.

Class f F 19 C 14 B 10 A 7 50

2. Categorical distributions are used with nominal or ordinal data, ungrouped distributions are used with data having a small range, and grouped distributions are used when the range of the data is large.

Percent 38 28 20 14 100

The class with the most data values is professional football. The class with the least number of data values is auto racing.

14.

Class f A 4 M 28 H 6 S 2 40

3. Five to twenty classes. Width should be an odd number so that the midpoint will have the same place value as the data.

4. An open-ended frequency distribution has either a first class with no lower limit or a last class with no upper limit. They are necessary to accomodate all the data.

15.

Limits 0 1 2 3 4 5 6 7

5.

Boundaries: 42.5  47.5 Midpoint: 45 Width: 5 6.

Boundaries: 124.5  131.5 Midpoint: 128 Width: 7 7.

Boundaries: 8.235  11.365 Midpoint: 9.8 Width: 3.13

Percent 10% 70% 15% 5% 100%

Boundaries f -0.5 - 0.5 2 0.5 - 1.5 5 1.5 - 2.5 24 2.5 - 3.5 8 3.5 - 4.5 6 4.5 - 5.5 4 5.5 - 6.5 0 6.5 - 7.5 1 50

Less than -0.5 Less than 0.5 Less than 1.5 Less than 2.5 Less than 3.5 Less than 4.5 Less than 5.5 Less than 6.5 Less than 7.5

8.

Boundaries: 16.25  18.55 Midpoint: 17.4 Width: 2.3 9.

Class width is not uniform.

cf 0 2 7 31 39 45 49 49 50

The category "twice a week" has more values than any other category.

10.

Class limits overlap, and class width is not uniform.

11.

A class has been omitted.

7

Chapter 2 - Frequency Distributions and Graphs 16.

Limits 3 4 5 6 7 8 9

Boundaries 2.5 - 3.5 3.5 - 4.5 4.5 - 5.5 5.5 - 6.5 6.5 - 7.5 7.5 - 8.5 8.5 - 9.5

Less than 2.5 Less than 3.5 Less than 4.5 Less than 5.5 Less than 6.5 Less than 7.5 Less than 8.5 Less than 9.5

18. continued Limits Boundaries 54 - 62 53.5 - 62.5 63 - 71 62.5 - 71.5 72 - 80 71.5 - 80.5 81 - 89 80.5 - 89.5 90 - 98 89.5 - 98.5 99 - 107 98.5 - 107.5 108 - 116 107.5 - 116.5

f 2 4 4 1 4 3 2 20

cf 0 2 6 10 11 15 18 20

Less than 53.5 Less than 62.5 Less than 71.5 Less than 80.5 Less than 89.5 Less than 98.5 Less than 107.5 Less than 116.5

17.

H œ 514 L œ 465 Range œ 514  465 œ 49 Width œ 49 ƒ 6 œ 8.2 round up to 9 Limits 465 - 473 474 - 482 483 - 491 492 - 500 501 - 509 510 - 518

Boundaries 464.5 - 473.5 473.5 - 482.5 482.5 - 491.5 491.5 - 500.5 500.5 - 509.5 509.5 - 518.5

Less than 464.5 Less than 473.5 Less than 482.5 Less than 491.5 Less than 500.5 Less than 509.5 Less than 518.5

f 7 6 8 4 1 3 1 30

cf 0 7 13 21 25 26 29 30

19.

H œ 70 L œ 27 Range œ 70  27 œ 43 Width œ 43 ƒ 7 œ 6.1 or 7

f 9 7 7 6 7 4 40

Limits 27 - 33 34 - 40 41 - 47 48 - 54 55 - 61 62 - 68 69 - 75

cf 0 9 16 23 29 36 40

Boundaries f 26.5 - 33.5 7 33.5 - 40.5 14 40.5 - 47.5 15 47.5 - 54.5 11 54.5 - 61.5 3 61.5 - 68.5 3 68.5 - 75.5 2 55

Less than 26.5 Less than 33.5 Less than 40.5 Less than 47.5 Less than 54.5 Less than 61.5 Less than 68.5 Less than 75.5

18.

H œ 110 L œ 54 Range œ 110  54 œ 56 Width œ 56 ƒ 7 œ 8 round up to 9

cf 0 7 21 36 47 50 53 55

20.

H œ 177,500 L œ 70,000 Range œ 177,500  70,000 œ 107,500 Width œ 107,500 ƒ 6 œ 17,916.67 round up to 17,917

8

Chapter 2 - Frequency Distributions and Graphs 20. continued Limits 70,000 - 87,916 87,917 - 105,833 105,834 - 123,750 123,751 - 141,667 141,668 - 159,584 159,585 - 177,502

Boundaries 69,999.5 - 87,916.5 87,916.5 - 105,833.5 105,833.5 - 123,750.5 123,750.5 - 141,667.5 141,667.5 - 159,584.5 159,584.5 - 177,502.5

Less than 69,999.5 Less than 87,916.5 Less than 105,833.5 Less than 123,750.5 Less than 141,667.5 Less than 159,584.5 Less than 177,502.5

22. continued Limits Boundaries 0 - 10 -0.5 - 10.5 11 - 21 10.5 - 21.5 22 - 32 21.5 - 32.5 33 - 43 32.5 - 43.5 44 - 54 43.5 - 54.5

f 1 3 7 6 5 3 25

Less than -0.5 Less than 10.5 Less than 21.5 Less than 32.5 Less than 43.5 Less than 54.5

cf 0 1 4 11 17 22 25

Boundaries 11.5 - 20.5 20.5 - 29.5 29.5 - 38.5 38.5 - 47.5 47.5 - 56.5 56.5 - 65.5 65.5 - 74.5 74.5 - 83.5 83.5 - 92.5

Less than 11.5 Less than 20.5 Less than 29.5 Less than 38.5 Less than 47.5 Less than 56.5 Less than 65.5 Less than 74.5 Less than 83.5 Less than 92.5

cf 0 7 13 15 15 16

23.

H œ 123 L œ 77 Range œ 123  77 œ 46 Width œ 46 ƒ 7 œ 6.6 or 7

21.

H œ 88 L œ 12 Range œ 88  12 œ 76 Width œ 76 ƒ 9 œ 8.4 round up to 9 Limits 12 - 20 21 - 29 30 - 38 39 - 47 48 - 56 57 - 65 66 - 74 75 - 83 84 - 92

f 7 6 2 0 1 16

Limits 77 - 83 84 - 90 91 - 97 98 - 104 105 - 111 112 - 118 119 - 125

f 7 7 3 3 4 3 0 2 1 30

Boundaries 76.5 - 83.5 83.5- 90.5 90.5- 97.5 97.5- 104.5 104.5 - 111.5 111.5 - 118.5 118.5 - 125.5

Less than 76.5 Less than 83.5 Less than 90.5 Less than 97.5 Less than 104.5 Less than 111.5 Less than 118.5 Less than 125.5

cf 0 7 14 17 20 24 27 27 29 30

cf 0 1 2 8 22 30 31 32

24.

H œ 3462 L œ 3 Range œ 3462  3 œ 3459 Width œ 3459 ƒ 9 œ 384.3 round up to 385

22.

H œ 51.7 L œ 1.2 Range œ 51.7  1.2 œ 50.5 Width œ 50.5 ƒ 5 œ 10.1 round up to 11

9

f 1 1 6 14 8 1 1 32

Chapter 2 - Frequency Distributions and Graphs 24. continued Limits 3 - 387 388 - 772 773 - 1157 1158 - 1542 1543 - 1923 1924 - 2312 2313 - 2697 2698 - 3082 3083 - 3467

Boundaries 2.5 - 387.5 387.5 - 772.5 772.5 - 1157.5 1157.5 - 1542.5 1542.5 - 1923.5 1923.5 - 2312.5 2312.5 - 2697.5 2697.5 - 3082.5 3082.5 - 3467.5

Less than 2.5 Less than 387.5 Less than 772.5 Less than 1157.5 Less than 1542.5 Less than 1923.5 Less than 2312.5 Less than 2697.5 Less than 3082.5 Less than 3467.5

26. continued Width œ 20.6 ƒ 6 œ 3.43 round up to 3.5

f 33 11 3 2 0 0 1 0 1 51

Limits 17.3 - 20.2 20.3 - 23.2 23.3 - 26.2 26.3 - 29.2 29.3 - 32.2 32.3 - 35.2 35.3 - 38.2

cf 0 33 44 47 49 49 49 50 50 51

Less than 17.25 Less than 20.25 Less than 23.25 Less than 26.25 Less than 29.25 Less than 32.25 Less than 35.25 Less than 38.25

Boundaries 6.15 - 7.05 7.05 - 7.95 7.95 - 8.85 8.85 - 9.75 9.75 - 10.65 10.65 - 11.55 11.55 - 12.45

28.

Class 0 1 2 3 4 5 6 7 8 9

f 1 7 9 7 8 4 4 40

cf 0 4 10 28 36 42 49 50

f 1 4 5 7 4 4 3 3 5 5

No. Zero appears only once and 3 appears 7 times.

cf 0 1 8 17 24 32 36 40

EXERCISE SET 2-2 1. frequency

Less than 6.15 Less than 7.05 Less than 7.95 Less than 8.85 Less than 9.75 Less than 10.65 Less than 11.55 Less than 12.45

f 4 6 18 8 6 7 1 50

27. The percents add up to 101%. They should total 100% unless rounding was used.

25.

H œ 12.3 L œ 6.2 Range œ 12.3  6.2 œ 6.1 Width œ 6.1 ƒ 7 œ 0.87 round up to 0.9 Limits 6.2 - 7.0 7.1 - 7.9 8.0 - 8.8 8.9 - 9.7 9.8 - 10.6 10.7 - 11.5 11.6 - 12.4

Boundaries 17.25 - 20.25 20.25 - 23.25 23.25 - 26.25 26.25 - 29.25 29.25 - 32.25 32.25 - 35.25 35.25 - 38.25

50 40 30 20 10 0 89.598.5

26.

H œ 37.9 L œ 17.3 Range œ 37.9  17.3 œ 20.6

98.5107.5

107.5116.5 I.Q.

10

116.5125.5

125.5134.5

Chapter 2 - Frequency Distributions and Graphs

frequency

1. continued

2. continued

60

20

40

15

20

f 10

0 85

94

103

112

121

130

5

139

0

I.Q.

0.5-25.5 25.5-50.5 50.5-75.5

75.5100.5

100.5125.5

125.5150.5

150.5200.5

200.5225.5

cumulative frequency

Number of bears

120 100 80 60 40 20 0 89.5

20 15 98.5

107.5

116.5

125.5

134.5

f 10

I.Q.

5

Eighty applicants do not need to enroll in the summer programs.

0 13

38

63

88

113 138 163 188 213 238

Number of bears

2.

Limits 1 - 25 26 - 50 51 - 75 76 - 100 101 - 125 126 - 150 151 - 175 176 - 200 201 - 225 226 - 250

Boundaries 0.5 - 25.5 25.5 - 50.5 50.5 - 75.5 75.5 - 100.5 100.5 - 125.5 125.5 - 150.5 150.5 - 175.5 175.5 - 200.5 200.5 - 225.5 225.5 - 250.5

Less than 0.5 Less than 25.5 Less than 50.5 Less than 75.5 Less than 100.5 Less than 125.5 Less than 150.5 Less than 175.5 Less than 200.5 Less than 225.5 Less than 250.5

\7 13 38 63 88 113 138 163 188 213 238

f 18 12 7 6 2 3 0 2 0 2 52

60 50 40 cf 30 20 10 0 0.5 25.5 50.5 75.5 101 126 151 176 201 226 251 Number of bears

Thirty-seven counties had 75 or fewer bears killed.

cf 0 18 30 37 43 45 48 48 50 50 52

3.

Limits 3 - 45 46 - 88 89 - 131 132 - 174 175 - 217 218 - 260

Boundaries 2.5 - 45.5 45.5 - 88.5 88.5 - 131.5 131.5 - 174.5 174.5 - 217.5 217.5 - 260.5

Less than 2.5 Less than 45.5 Less than 88.5 Less than 131.5 Less than 174.5 Less than 217.5 Less than 260.5

11

cf 0 19 38 48 49 49 50

\7 24 67 110 153 196 239

f 19 19 10 1 0 1 50

225.5250.5

Chapter 2 - Frequency Distributions and Graphs 3. continued

4. continued

20

10 8

frequency

15

6

10

4 2

5

0

0

69.5-116.5 116.5-163.5 163.5-210.5 210.5-257.5 257.5-304.5 304.5-351.5 351.5-398.5 2.5-45.5

45.5-88.5

88.5-131.5 131.5-174.5 174.5-217.5 217.5-260.5

Number of faculty

Counties, parishes, or divisions

The distribution is positively skewed.

10

frequency

8

frequency

20 15

6 4 2

10

0

5

93

140

187

24

67

110

153

196

281

328

375

239

cumulative frequency

Counties, parishes, or divisions

cumulative frequency

234

Number of faculty

0

60 50 40 30 20 10

30 25 20 15 10 5 0 69.5

116.5

163.5

0

210.5

257.5

304.5

351.5

398.5

Number of faculty 2.5

45.5

88.5

131.5

174.5

217.5

260.5

Counties, parishes, or divisions

"# #)

Ĺ“ 0.429 or 42.9% have 180 or more.

The histogram and frequency polygon are positively skewed.

4.

Limits 70 - 116 117 - 163 164 - 210 211 - 257 258 - 304 305 - 351 352 - 398

Boundaries 69.5 - 116.5 116.5 - 163.5 163.5 - 210.5 210.5 - 257.5 257.5 - 304.5 304.5 - 351.5 351.5 - 398.5

Less than 69.5 Less than 116.5 Less than 163.5 Less than 210.5 Less than 257.5 Less than 304.5 Less than 351.5 Less than 398.5

\7 93 140 187 234 281 328 375

f 5 9 6 6 0 1 1 28

5.

Limits 1 - 43 44 - 86 87 - 129 130 - 172 173 - 215 216 - 258 259 - 301 302 - 344

cf 0 5 14 20 26 26 27 28

Boundaries 0.5 - 43.5 43.5 - 86.5 86.5 - 129.5 129.5 - 172.5 172.5 - 215.5 215.5 - 258.5 258.5 - 301.5 301.5 - 344.5

Less than 0.5 Less than 43.5 Less than 86.5 Less than 129.5 Less than 172.5 Less than 215.5 Less than 258.5 Less than 301.5 Less than 344.5

12

cf 0 24 41 44 48 49 49 49 50

\7 22 65 108 151 194 237 280 323

f 24 17 3 4 1 0 0 1 50

Chapter 2 - Frequency Distributions and Graphs 5. continued The distribution is positively skewed.

6. continued The distribution is left skewed or negatively skewed.

30 25

7.

Limits 21 - 29 30 - 38 39 - 47 48 - 56 57 - 65 66 - 74 75 - 83

Frequency

20 15 10 5 0 0.5-43.5

43.5-86.5

86.5-129.5

129.5-172.5 172.5-215.5 215.5-258.5 258.5-301.5 301.5-344.5

Accidents

30 Frequency

25 20 15

Boundaries \7 20.5 - 29.5 25 29.5 - 38.5 34 38.5 - 47.5 43 47.5 - 56.5 52 56.5 - 65.5 61 65.5 - 74.5 70 74.5 - 83.5 79

10 5

f 5 10 13 10 4 3 1 46

0 22

65

108

151

194

237 280

323

Cumulative Frequency

Accide nts

60 50 40 30 20 10 0 0.5

43.5

86.5

cf 0 5 15 28 38 42 45 46

Less than 20.5 Less than 29.5 Less than 38.5 Less than 47.5 Less than 56.5 Less than 65.5 Less than 74.5 Less than 83.5

129.5 172.5 215.5 258.5 301.5 344.5 Accide nts

14 12

6.

10 14

f

frequency

12

8 6

10

4

8

2

6

0 20.5-29.5 29.5-38.5 38.5-47.5 47.5-56.5 56.5-65.5 65.5-74.5 74.5-83.5

4 2

Points

0 39.85-42.85

42.85-45.85

45.85-48.85

48.85-51.85

51.85-54.85

54.85-57.85

M illions of Dolla rs

14 12 10 8 f 6 4 2 0

14 12 frequency

10 8 6

25

4

34

43

52

61

70

79

Points

2 0 38.35

41.35

44.35

47.35

50.35

53.35

56.35

59.35

Millions of Dollars

60

cumulative frequency

50 35

40

30

cf 30

25

20

20

10

15

0

10

20.5

5

29.5

38.5

47.5

56.5

Points

0 38.85

42.85

45.85

48.85

51.85

54.85

57.85

Millions of Dollars

13

65.5

74.5

83.5

Chapter 2 - Frequency Distributions and Graphs 8.

9. continued With minor differences, the histograms are fairly similar.

15

10.

10

20

5 frequency

Frequency

20

0 5.5-8.5

8.5-11.5 11.5-14.5 14.5-17.5 17.5-20.5 20.5-23.5 23.5-26.5

Costs of utilities

15 10 5 0 17.5 22.5

27.5 32.5

32.5 37.5

37.5 42.5

42.5 47.5

% At or Above Reading Level

15 10

20

5

frequency

Frequency

20

22.5 27.5

0 7

10

13

16

19

22

25

Costs of utilities

15 10 5

Cumulative frequency

0 17.5 22.5

35 30 25 20 15 10 5 0

27.5 32.5

8.5

11.5

14.5

17.5

20.5

23.5

37.5 42.5

42.5 47.5

The distribution of math percentages is more bell-shaped than the distribution of reading percentages, and its peak in the class of 32.5 ď‚ 37.5 is not as high as the peak of the reading percentages.

26.5

Cos ts of utilitie s

The distribution is positively skewed.

9.

Boundaries 9.5 - 14.5 14.5 - 19.5 19.5 - 24.5 24.5 - 29.5 29.5 - 34.5 24.5 - 39.5 39.5 - 44.5 44.5 - 49.5

f (now) 6 4 3 2 5 1 2 1 24

11.

Limits 60 - 64 65 - 69 70 - 74 75 - 79 80 - 84 85 - 89 90 - 94 95 - 99

f(5 years ago) 5 4 2 3 6 2 1 1 24

8

Boundaries \7 59.5 - 64.5 62 64.5 - 69.5 67 69.5 - 74.5 72 74.5 - 79.5 77 79.5 - 84.5 82 84.5 - 89.5 87 89.5 - 94.5 92 94.5 - 99.5 97

6 f4 2 0 9.5-14.5

32.5 37.5

% At or Above Math Level

5.5

Limits 10 - 14 15 - 19 20 - 24 25 - 29 30 - 34 35 - 39 40 - 44 45 - 49 Total

22.5 27.5

14.519.5

19.524.5

24.529.5

29.534.5

34.539.5

39.544.5

Less than 59.5 Less than 64.5 Less than 69.5 Less than 74.5 Less than 79.5 Less than 84.5 Less than 89.5 Less than 94.5 Less than 99.5

44.549.5

Sulfur Dioxide (now)

7 6 5 4 f 3 2 1 0 9.5-14.5 14.5-19.5 19.5-24.5 24.5-29.5 29.5-34.5 34.5-39.5 39.5-44.5 44.5-49.5 Sulfur Dioxide (5 years ago)

14

cf 0 2 3 8 20 38 44 49 50

f 2 1 5 12 18 6 5 1 50

Chapter 2 - Frequency Distributions and Graphs 11. continued

12. continued

20

60

15

50

f 10

40

5

cf 30

0 59.5-64.5 64.5-69.5 69.5-74.5 74.5-79.5 79.5-84.5 84.5-89.5 89.5-94.5 94.5-99.5

20

Blood Glucose Levels

10 0 10.5

15.5

20.5

20

25.5

30.5

35.5

40.5

45.5

Waiting Times

15

Ten patients waited longer than 30 minutes.

f 10 5

13.

62

67

72

77

82

87

92

relative frequency

0 97

Blood Glucose Levels

0.4 0.3 0.2 0.1 0 89.598.5

60

98.5107.5

107.5116.5

116.5125.5

125.5134.5

I. Q.

50 40 relative frequency

cf 30 20

10 0 59.5

64.5

69.5

74.5

79.5

84.5

89.5

94.5

99.5

Blood Glucose Levels

0.4 0.3 0.2 0.1 0 85

94

103

112

121

130

139

I. Q.

cumulative relative frequency

12.

20 15 f 10 5

1 0.8 0.6 0.4 0.2 0 89.5

98.5

107.5

0

116.5

125.5

134.5

I. Q.

10.515.5

15.520.5

20.525.5

25.530.5

30.535.5

35.540.5

40.545.5

The proportion of applicants who need to enroll in a summer program is 0.26 or 26%.

Waiting Times

14.

Boundaries 0.5 - 25.5 25.5 - 50.5 50.5 - 75.5 75.5 - 100.5 100.5 - 125.5 125.5 - 150.5 150.5 - 175.5 175.5 - 200.5 200.5 - 225.5 225.5 - 250.5

20 15 f 10 5 0 13

18

23

28

33

38

43

Waiting Times

15

\7 13 38 63 88 113 138 163 188 213 238

rf 0.35 0.23 0.13 0.12 0.04 0.06 0.00 0.04 0.00 0.04 1.01

Chapter 2 - Frequency Distributions and Graphs 14. continued

15.

Boundaries 0.5 - 43.5 43.5 - 86.5 86.5 - 129.5 129.5 - 172.5 172.5 - 215.5 215.5 - 258.5 258.5 - 301.5 301.5 - 344.5

crf Less than 0.5 0 Less than 25.5 0.35 Less than 50.5 0.58 Less than 75.5 0.71 Less than 100.5 0.83 Less than 125.5 0.87 Less than 150.5 0.93 Less than 175.5 0.93 Less than 200.5 0.97 Less than 225.5 0.97 Less than 250.5 1.01 (differences in totals are due to rounding)

\7 22 65 108 151 194 237 280 323

crf 0 0.48 0.82 0.88 0.96 0.98 0.98 0.98 1.00

Less than 0.5 Less than 43.5 Less than 86.5 Less than 129.5 Less than 172.5 Less than 215.5 Less than 258.5 Less than 301.5 Less than 344.5

0.4 0.3 rf 0.2 0.1 0 0.5- 25.5- 50.5- 75.5- 100.5- 125.5- 150.5- 175.5- 200.5- 225.525.5 50.5 75.5 100.5 125.5 150.5 175.5 200.5 225.5 250.5 Bear Kills

rf 0.48 0.34 0.06 0.08 0.02 0.00 0.00 0.02 1.00

0.6 0.5 0.4 rf 0.3 0.2 0.1 0

0.4 0.3 rf 0.2 0.1 0 13

38

63

88 113 138 163 188 213 238

0.543.5

Bear Kills

43.5- 86.5- 129.5- 172.5- 215.5- 258.5- 301.586.5 129.5 172.5 215.5 258.5 301.5 344.5 Number of accidents

1.2

0.6

1

0.5

0.8

0.4

crf 0.6

rf 0.3

0.4

0.2

0.2

0.1 0

0

22

0.5 25.5 50.5 75.5 100.5 125.5 150.5 175.5 200.5 225.5 250.5

65

108 151 194 237 280 323 Number of accidents

Bear Kills

16

Chapter 2 - Frequency Distributions and Graphs 15. continued

17.

Boundaries 79.5 - 108.5 108.5 - 137.5 137.5 - 166.5 166.5 - 195.5 195.5 - 224.5 224.5 - 253.5 253.5 - 282.5

1.2 1 0.8 crf 0.6 0.4 0.2 0 0.5 43.5 86.5 129.5 172.5 215.5 258.5 301.5 344.5

\7 94 123 152 181 210 239 268

Number of accidents

rf 0.17 0.28 0.04 0.20 0.22 0.04 0.04 0.99*

*due to rounding 16.

Boundaries 39.85 - 42.85 42.85 - 45.85 45.85 - 48.85 48.85 - 51.85 51.85 - 54.85 54.85 - 57.85

\7 41.35 44.35 47.35 50.35 53.35 56.35

rf 0.06 0.06 0.16 0.16 0.39 0.16 0.99 (difference is due to rounding) crf Less than 39.85 0 Less than 42.85 0.13 Less than 45.85 0.13 Less than 48.85 0.29 Less than 51.85 0.45 Less than 54.85 0.84 Less than 57.85 1.00

relative frequency

0.3 0.25 0.2 0.15 0.1 0.05 0 79.5-108.5 108.5-137.5 137.5-166.5 166.5-195.5 195.5-224.5 224.5-253.5 153.5- 282.5 C alor ie s

0.3 relative frequency

0.5

rf

0.4 0.3 0.2 0.1 0 39.8542.85

42.8545.85

45.8548.85

48.8551.85

51.8554.85

crf 0.00 0.17 0.45 0.49 0.69 0.91 0.95 0.99

Less than 79.5 Less than 108.5 Less than 137.5 Less than 166.5 Less than 195.5 Less than 224.5 Less than 253.5 Less than 282.5

0.25 0.2 0.15 0.1 0.05 0

54.8557.85

65

94

123

152

181

210

239

268

297

Calo r ie s

cumulative relative frequency

Salaries

0.5 0.4 0.3 rf 0.2 0.1 0

1.2 1 0.8 0.6 0.4 0.2 0 79.5

108.5

137.5

166.5

195.5

Calor ie s

41.35

44.35

47.35

50.35

53.35

56.35

Salaries

The histogram has two peaks.

1.2 1 0.8 crf 0.6 0.4 0.2 0 39.85

42.85

45.85

48.85

51.85

54.85

57.85

Salaries

17

224.5

253.5

282.5

Chapter 2 - Frequency Distributions and Graphs 18.

Boundaries 11.5 - 19.5 19.5 - 27.5 27.5 - 35.5 35.5 - 43.5 43.5 - 51.5 51.5 - 59.5

\7 15.5 23.5 31.5 39.5 47.5 55.5

crf 0.000 0.175 0.600 0.850 0.950 0.975 1.000

Less than 11.5 Less than 19.5 Less than 27.5 Less than 35.5 Less than 43.5 Less than 51.5 Less than 59.5

Boundaries 21.5 - 24.5 24.5 - 27.5 27.5 - 30.5 30.5 - 33.5 33.5 - 36.5 36.5 - 39.5 39.5 - 42.5

0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0

Xm 23 26 29 32 35 38 41

f 1 3 0 6 5 3 2 20

cf 0 1 4 4 10 15 18 20

Less than 21.5 Less than 24.5 Less than 27.5 Less than 30.5 Less than 33.5 Less than 36.5 Less than 39.5 Less than 42.5 8

11.5-19.5

19.5-27.5

27.5-35.5

35.5-43.5

43.5-51.5

fr e q ue n cy

relative frequency

19.

Limits 22 - 24 25 - 27 28 - 30 31 - 33 34 - 36 37 - 39 40 - 42

rf 0.175 0.425 0.25 0.10 0.025 0.025 1.000

51.5-59.5

6 4 2 0

Gram s

23

26

29

32

35

38

41

Seconds

0.35 0.3 0.25 0.2 0.15 0.1

fr e que ncy

relative frequency

0.45 0.4

0.05 0 7.5

15.5

23.5

31.5

39.5

47.5

55.5

63.5

Gram s

25 20 15 10 5 0 21.5 24.5 27.5 30.5 33.5 36.5 39.5 42.5 Seconds

cumulative relative frequency

1.2 1

20. a. 0 b. 14 c. 10 d. 16

0.8 0.6 0.4 0.2 0 11.5

19.5

27.5

35.5

43.5

51.5

59.5

Grams

The histogram is positively skewed.

18

Chapter 2 - Frequency Distributions and Graphs 21.

Boundaries 468.5 - 495.5 495.5 - 522.5 522.5 - 549.5 549.5 - 576.5 576.5 - 603.5 603.5 - 630.5

1. continued \7 482 509 536 563 590 617

f 6 15 10 7 6 6 50

200 150 100 50 0 Dogs

Fish

Other

Pets

f 0 6 21 31 38 44 50

Less than 468.5 Less than 495.5 Less than 522.5 Less than 549.5 Less than 576.5 Less than 603.5 Less than 630.5

Cats

Other Fish Pets Cats Dogs 0

50

100

150

200

20 15

2.

f 10

Wendy's KFC Pizza Hut Burger King Subway

5 0 468.5-495.5 495.5-522.5 522.5-549.5 549.5-576.5 576.5-603.5 603.5-630.5 Average Mathematics Score

f $8.7 14.2 9.3 12.7 10.0 Sales of Fast Foods

20 Subway

15 Pizza Hut

f 10

Wendy's

5

0

0 482

509

536

563

590

2

4

6

8

10

12

14

Dollars (billions)

617

Average Mathematics Score

Dollars (billions)

15

EXERCISE SET 2-3 1.

Dogs Cats Fish Other

10 5 0

f 78 86 160 53

KFC

Burger King

Subway

Pizza Hut

Sales of Fast Foods

19

Wendy's

16

Chapter 2 - Frequency Distributions and Graphs 7.

Calories burned per minute

3.

16 14 12 10 8 6 4 2 0 Running

Skiing

Tennis

Golfing

Bicycling

$70.00 $60.00 $50.00 $40.00 Dollars $30.00 $20.00 $10.00 $0.00

Walking

2005

2007

2009

2011

2012

Year

4.

There was a considerable increase between 2005 and 2007, then small increases after 2007.

700 600 Number

500 400

8.

300 200

$140

100

$120

0 North America

Europe

Asia

South America

Australia

Africa

$100 $80 Amount

$60 $40

5.

$20 $0

$150.00

2007

2008

2009

2010

2011

2012

Year

$100.00 Billions $50.00

There was an increase in spending between 2007 and 2008 followed by a decrease in spending between 2008 and 2009. Spending showed slight increases in 2010, 2011, and 2012.

$0.00 2010

2011

2012

2013

2014

2015

Year

There is a steady increase over the years.

9.

6.

1,500,000

Grading of Schools

1,450,000

D 5%

1,400,000 1,350,000 Number 1,300,000

C 15%

1,250,000 1,200,000

F 1% A 35%

1,150,000 1,100,000

B 44%

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 Year

Crime decreased between 2001 and 2004, increased between 2004 and 2006, then decreased steadily from 2007 to 2010.

More people graded their child's school as B than any other grade. Very few people graded the schools as D or F.

20

Chapter 2 - Frequency Distributions and Graphs 10.

13.

Personal Business Visit friends or family Work-related Leisure

146 330 225 299 1000

14.6% 33.0% 22.5% 29.9% 100%

52.56° 118.8° 81.0° 107.64° 360° ì 21

Per s ona l L eis u r e

14 .6 %

ì ì ì ì ì 23

ì ì ì 22

ì ì ì ì ì ì ì ì 25

ì ì ì ì ì ì ì 24

ì ì ì ì ì 26

ì ì ì 27

ì ì ì ì 28

ì ì ì ì ì 30

ì ì ì 29

31

ì 32

ì ì 33

ì ì ì ì 34

ì 35

17

ì 18

29 .9 %

The dotplot is somewhat positively skewed and shows that the majority of the players are between 21 and 30 years old. There are 2 peaks at 24 years old, with 7 players, and at 25 years old, with 8 players.

V is it 33 .0 %

W ork 2 2.5%

About "3 of the travelers visit friends or relatives, with the fewest travelling for personal business.

14. ì 3

11.

Energy Consumption Renewable 8%

6

ì ì 9

ì 10

11

12

ì ì 14

ì 13

ì 15

16

15. ì ì ì ì ì 72 73 74

Coal 21%

Petroleum 37%

ì ì ì ì 75

ì ì ì ì ì 77

ì 76

ì ì ì ì ì ì ì 78 79 80 81 82 83

ì ì ì ì 84

ì ì 85

ì ì ì ì ì ì ì ì ì 86 87 88 89

ì ì 90

ì 91

ì ì ì ì 29

ì ì 30

The data peaks at age 77 and gaps between the ages of 80 and 84. The data clusters between ages 72 to 80 and between ages 84 to 91.

Fossil fuels accounted for 83% of total usage.

12.

White Silver Black Red Gray Blue Other

5

ì ì 8

The number of teacher strikes ranges from 3 strikes to 18 strikes. The data clusters between 7 and 10 strikes and between 13 and 15 strikes.

Natural Gas 25%

Nuclear 9%

4

ì ì ì 7

16.

19% 18% 16% 13% 12% 12% 10%

68.4° 64.8° 57.6° 46.8° 43.2° 43.2° 36.0°

ì ì ì ì ì 11 12 13

ì ì 14

ì 15

16

ì ì ì ì ì ì ì ì ì ì ì ì ì ì ì ì ì 17 18 19 20 21 22

ì ì ì 24

ì 23

ì ì ì ì ì ì ì ì ì ì ì ì 25 26 27

ì 28

ì 31

ì 33

32

The commuting times range from 11 minutes to 33 minutes. The data clusters between 17 and 31 minutes and gaps at 16 and 32 minutes.

Other 10%

Blue 12% Gray 12% Red 13%

Popular Vehicle Colors

17.

5 5 6 6 7

White 19% Silver 18% Black 16%

0 6 0 5 0

0 0 6 6 1 3 6 3

0 7 4

0 7

0 8

1 8

1 1 1 1 8 8 9

2

2

2

2

2 2 4

Most of the players have 50 to 54 home runs. The greatest number of home runs is 73.

21

4

4

4

4

4

4

Chapter 2 - Frequency Distributions and Graphs 18.

23.

10 11 12 13 14 15 16 17 18 19

0 0 !

0 ! ! !

0 0 0

0 0 !

0 !

0 0

0 5 0 0 0 0 0

0

0

0 0 0

0 0 &

0

0

35.0%

0 5

30.0% 25.0%

5

20.0% % 15.0% 10.0%

0

5.0% 0.0% Govt. Admin Nursing Home Prescriptions

19.

South America 2

1

0

0

0

0 0

0

0 1 5 9

0 0 1 2 2 3 3

3 & .1

4 5 2

4 5 5 3 4

6

6

6 6 6

7

8

8

Govt. Admin 10% Nursing Home 6%

Other 24%

Prescriptions 10%

Math 7 6 4

5 3 3

5 2 3

Reading 2 1 2

5 6 7 8

1 1 0 0 0

5 1

6 6

6 7 9 6 6 7

7

7

Drs. and Clinics 20%

Hospital 30%

20.

9 9 9 8 6

Other

9

The majority of the South American rivers are longer than those in Europe.

9

Hospital

Europe #

4

Drs. and Clinics

8

24.

The reading scores are somewhat higher than the math scores.

Patents 120,000 100,000

21. a. Pareto chart b. Pareto chart c. Pie graph d. Pie graph e. Pareto chart f. Time series graph

80,000 60,000 40,000 20,000 0

Japan 22.4%

22. a. Time series graph b. Pie graph c. Pareto chart d. Pie graph e. Time series graph f. Pareto chart

Germany 6.2%

US 53.8%

South Korea 5.8% Taiwan 4.1% Canada 2.4% Italy 0.9%

Israel 0.9%

China 1.3%

The bar graph is better since there are too many categories for the pie graph.

22

United Kingdom 2.1%

Chapter 2 - Frequency Distributions and Graphs 25. The bottle for 2011 is much bigger in area than the bottle for 1988. This causes the eye to see a much bigger difference than the actual difference.

REVIEW EXERCISES - CHAPTER 2 1.

Class Newspaper Television Radio Internet

26.

65 years and over 13.1%

Under 20 years 27.0%

2.

Class Czech Republic Sweden Canada USSR Russia Finland Slovakia Total

20 years and over 59.9%

Yes. The percentages add up to more than 100%. Since the category "20 years and over" also includes the category "65 years and over", subtract 13.1% from 73% to obtain the percentage for "20 years and over".

3.

Class 11 12 13 14 15 16 17 18 19 20 21 22

5000

Number

4000 County 1

2000

County 2

1000 0 2005

2006

2007

2008

2009

2010

2011

Year

There is no way to tell if the crime rate is decreasing by looking at the graph.

less than 10.5 less than 11.5 less than 12.5 less than 13.5 less than 14.5 less than 15.5 less than 16.5 less than 17.5 less than 18.5 less than 19.5 less than 20.5 less than 21.5 less than 22.5

Parking $34

Transportation $65 Flight $440

Phone usage $95

f 7 6 5 4 3 2 1 28

f 1 2 2 2 1 2 4 2 2 1 0 1 20

28.

Meal, $38

Percent 20 32 24 24 100

Percent 25.0 21.4 17.9 14.3 10.7 7.1 3.6 100

Omit the years when no games were held.

27.

3000

f 10 16 12 12 50

Entertainment $139

Hotel stay $323

Note: Other graphs could be drawn to illustrate this data.

23

cf 0 1 3 5 7 8 10 14 16 18 19 19 20

Chapter 2 - Frequency Distributions and Graphs 4.

Limits Boundaries f 8 7.5 - 8.5 11 9 8.5 - 9.5 10 10 9.5 - 10.5 4 11 10.5 - 11.5 2 12 11.5 - 12.5 2 13 12.5 - 13.5 4 14 13.5 - 14.5 2 15 14.5 - 15.5 1 36

less than 7.5 less than 8.5 less than 9.5 less than 10.5 less than 11.5 less than 12.5 less than 13.5 less than 14.5 less than 15.5 5.

Limits 15 - 19 20 - 24 25 - 29 30 - 34 35 - 39

6. continued Less than 50.5 Less than 59.5 Less than 68.5 Less than 77.5 Less than 86.5 Less than 95.5 Less than 104.5 7.

Limits 15 - 19 20 - 24 25 - 29 30 - 34 35 - 39

cf 0 11 21 25 27 29 33 35 36

Less than 14.5 Less than 19.5 Less than 24.5 Less than 29.5 Less than 34.5 Less than 39.5

Limits 51 - 59 60 - 68 69 - 77 78 - 86 87 - 95 96 - 104

cf 0 3 21 39 47 50

Boundaries 50.5 - 59.5 59.5 - 68.5 68.5 - 77.5 77.5 - 86.5 86.5 - 95.5 95.5 - 104.5

rf 0.06 0.36 0.36 0.16 0.06 1.00

crf 0.00 0.06 0.42 0.78 0.94 1.00

8.

Boundaries 50.5 - 59.5 59.5 - 68.5 68.5 - 77.5 77.5 - 86.5 86.5 - 95.5 95.5 - 104.5

Less than 50.5 Less than 59.5 Less than 68.5 Less than 77.5 Less than 86.5 Less than 95.5 Less than 104.5

6.

Limits 51 - 59 60 - 68 69 - 77 78 - 86 87 - 95 96 - 104

Boundaries 14.5 - 19.5 19.5 - 24.5 24.5 - 29.5 29.5 - 34.5 34.5 - 39.5

Less than 14.5 Less than 19.5 Less than 24.5 Less than 29.5 Less than 34.5 Less than 39.5

Boundaries f 14.5 - 19.5 3 19.5 - 24.5 18 24.5 - 29.5 18 29.5 - 34.5 8 34.5 - 39.5 3 50

cf 0 5 17 28 36 39 41

f 5 12 11 8 3 2 41

24

rf 0.122 0.293 0.268 0.195 0.073 0.049 1.000

crf 0.000 0.122 0.415 0.683 0.878 0.951 1.000

Chapter 2 - Frequency Distributions and Graphs 9.

11.

20

0.4

15

0.3

10

rf 0.2

5

0.1 0

0 14.5-19.5

19.5-24.5

24.5-29.5

29.5-34.5

14.5-19.5

34.5-39.5

19.5-24.5

29.5-34.5

34.5-39.5

0.4

20 frequency

24.5-29.5

Percent complet ing 4 years of college

Percent completing 4 years of college

15

0.3

10

rf 0.2

5

0.1

0 17

22

27

32

0

37

17

Percent completing 4 years of college

22

27

32

37

cumulative frequency

Percent completing 4 years of college 60 40

1.5

20

1

0 14.5

19.5

24.5

29.5

34.5

crf

39.5

0.5

Percent completing 4 years of college

0 14.5

19.5

10.

24.5

29.5

34.5

39.5

Percent completing 4 years of college

15 10

12.

f 5

0.4

0 50.5-59.5

59.5-68.5

68.5-77.5

77.5-86.5

0.3 rf 0.2

86.5-95.5 95.5-104.5

Age

0.1 0 50.5-59.5

59.5-68.5 68.5-77.5

15

77.5-86.5

86.5-95.5 95.5-104.5

Age

10 f 5

0.4 0.3

0 55

64

73

82

91

rf 0.2

100

0.1

Age

0 55

64

73

82

91

100

Age

50 40 30 cf 20 10 0

1.5 crf 50.5

59.5

68.5

77.5

86.5

95.5

1 0.5

104.5

0

Age

50.5

59.5

68.5

77.5 Age

25

86.5

95.5

104.5

Chapter 2 - Frequency Distributions and Graphs 13.

16.

16

100 80 60 Percent 40 20 0

14 12 Cos t in billions

Drink

Talk on cell phone

Eat

Road Range

10 8 6

Smoke

4 2 0 V et Care

Supplies

Grooming

Purchases

Smoke Road Range

17.

Eat Talk on cell phone

800

Drink

600

0

20

40

60

80

Launches 400

100

200

Percent

0 60-69

70-79

80-89

90-99

00-09

Decade

14.

Launches declined steadily from the 1960s through the 1970s and 1980s. Launches increased in the 1990s then decreased in the 2000s.

250 Calories

200 150 100 50

18.

0 Peanuts

Almonds

Macadamia

Pecans

Cashews

12.0% 10.0% 8.0% Perce nt 6.0% 4.0% 2.0% 0.0%

Cashews Pecans Macadamia

2003 2004 2005 2006 2007 2008 2009

Almonds

Year

Peanuts 0

50

100

150

200

The dropout rate increased slightly from 2003 to 2004, then decreased slightly each year until 2008. There was a slight increase in 2009.

250

Calories

15.

19.

300 250

Spending of College Freshmen

200

Shoes 6%

150 100

Clothing 11%

50 0 Websites

Online images

Online games

Online videos

DormItems 27%

26

Electronics 56%

Chapter 2 - Frequency Distributions and Graphs 20.

25.

The graphs are misleading because no scale is used on the B and C axes.

Undecided 8%

26.

The difference between payoffs appears large, but is only 3%. The scale on the C axis may be truncated.

No 26% Yes 66%

CHAPTER 2 QUIZ 21. ì ì ì 26

ì ì 27

ì 28

ì 29

ì ì ì 32 33

ì ì 31

30

34

35

36

37 38

39

40

41 42 43 44

45

46

47

The graph shows almost all but one of the touchdowns per season for Manning's career were between 26 and 33.

22.

ì ì ì 9

ì ì ì ì ì ì ì ì ì 10 11

ì ì ì ì ì ì 12

ì 13

ì ì ì ì ì 15

ì ì ì 14

ì 16

ì ì ì ì 17 18

ì 19

ì ì ì 20

ì ì 21

ì ì 22

The distribution is somewhat positively skewed, and the majority of the CDs (27) had between 9 and 15 songs on them.

23.

2 3 4 5 6 7

9 2 1 1 2 2

9 4 2 3 2 3

5 3 5 2

6 7 8 3

8 7

ì 48 49

1. False 2. False 3. False 4. True 5. True 6. False 7. False 8. c 9. c 10. b 11. b 12. Categorical, ungrouped, grouped 13. 5, 20 14. Categorical 15. Time series 16. Stem and leaf plot 17. Vertical or y 18.

Class H A M C

8

7

f 6 5 6 8 25

cf 6 11 17 25

19.

24.

10 11 12 13 14 15 16 17 18 19 20 21

2 3

8

2

4

8 Condominium 32%

Mobile Home 24%

6 4 2 5 0

6 9

6

9

27

House 24%

Apartment 20%

Chapter 2 - Frequency Distributions and Graphs 20.

Limits Boundaries 1 0.5  1.5 2 1.5  2.5 3 2.5  3.5 4 3.5  4.5 5 4.5  5.5 6 5.5  6.5 7 6.5  7.5 8 7.5  8.5 9 8.5  9.5

22.

Limits 0 - 214 215 - 429 430 - 644 645 - 859 860 - 1074 1075 - 1289 1290 - 1504

f 1 5 3 4 2 6 2 3 4 30

Boundaries -0.5 - 214.5 214.5 - 429.5 429.5 - 644.5 644.5 - 859.5 859.5 - 1074.5 1074.5 - 1289.5 1289.5 - 1504.5

cf 0 20 35 40 45 47 49 51

Less than 0 Less than 214.5 Less than 429.5 Less than 644.5 Less than 859.5 Less than 1074.5 Less than 1289.5 Less than 1504.5

cf 0 1 6 9 13 15 21 23 26 30

less than 0.5 less than 1.5 less than 2.5 less than 3.5 less than 4.5 less than 5.5 less than 6.5 less than 7.5 less than 8.5 less than 9.5

\7 107 322 537 752 967 1182 1397

f 20 15 5 5 2 2 2 51

rf 0.39 0.29 0.10 0.10 0.04 0.04 0.04 1.00

crf 0 0.39 0.68 0.78 0.88 0.92 0.96 1.00

23.

25 20 f

15 10 5 0

21.

0.5-214.5 214.5429.5

429.5644.5

859.5- 1074.5- 1289.51074.5 1289.5 1504.5

Billions of BTU

6 Number

644.5859.5

4 2

25

0

20

1

2

3

4

5

6

7

8

9

15 f

Items Purchased

10 5 0

6 Number

107

322

4

537

752

967

1182

1397

Billions of BTU

2 0 0

1

2

3

4

5

6

7

8

9

10

60 50 40

Items Purchased

Number

cf 30 30 25 20 15 10 5 0 0.5

20 10 0 0

214.5

429.5

644.5

859.5 1074.5 1289.5 1504.5

Billions of BTU

1.5

2.5

3.5

4.5

5.5

6.5

7.5

8.5

9.5

Items Purchased

28

Chapter 2 - Frequency Distributions and Graphs 24.

27.

1 2 3 4 5 6 7 8 9

400 Ton s

300 200 100 0 Paper

Iron/Steel Aluminum

Yard

Glass

Plastics

waste

5 6 1 1 3 2 6 6 8

9 8 5 7 3 3 9 8

8 8 4 7

8

9

8

9

28.

Type of Waste

Plastics Glass Yard Waste

ì ì ì 2

Aluminum Iron/steel Paper 0

100

200

300

25.

Ot her 12 % Phishing 5%

Lo st o r st o len 44%

St o len mail 11%

R et ail p urchases 18 %

26.

Number of deaths

4000 3000 2000 1000 0 2020

2025

2030

ì ì ì 4

ì ì ì ì 5

ì ì ì 6

ì ì ì ì ì 7

ì ì ì ì 8

ì ì ì ì ì 9

ì ì ì 10

ì ì ì ì 11

ì ì 12

ì 13

ì ì 14

29.

The bottles have different areas, so your eyes will compare areas instead of heights.

400

Tons

C o mp ut er hackers 10 %

ì ì ì ì ì ì ì 3

2035

Year

29

ì 15

ì ì 16

ì 17