Elementary statistics a step by step approach 8th edition bluman solutions manual

EXERCISE SET 2-1

1. Frequency distributions are used to organize data in a meaningful way, to facilitate computational procedures for statistics, to make it easier to draw charts and graphs, and to make comparisons among different sets of data.

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.

3.

a. 31.538.535 ßœœß $#$)(! ## 38.531.5œ(

b. 85.5104.595 ßœœß )'"!%"*! ## 104.585.5œ"*

c. 894.5905.5900 ßœœß )*&*!&")!! ## 905.5894.5œ""

d.12.2513.5512.9 ßœœß "#Þ$"$Þ&#&Þ) ## 13.5512.251.3 œ

e. 3.1754.9654.07 ßœœß $Þ")%Þ*')Þ"% ## 4.9653.1751.79 œ

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

5.

a. Class width is not uniform.

b. Class limits overlap, and class width is not uniform.

c. A class has been omitted.

d. Class width is not uniform.

6. 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.

8. continued Width3156.2 or 7 œƒœ

LimitsBoundariesf

21 - 2720.5 - 27.56

28 - 3427.5 - 34.59

35 - 4134.5 - 41.55

42 - 4841.5 - 48.57

49 - 5548.5 - 55.5 30 3

cf

Less than 20.50

Less than 27.56

Less than 34.515

Less than 41.520

Less than 48.527

Less than 55.530

9. H325 L165œœ Range325165160 œœ Width160820 round up to 21 œƒœ

LimitsBoundariesf

165 - 185164.5 - 185.54

186 - 206185.5 - 206.56

207 - 227206.5 - 227.515

228 - 248227.5 - 248.513

249 - 269248.5 - 269.59

270 - 290269.5 - 290.51

291 - 311290.5 - 311.51

312 - 332311.5 - 332.51

A peak occurs in class 207 - 227. There are no empty classes. Each of the three highest classes has one data value.

cf

Less than 164.50

Less than 185.54

Less than 206.510

Less than 227.525

ClassTallyfPercent

7. A 410% M2870% H615% S25% 40100%

8. H52 L21œœ Range522131 œœ

Less than 248.538

Less than 269.547

Less than 290.548

Less than 311.549

Less than 332.550

10. H110 L54œœ Range1105456 œœ Width5678 round up to 9 œƒœ

10. continued

LimitsBoundariesf

54 - 6253.5 - 62.57

63 - 7162.5 - 71.56

72 - 8071.5 - 80.58

81 - 8980.5 - 89.54

90 - 9889.5 - 98.51

99 - 10798.5 - 107.53

108 - 116107.5 - 116.5 30 1

Less than 53.50

Less than 62.57

Less than 71.513

Less than 80.521

Less than 89.525

Less than 98.526

Less than 107.529

Less than 116.530

11. H780 L746œœ

Range78074634 œœ

Width3456.8 round up to 7 œƒœ

LimitsBoundariesf

746 - 752745.5 - 752.54

753 - 759752.5 - 759.56

760 - 766759.5 - 766.58

767 - 773766.5 - 773.59

774 - 780773.5 - 780.5

Less than 745.50

Less than 752.54

Less than 759.510

Less than 766.518

Less than 773.527

Less than 780.530

12. H91,570 L5427œœ

Range91,570542786,143 œœ

Width86,143712,306.1 œƒœ Round up to 12,307

The majority of the data values are in the lowest class. There are no empty classes in the distribution.

Less than 5426.50

Less than 17,733.517

Less than 30,040.518

Less than 42,347.519

Less than 54,654.520

Less than 66,961.521

Less than 79,268.522

Less than 91,575.525

Less than 33.57

Less than 40.521

Less than 47.536

Less than 54.547

Less than 61.550

Less than 68.553

Less than 75.555

14. continued

LimitsBoundariesf

0 - 10-0.5 - 10.57

11 - 2110.5 - 21.56

22 - 3221.5 - 32.52

33 - 4332.5 - 43.50

44 - 5443.5 - 54.5 16 1

cf

Less than -0.50

Less than 10.57

Less than 21.513

Less than 32.515

Less than 43.515

Less than 54.516

15. H635 L6œœ

Width6356629 œœ

Range6295125.8 round up to 127 œƒœ

LimitsBoundariesf

6 - 132 5.5 - 132.516

133 - 259132.5 - 259.53

260 - 386259.5 - 386.50

387 - 513386.5 - 513.50

514 - 640513.5 - 640.5 20 1

The greatest concentration of data values is in the lowest class. All but one of the data values are in the lowest two classes. There is one extremely large data value occurring in the highest class.

cf

Less than 5.50

Less than 132.516

Less than 259.519

Less than 386.519

Less than 513.519

Less than 640.520

16.

Width857140717 œœ

Range717889.6 or 91

16. continued

139.50

Less than 229.511

Less than 321.516

Less than 412.520 Less than 503.524 Less than 594.528

Less than 685.529

Less than 776.529

Less than 867.530

17. H123 L77œœ Range1237746

Less

76.50

83.51

Less than 90.52

Less than 97.58

Less than 104.522

Less than 111.530

Less than 118.531

Less than 125.532

18. H31.5 L7.5œœ

H857 L140œœ

18. continued

7.5 - 12.47.45 - 12.451

12.5 - 17.412.45 - 17.454

17.5 - 22.417.45 - 22.4510

22.5 - 27.422.45 - 27.456

27.5 - 32.427.45 - 32.45 25 4

Less than 7.450

Less than 12.451

Less than 17.455

Less than 22.4515

Less than 27.4521

Less than 32.4525

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

2.

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

Less

Less

163.514

Less than 257.526

Less than 304.526

351.527 Less

42.9% have 180 or more. The histogram and frequency polygon are positively skewed.

Chapter 2 - Frequency Distributions and Graphs

3. LimitsBoundariesf

3 - 45 2.5 - 45.519

46 - 8845.5 - 88.519

89 - 131 88.5 - 131.510

132 - 174131.5 - 174.51

175 - 217174.5 - 217.50

218 - 260217.5 - 260.5 50 1

Less than 2.50

Less than 45.519

Less than 88.538

Less than 131.548

Less than 174.549

Less than 217.549

Less than 260.550

2.5-45.545.5-88.588.5-131.5131.5-174.5174.5-217.5217.5-260.5

parishes, or divisions

The distribution is positively skewed.

The distribution is left skewed or negatively skewed.

5. LimitsBoundariesf

2.545.588.5131.5174.5217.5260.5

Less than 0.50

Less than 43.524

Less than 86.541

Less than 129.544

Less than 172.548

Less than 215.549

Less than 258.549

Less than 301.549

Less than 344.550

The distribution is positively skewed.

Chapter 2 - Frequency Distributions and Graphs

Less than 5.50

Less than 8.512

Less than 11.528

Less than 14.531

Less than 17.532

Less than 20.532

Less than 23.532

Less than 26.533

The distribution is positively skewed.

Chapter 2 - Frequency Distributions and Graphs

Both distributions are positively skewed, but the data are somewhat more spread out in the first three classes in 1998 than in 2003. There are two large data values in the 2003 data.

Less than 83.050

Less than 90.053

Less than 97.058

Less than 104.0514

Less than 111.0521

Less than 118.0524

Less than 125.0525

The data values fall somewhat on the left side of the distribution. The histogram is right skewed. There are no gaps in the histogram.

The distribution of math percentages is more bell-shaped than the distribution of reading percentages, and its peak in the class of 32.537.5 is not as high as the peak of the reading percentages.

11. LimitsBoundariesf

140 - 230139.5 - 229.511

231 - 321230.5 - 321.5 5

322 - 412321.5 - 412.5 4

413 - 503412.5 - 503.5 4

504 - 594503.5 - 594.5 4

595 - 685594.5 - 685.5 1

686 - 776685.5 - 776.5 0

777 - 867776.5 - 867.5 30 1

Less than 139.50

Less than 229.511

Less than 321.516

Less than 412.520

Less than 503.524

Less than 594.528

Less than 685.529

Less than 776.529

Less than 867.530

The distribution is positively skewed.

The histogram shows that state gasoline taxes are somewhat normal with the peak in the middle of the graph.

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

14. LimitsBoundariesrf 1 - 43 0.5 - 43.50.48

44 - 86 43.5 - 86.50.34 87 - 129 86.5 - 129.50.06

130 - 172129.5 - 172.50.08

173 - 215172.5 - 215.50.02

216 - 258215.5 - 258.50

259 - 301258.5 - 301.50

302 - 344301.5 - 344.50.02

Less than 0.50

Less than 43.50.48

Less than 86.50.82

Less than 129.50.88

Less than 172.50.96

Less than 215.50.98

Less than 258.50.98

Less than 301.50.98

Less than 344.51.00

Of the states 82% have fewer than 87 accidents per year.

15. H270 L80œœ Range27080190

Width190727.1 or 28

*due

Less than 79.50.00

Less than 108.50.17

Less than 137.50.45

Less than 166.50.49

Less than 195.50.69

Less than 224.50.91

Less than 253.50.95

Less than 282.50.99

Chapter 2 - Frequency Distributions and Graphs

The histogram has two peaks.

Less than 19.50.175

Less than 27.50.600

Less than 35.50.850

Less than 43.50.950

Less than 51.50.975

Less than 59.51.000

Less than 27.50.87

Less than 55.50.90

Less than 83.50.90

Less than 111.50.93

Less than 139.50.93

Less than 167.50.96

Less than 195.50.99

Chapter 2 - Frequency Distributions and Graphs

18. continued

Based on the histograms, the older dogs have longer reaction times. Also, the reaction times for older dogs is more variable.

19. LimitsBoundariesXf m

22 - 2421.5 - 24.5231

25 - 2724.5 - 27.5263

28 - 3027.5 - 30.5290

31 - 3330.5 - 33.5326

34 - 3633.5 - 36.5355 37 - 3936.5 - 39.5383

Less than 21.50

Less than 24.51

Less than 27.54

Less than 30.54

Less than 33.510

Less than 36.515

Less than 39.518

Less than 42.520

10.

Personal Business14614.6%52.56° Visit friends or family33033.0%118.8°

Work-related22522.5%81.0° Leisure29929.9%107.64° 1000100%360°

Sales of coffee are increasing.

7.

After a slight increase in 2005, the average temperature has declined somewhat in the following years. 9.

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

11.

The atmospheric concentration of carbon dioxide has been steadily increasing over the years.

12. White19%68.4° Silver18%64.8° Black16%57.6° Red13%46.8°

Gray12% 43.2°

Blue12% 43.2° Other10%36.0°

The pie graph better represents the data since we are looking at parts of a whole.

14.

a. time series graph

b. pie graph

c. Pareto chart

d. pie graph

e. time series graph

f. Pareto chart

15.

The distribution is somewhat symmetric and unimodal. The majority of the Presidents were in their 50's when inaugurated.

16.

17.

The

are similar but variety 2 seems to be more variable than variety 1. 18.

The United States has many more launches than Japan. The number of launches is relatively stable for Japan, while launches varied more for the U. S. The U. S. launches decreased slightly in 1995 and increased after that year.

In 1950, veal production was considerably higher than lamb. By 1970, production was approximately the same for both.

24. The bottle for 2004 is much wider, giving a distorted view of the difference since only the heights of the bottles should be compared.

25. The values on the axis start at 3.5. C Also there are no data values shown for the years 2004 through 2011.

7.

15 - 1914.5 - 19.53

20 - 2419.5 - 24.518

25 - 2924.5 - 29.518

30 - 3429.5 - 34.58

35 - 3934.5 - 39.5 50 3 cf

Less than 14.50

Less than 19.53

Less than 24.521

Less than 29.539

Less than 34.547

8. 0 5 10 15 20

0 5 10 15 20

Chapter 2 - Frequency Distributions and Graphs

The typical value of the franchises is between $169.5 - $188.5 million. All but one of the franchises are valued between $169.5 and $245.5 million.

Less than 50.50.000

Less than 59.50.125

Less than 68.50.425

Less than 77.50.700

Less than 86.50.900

Less than 95.50.950

Less than 104.51.000

Bank failures increased in 2002 from 4 to 11, then dropped until 2008, when they increased to 28. The year 2009 brought an increase to 98.

There has been a steady increase in the amount of gold produced by Columbia over the recent years. 18.

The majority of people surveyed would like to spend the rest of their careers with their present employer.

The distribution of aptitude scores is fairly uniform.

1.

2.

Chapter 2 - Frequency Distributions and Graphs

The distribution is positively skewed with one more than half of the data values in the lowest class.