Final Assignment on Statistics

7/29/2019 Final Assignment on Statistics

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Chapter 1

1. 2 Areas of Statistics

1.1. Descriptive statistics - statistician tries to describe a situation.

- consists of the collection, organization, summarization and

presentation of data

1.2. Inferential statistics - statistician tries to make inferences from samples to populations

- use the data to draw conclusions about the population

2. Probability - the chance of an event occuring

2 Areas where probability is used:

2.1. Various forms of gambling

2.2. Insurance industry

3. Ways statistics can be used in everday life

4. Difference between sample & population

4.1. Sample - is a group of subjects selected from a population

4.2. Population - consists of all subjects that are being studied

5. Why are samples used in statistcs?

- As it is not possible to use the entire population for a statistical data

6. a. Inferential e. Inferential

b. Descriptive f. Inferential

c. Descriptive g. Descriptive

d. Descriptive h. Inferential

7. a. Ratio level f. Ordinal level

b. Ordinal level g. Ratio level

c. Ratio level h. Ratio leveld. Interval level i. Nominal leve

e. Rato level j. Ratio level

8. a. Quantitative e. Quantitative

b. Qualitative f. Quantitative

c. Quantitative g. Quantitative

d. Quantitative

9. a. Discrete e. Discrete

b. Continuous f. Discrete

c. Continuous g. Continuousd. Continuous


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10. Give boundaries of each value:

Boundaries

a. 42.8 miles 42.75 - 42.85

b. 1.6 milliliters 1.55 - 1.65

c. 5.36 ounces 5.355 - 5.365

d. 18 tons 17.5 - 18.5e. 93.8 tons 93.7 - 93.85

f. 40 inches 39.5 - 40.5

11. 4 Basic Sampling Methods

a. Random Sampling - are selected by using chance methods or random numbers

b. Systematic sampling - numbering each subject of the population & then selecting every

Kth subject

c. Stratified sampling - subjects are selected by dividing the population into groups

(called strata), then sampling from each group

d. Cluster sampling - the population is divided into groups called clusters by some meanssuch as geographic area or schools in a large district

12. a. Cluster sampling d. Systematic sampling

b. Systematic sampling e. Stratified sampling

c. Random sampling

13. Examples

1. Religion 1. Grade 1. Temperature 1. Age

2. Political Party 2. Rating Scale 2. Score 2. Height

3. Marital Status 3. Ranking 3. IQ 3. Weight

14. a. Population- Airlines Serving Meals

Sampling method would be Random Sampling.

b. Population - U.S Children

Sampling method would be stratified random sample from each area codes.

c. Population - Car Crashes

Sampling method would be Systematic sampling of every 10 mins.

d. Population - older people with mild to moderate hypertension

Sampling method would be Cluster Sampling.

e. Population - Gifts for moms on mother's daySampling method would be Random Sampling.

15. a.

16. a. This is just a mere observation, there was no manipulated variables.

b. This is just a mere observation, there was no manipulated variables.

c. This is just a mere observation, there was no manipulated variables.

Nominal Ordinal Interval Ratio


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d. This is just a mere observation, there was no manipulated variables.

e. This is just a mere observation, there was no manipulated variables.

f. This is just a mere observation, there was no manipulated variables.

17. a. Experimental

b. Observational

c. Observational

d. Experimental

18. a. Independent -Herb and Placebo

Dependent - numbers of respiratory tract infection.

b. Independent - Running Red Lights

Dependent - Color of Vehicles

c. Independent - hostility of the subject

Dependent - Cholesterol Levels

d. Independent - diets

Dependent - blood pressure.

19. a. The way they use the Herb and Placebo.b. The condition of the traffic.

c. The diet of the subjects.

d. The lifestyle of the subject.

20. The sampling size is too small for the study. Only 20 people were used.

21. Non-conclusive for there was no indication of sampling size and how it was measured.

22. It is meaningless for there was no definition of the said statement.

23. The statement means that the result is not proven to have the same effect on the target population.

24. What's misleading is that there was no statistical data to prove the statement.

25. The statement did not state the population or type of subject whom it had an effect of 74% calories

26. The population and sampling size may not be enough for the claim.

27. The conditions and target population should be stated to define the statement clearly.

28. No, we cannot infer. The statement only defines the risk of violent and criminal behaviour

but does not conclude.

29. The sampling or population may not be the same and that the confounding variables are not conside


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burning capability.

red properly.


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1. True

2. True

3. False. The highest level is the Ratio Scale.

4. True

5. False. Quantitave variable for it has a numerical value6. True

7. False. It's 5.5 6.5.

8. c. Discrete

9. b. 25.55 - 25.65

10. d. stratified sampling

11. a. Nominal

12. c. Observational Study

13. a. Confounding variable

14. Descriptive and inferential

15. prediction and decision making

16. population

17. samples

18. a. saves time and money when the population is large.

b. statistics uses samples not population

c. Samples represents the population

19. a. Random Sampling

b. Stratified Sampling

c. Cluster Sampling

d. Systematic Sampling

20. Quasi-experimental Studies

21. Cluster Method22. a. Descriptive

b. Inferential

c. Descriptive

d. Inferential

e. Descriptive

23. a. Ordinal Level

b. Ratio Level

c. Nominal Level

d. Interval Level

e. Ratio Level

24. a. Continuousb. Discrete

c. Continuous

d. Continuous

e. Discrete

25. a. 47.5 - 48.5 secs

b. 0.555 - 0.565 cm

c. 9.05 - 9.15 quartz

d. 13.65 - 13.75 pounds


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e. 6.5 - 7.5 ft


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Exercise 2.2

1. a. To organize data in a more meaningful and intelligent way.

b. To Summarize Large data.

c. To gain some insights on the collected data.

d. To make ready comparison on data collected.

e. To facilitate computational procedures for measures of average and spreads.

2. Categorical Frequency Distribution - This distribution is for data that can be placed

in specific category, such as nominal or ordinal level.

Grouped Frequency Distribution - is usually ised when the data is too large and it must

be grouped into classes that are more than 1 unit in width.

Cummulative Frequency Distribution - is the frequency distribution wherein the

the distribution is added to form the total frequency.

3. a. 12- 18 : since the range of date is small classes can be divided consisting of single

unit there will be 6 classes ( 12, 13, 14, 15, 16, 17 ,18) . Xm = (12 + 18)/2 = 15 : Width = (18

Class Boundaries 11.5-12.5; 12.5-13.5; 13.5-14.5; 14.5-15.5; 15.5-16.5; 16.5-17.5; 17.5=18.

b. 56 - 74 : 6 Classes 56-58; 59-61; 62-64; 65-67; 68-70; 71-74;

Xm = (56+47)/2 = 65; Width = (74-56)/6 = 3;

Class Boundaries 55.5-58.5; 58.5-61.5; 61.5-64.5; 64.5-67.5; 67.5-70.5; 70.5-74.5;

c. 695-705 : 10 Classes of single unit 695; 696; 697; 698; 699; 700; 701; 702; 703; 704; 705;

Xm = (705 + 695) / 2 = 700; Width = (705-695)/10=1;

Class Boundaries

694.5 695.5

695.5 696.5

696.5 697.5

697.5 698.5698.5 699.5

699.5 700.5

700.5 701.5

701.5 702.5

702.5 703.5

703.5 704.5

704.5 705.5

d. 13.6 14.7

Xm 14.15

No of Classes 11 classes

Width 0.1Classes

13.6 13.55 13.65

13.7 13.65 13.75

13.8 13.75 13.85

13.9 13.85 13.95

14 13.95 14.05

14.1 14.05 14.15

14.2 14.15 14.25

Boundaries


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14.3 14.25 14.35

14.4 14.35 14.45

14.5 14.45 14.55

14.6 14.55 14.65

14.7 14.65 14.75

4. There Should be between 5 to 20 classes to have enough classes though there is no hard rule onumber of classes.

The class width is preferably an odd number to ensure that the midpoint of each class has the s

place value.

5. a. The Width is not uniform at 6. the fourth class 45-49 has only width of 5 and others have 6

b. The classes overlapped to each other such as 9 is present on class 1 and class 2 etc.

c. This has only 4 classes that may not be enough to represent the clear picture of data.

d. The class width is not uniform, some are 4 and some are 6.

6. An open ended frequency distribution is when one either first or last class has indeterminate

boundaries. This is in many situations the very small or very large values of observations falling

in the end-classes are so different to the other observations in the class that there is considera

of information in putting them in one class at the end with a closed class interval. In such situat

the best procedure would be to specify the open end class interval and all the values of the obs

in the class or at least indicate their average value and the range, as this would avoid loss of

relevant information and would allow further calculations on the data.

7. Distribution

A llll 4

M lllll-lllll-lllll-lllll-lllll-lll 28

H lllll-l 6S ll 2

8. Common Herb Heigths (6 classes)

7 36

Xm 21.5


Width 5

7 11 6.5 11.5

12 16 11.5 16.5

17 21 16.5 21.522 26 21.5 26.5

27 31 26.5 31.5

32 36 31.5 36.5

9. Charging Elephant Speeds (5 classes)

19 32

Xm 25.5


Classes Boundaries


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Width 2.6 3

19 21 18.5 21.5

22 24 21.5 24.5

25 27 24.5 27.5

28 30 27.5 30.5

31 33 30.5 33.5

10. Energy Consumption (10 classes)

164 11588

Xm 5876


Width 1142.4 1143

164 1306 163.5 1306.5

1307 2449 1306.5 2449.5

2450 3592 2449.5 3592.5

3593 4735 3592.5 4735.5

4736 5878 4735.5 5878.5

5879 7021 5878.5 7021.5

7022 8164 7021.5 8164.5

8165 9307 8164.5 9307.5

9308 10450 9307.5 10450.5

10451 11593 10450.5 11593.5

11. GRE Scores of Top Ranked Engineering (6 classes)

746 780

Xm 763No of Classes 6 classes

Width 5.666666667 6

746 751 745.5 751.5

752 757 751.5 757.5

758 763 757.5 763.5

764 769 763.5 769.5

770 775 769.5 775.5

776 781 775.5 781.5

12. Unhealthy Days in Cities (7 classes)0 93

Xm 46.5


Width 13.28571429 14

0 13 -0.5 13.5

14 27 13.5 27.5

28 41 27.5 41.5

Classes Boundaries

Classes Boundaries

Classes Boundaries

Classes Boundaries


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42 55 41.5 55.5

56 69 55.5 69.5

70 83 69.5 83.5

84 97 83.5 97.5

13. Age of Signers for Declaration of Independence (7 classes)

27 70Xm 48.5


Width 6.142857143 7

27 33 26.5 33.5

34 40 33.5 40.5

41 47 40.5 47.5

48 54 47.5 54.5

55 61 54.5 61.5

62 68 61.5 68.5

69 75 68.5 75.5

14. Speed Limits and Fatalities (8 classes)

70 4040

Xm 2055


Width 496.25 497

70 567 69.5 567.5568 1065 567.5 1065.5

1066 1563 1065.5 1563.5

1564 2061 1563.5 2061.5

2062 2559 2061.5 2559.5

2560 3057 2559.5 3057.5

3058 3555 3057.5 3555.5

3556 4053 3555.5 4053.5

15. Wealthiest people in the United States (7 classes)

31 90Xm 60.5


Width 8.428571429 9

31 40 30.5 40.5

41 50 40.5 50.5

51 60 50.5 60.5

61 70 60.5 70.5

Classes Boundaries

Classes Boundaries

Classes Boundaries


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71 80 70.5 80.5

81 90 80.5 90.5

91 100 90.5 100.5

Peak age of wealthy people in the US is from 61 to 70 years old, extreme values at 41 t

16. US National Park Acreage (8 classes)

5 775

Xm 390


Width 96.25 97

5 102 4.5 102.5

103 200 102.5 200.5

201 298 200.5 298.5

299 396 298.5 396.5

397 494 396.5 494.5

495 592 494.5 592.5

593 690 592.5 690.5

691 788 690.5 788.5

17. Heights of Alaskan Volcanoes (10 classes)

150 11413

Xm 5781.5No of Classes 10 classes

Width 1126.3 1127

150 1277 149.5 1277.5

1278 2405 1277.5 2405.5

2406 3533 2405.5 3533.5

3534 4661 3533.5 4661.5

4662 5789 4661.5 5789.5

5790 6917 5789.5 6917.5

6918 8045 6917.5 8045.5

8046 9173 8045.5 9173.59174 10301 9173.5 10301.5

10302 11429 10301.5 11429.5

18. Homerun Records (8 classes)

McGwire 306 550

Xm 428

Classes Boundaries

Classes Boundaries


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Width 30.5 31

306 337 305.5 337.5

338 369 337.5 369.5

370 401 369.5 401.5

402 433 401.5 433.5434 465 433.5 465.5

466 497 465.5 497.5

498 529 497.5 529.5

530 561 529.5 561.5

Sosa 340 500

Xm 420


Width 20 20

340 360 339.5 360.5

361 381 360.5 381.5

382 402 381.5 402.5

403 423 402.5 423.5

424 444 423.5 444.5

445 465 444.5 465.5

466 486 465.5 486.5

487 507 486.5 507.5

Classes Boundaries

Classes Boundaries


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-12) / 6 = 1

;

e.


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ame

le loss

ions

rvations

Tally Freq

ll 2

lllll 5

lllllllll 9ll 2

0

l 1


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Tally Freq

ll 2

lllll-lllll-lll 13

lllll-lllll-lll 11

lll 3

l 1

Tally Freq

lllll-lllll-lllll-lllll-lllll 25

lllll-lllll-ll 12

lllll 5

lllll 5

l 1

0

0

l 1

0

l 1

Tally Freq

llll 4

llll 4

lllll-ll 7

lllll-l 6

lllll-l 6

lll 3

Tally Freq

lllll-lllll-llll 14

lllll-llll 9

lllll 5


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l 1

l 1

l 1

ll 2

Tally Freq

lllll-ll 7

lllll-lllll-lll 13

lllll-lllll-lllll 15

lllll-lllll-l 11

lll 3

llll 4

ll 2

Tally Freq

lllll-lllll-llll 14lllll 5

lllll 5

0

0

l 1

0

ll 2

Tally Freq

6

3

9

12


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11

4

0

0 50 class.

Tally Freq

lllll-lllll-lllll-ll 17

lllll-l 6

lllll-l 6

ll 2

ll 2

lll 3

l 1

ll 2

Tally Freq

ll 2

ll 2

lllll- 5

lllll-lll 8

lllll-ll 7

lll 3

lllll-ll 7

lll 3lll 3

ll 2


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Tally Freq

l 1

lllll- 5

lllll-lllll-lllll-lllll- 20

lllll-lllll-lllll-lllll-ll 22lllll-lllll-ll 12

lllll 5

llll 4

l 1

Tally Freq

ll 2

lllll-lllll-lllll-lll 18

lllll-lll 8

lllll-lllll-lllll-llll 19

lllll-lllll-lll 13

ll 2

lll 3

l 1


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Chapter 2-3

1) Do students need summer Development

Exam Scores Frequency

90-98 699-107 22

108-116 43

117-125 28

126-134 9

Histogram :

45

40

35

Frequency 30

25

20

15

10

5

0

89.5 98.5 107.5

Polygon Distribution :

Exam Scores Midpoints Frequency

90-98 94 699-107 103 22

108-116 112 43

117-125 111 28

126-134 130 9

Entra

50

Polygon For Entrance Ex


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Frequency

Ogive Distribution :

Exam Scores Frequency Cumulative

89.5 0 0

98.5 6 6

107.5 22 28

116.5 43 71

125.5 28 99

134.5 9 108

Cummulative

Frequency

2) Length of Employee Service

Class Limits Frequency Class Boundary

1-5 21 0.5

6-10 25 5.5

11-15 15 10.5

Entrance Exam Scores

Entrance Exam Scores

0

5

10

15

20

25

30

35

40

94 103 112

0

20

40

60

80

100

120

89.5 98.5 107.5 116.

Ogive For Entrance Exa


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16-20 0 15.5

21-25 8 20.5

26-30 6 25.5

30.5

Histogram :

30

25

Frequency

20

15

10

5

0

0.5 5.5


Length Midpoints Frequency

1-5 3 21

6-10 8 25

11-15 13 1516-20 18 0

21-25 23 8

26-30 28 6

Frequency

Length of Empl

0

5

10

15

20

25

30

3 8 13

Polygon For L


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Length Frequency Cumulative

0.5 0 0

5.5 21 21

10.5 25 4615.5 15 61

20.5 0 61

25.5 8 69

30.5 6 75

Cummulative

Frequency

3) LPGA Scores Data are Skewed to the left.


202-204 2 201.5

205-207 7 204.5

208-210 16 207.5

211-213 26 210.5

214-216 18 213.5

217-219 4 216.5

219.5

Histogram :

30

25

Frequency

20

Length of

0

10

20

30

40

50

60

70

80

0.5 5.5 10.5

Ogive For Le


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15

10

5

0201.5 204.5


Length Midpoints Frequency

202-204 203 2

205-207 206 7

208-210 209 16

211-213 212 26

214-216 215 18

217-219 218 4

Frequency


Length Length Frequency Cumulative202-204 201.5 0 0

205-207 204.5 2 21

208-210 207.5 7 28

211-213 210.5 16 44

214-216 213.5 26 70

217-219 216.5 18 88

219.5 4 92

LPGA S

0

5

10

15

20

25

30

203 206 209

Polygon For


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Cummulative

Frequency

4) NFL Salaries Data are Skewed to the left.


39.9-42.8 2 39.85

42.9-45.8 2 42.85

45.9-48.8 5 45.85

48.9-51.8 5 48.85

51.9-54.8 12 51.85

54.9-57.8 5 54.85

57.85

Histogram :

Frequency

15

10

5

0

39.85 42.85


LPGA S

0

10

20

30

40

5060

70

80

90

100

201.5 204.5 207.5

Ogive For


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Salaries Midpoints Frequency

39.9-42.8 41.35 2

42.9-45.8 44.35 2

45.9-48.8 47.35 5

48.9-51.8 50.35 5

51.9-54.8 53.35 12

54.9-57.8 56.35 5

Frequency


Frequency Salaries Frequency Cumulative

39.9-42.8 39.85 0 042.9-45.8 42.85 2 2

45.9-48.8 45.85 2 4

48.9-51.8 48.85 5 9

51.9-54.8 51.85 5 14

54.9-57.8 54.85 12 26

57.85 5 31

Cummulative

Frequency

NFL Sal

0

2

4

6

8

10

12

14

41.35 44.35 47.35

Polygon For

5

10

15

20

25

30

35

Ogive For


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5) Automobile Fuel EfficiencyClass Limits Frequency Class Boundary

7.5-12.5 3 7.45

12.5-17.5 5 12.55

17.5-22.5 15 17.55

22.5-27.5 5 22.55

27.5-32.5 2 27.55

32.55

Histogram :

Frequency

15

10

5

0

7.45 12.55


Efficiency Midpoints Frequency

7.5-12.5 10 3

12.5-17.5 15 5

17.5-22.5 20 1522.5-27.5 25 5

27.5-32.5 30 2

NFL Sal

0

39.85 42.85 45.85

14

16

Polygon For


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Frequency


Class Efficiency Frequency Cumulative

7.5-12.5 7.45 0 0

12.5-17.5 12.55 3 3

17.5-22.5 17.55 5 8

22.5-27.5 22.55 15 23

27.5-32.5 27.55 5 28

32.55 2 30

CummulativeFrequency

6) Speed Limits and Fatalities Skewed to the Right.

70 567 69.5 567.5 lllll-lllll-llll

568 1065 567.5 1065.5 lllll

1066 1563 1065.5 1563.5 lllll

1564 2061 1563.5 2061.5

Class Boundaries Frequ

Fuel Effi

Fuel Effi

0

2

4

6

8

10

12

10 15

0

5

10

15

20

25

30

35

7.45 12.55 17.55

Ogive For Fu


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2062 2559 2061.5 2559.5

2560 3057 2559.5 3057.5 l

3058 3555 3057.5 3555.5

3556 4053 3555.5 4053.5 ll

4053.5

Histogram :

16

14

12

Frequency

10

8

6

4

2

69.5 567.5 1065.5


70 567 69.5 567.5 lllll-lllll-llll

568 1065 567.5 1065.5 lllll

1066 1563 1065.5 1563.5 lllll

1564 2061 1563.5 2061.5

2062 2559 2061.5 2559.5

2560 3057 2559.5 3057.5 l

3058 3555 3057.5 3555.5

3556 4053 3555.5 4053.5 ll

4053.5

Frequency

Class Boundaries Frequ

8

10

12

14

16

Polygon For Speed vs Fa


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Class Frequency Cumulative

69.5 14 0

567.5 5 14

1065.5 5 19

1563.5 0 24

2061.5 0 24

2559.5 1 24

3057.5 0 25

3555.5 2 25

4053.5 27

CummulativeFrequency

8) How Quick are Dogs ?

Frequency

2.3 2.9 10 2.25 2.95

3.0 3.6 12 2.95 3.65

3.7 4.3 6 3.65 4.35

4.4 5.0 8 4.35 5.05

Class Limits Class Boundaries

Speed and fatalit

Speed and

0

2

4

6

318.5 816.5 1314.5 1812.5 2310.5

0

5

10

15

20

25

30

69.5 567.5 1065.5

Ogive For


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5.1 5.7 4 5.05 5.75

5.8 6.4 2 5.75 6.45

6.45

Histogram:

14

12

10

Frequency

8

6

4

2

0

2.25 2.95


Midpoints Frequency

2.3 2.9 2.6 103.0 3.6 3.3 12

3.7 4.3 4 6

4.4 5.0 4.7 8

5.1 5.7 5.4 4

5.8 6.4 6.1 2

Frequency

Class Limits

0

2

4

6

8

10

12

14

10 12 6

Polygon For


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Salaries Frequency Cumulative

2.3 2.9 2.25 10 03.0 3.6 2.95 12 10

3.7 4.3 3.65 6 22

4.4 5.0 4.35 8 28

5.1 5.7 5.05 4 36

5.8 6.4 5.75 2 40

6.45 42

Cummulative

Frequency

10) Making the Grade : No substantive Difference on the performance of the students on Reading and

MathFrequency

17.5 22.5 5

22.5 27.5 9

27.5 32.5 11

32.5 37.5 16

37.5 42.5 8

42.5 47.5 1

47.5

Class Limits Class Boundaries

Reaction Tim

Reaction Tim

Class Limits

0

5

10

15

20

25

30

35

40

45

2.25 2.95 3.65

Ogive For R


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16

14

12

Math Frequency

10

8

6

4

2

0

17.5 22.5 27.5 32.5

Percentage of Schools


Midpoints Frequency

17.5 22.5 20 5

22.5 27.5 25 9

27.5 32.5 30 11

32.5 37.5 35 1637.5 42.5 40 8

42.5 47.5 45 1

Frequency

Class Limits

0

2

4

6

8

10

12

14

16

18

20 25

Polyg


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17.5 22.5 5 0

22.5 27.5 9 5

27.5 32.5 11 14

32.5 37.5 16 2537.5 42.5 8 41

42.5 47.5 1 49

47.5 50

Cummulative

Frequency

12) Home Run Record Breakers

McGwire 306 550

Xm 428


Width 30.5 31

Classes Boundaries

306 337 305.5 337.5

338 369 337.5 369.5370 401 369.5 401.5

402 433 401.5 433.5

434 465 433.5 465.5

466 497 465.5 497.5

498 529 497.5 529.5

530 561 529.5 561.5

561.5

Class Limits

0

10

20

30

40

50

60

17.5 22.5

Og


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Sosa 340 500

Xm 420


Width 20 20

Classes Boundaries

340 360 339.5 360.5

361 381 360.5 381.5382 402 381.5 402.5

403 423 402.5 423.5

424 444 423.5 444.5

445 465 444.5 465.5

466 486 465.5 486.5

487 507 486.5 507.5

507.5

24

22

20

18

McGwire

Frequency 16

14

12

10

8

6

4

2

0 305.5 337.5 369.5 401.5

Distance



37/131

Midpoints Frequency

17.5 22.5 20 5

22.5 27.5 25 9

27.5 32.5 30 11

32.5 37.5 35 16

37.5 42.5 40 8

42.5 47.5 45 1

Frequency



17.5 22.5 5 022.5 27.5 9 5

27.5 32.5 11 14

32.5 37.5 16 25

37.5 42.5 8 41

42.5 47.5 1 49

47.5 50

Cummulative

Frequency

Class Limits

McG

Class Limits

0

2

4

6

8

10

12

14

16

18

20 25 30

Polygon F

10

20

30

40

50

60

Ogive Fo


38/131

14) Length of Employee ServiceClass Limits Frequency Class Boundary

1-5 21 0.5

6-10 25 5.5

11-15 15 10.5

16-20 0 15.5

21-25 8 20.5

26-30 6 25.5

75 30.5

Histogram :

60%

50%

Frequency

40%

30%

20%

10%

0

0.5 5.5


Length Midpoints

e

Frequency Frequency

1-5 3 28.00% 21

6-10 8 33.33% 2511-15 13 20.00% 15

16-20 18 0.00% 0

21-25 23 10.67% 8

26-30 28 8.00% 6

Relative Freq

28.00%

33.33%

20.00%

0.00%

10.67%

8.00%

McG

0

17.5 22.5 27.5

35.00%

Polygon For L


39/131

Frequency


Length Rel Frequency Cumulative

0.5 0.00% 0

5.5 28.00% 21

10.5 61.33% 46

15.5 81.33% 61

20.5 81.33% 61

25.5 92.00% 69

30.5 100.00% 75

Cummulative

Frequency

16) Protein Grams in Fast Food


12-19.5 7 11.95

19.6-27.1 17 19.55

27.2-34.7 6 27.15

Relative Freq

17.50%

42.50%

15.00%

Length of Empl

Length of

0.00%

5.00%

10.00%

15.00%

20.00%

25.00%

30.00%

3 8 13

0.00%

20.00%

40.00%

60.00%

80.00%

100.00%

120.00%

0.5 5.5 10.5

Ogive For Le


40/131

34.8-42.3 7 34.75

42.4-49.9 2 42.35

50-57.5 1 49.95

40 57.55

50%

40%

Histogram :

30%

25%

Frequency

20%

15%

10%

5%

0

11.95 19.55


Class Limits MidpointsRel

Frequency Frequency

12-19.5 15.75 17.50% 7

19.6-27.1 23.35 42.50% 17

27.2-34.7 30.95 15.00% 6

34.8-42.3 38.55 17.50% 7

42.4-49.9 46.05 5.00% 2

50-57.5 53.75 2.50% 1

Frequency

5.00%

2.50%

17.50%

5.00%

10.00%

15.00%

20.00%

25.00%

30.00%

35.00%

40.00%45.00%

Polygon For Pro


41/131

Ogive Distribution :Length Rel Frequency Frequency Cumm Freq

11.95 0.00% 0 0

19.55 17.50% 7 7

27.15 60.00% 17 24

34.75 75.00% 6 30

42.35 92.50% 7 37

49.95 97.50% 2 39

57.55 100.00% 1 40

40

Cummulative

Frequency

18) How Quick are Dogs


2.3-2.9 1 2.25

3.0-3.6 3 2.95

3.7-4.3 4 3.654.4-5.0 16 4.35

5.1-5.7 14 5.05

5.8-6.4 4 5.75

42 6.45

Histogram :

60%

38.10%

33.33%

9.52%

Protein in F

Relative Freq

2.38%

7.14%

9.52%

Protein in F

0.00%

15.75 23.35 30.95

0.00%

20.00%

40.00%

60.00%

80.00%

100.00%

120.00%

11.95 19.55 27.15

Ogive For Prot


42/131

50%

Frequency

40%

30%

20%

10%

0

2.25 2.95


Class Limits Midpoints

Rel

Frequency Frequency

2.3-2.9 2.6 2.38% 1

3.0-3.6 3.3 7.14% 3

3.7-4.3 4 9.52% 4

4.4-5.0 4.7 38.10% 16

5.1-5.7 5.4 33.33% 14

5.8-6.4 6.1 9.52% 4

Frequency


Length Rel Frequency Frequency Cumm Freq

2.25 0.00% 0 0

2.95 2.38% 1 1

3.65 9.52% 3 4

How Fast th

0.00%

5.00%

10.00%

15.00%

20.00%

25.00%

30.00%

35.00%

40.00%

2.6 3.3 4

Polygon For how


43/131

4.35 19.05% 4 8

5.05 57.14% 16 24

5.75 90.48% 14 38

6.45 100.00% 4 42

42

Cummulative

Frequency

20) From the result of Exercise 19

a) 0 zero

b) 14 fourteen

c) 10 ten

d) 16 sixteen

How Fast th

0.00%

20.00%

40.00%

60.00%

80.00%

100.00%

120.00%

2.25 2.95 3.65

Ogive For how


44/131

116.5 125.5 134.5

nce Exam Scores

m Scores


45/131

111 130

125.5 134.5

m Scores


46/131

10.5 15.5 20.5 25.5 30.5

Length of Employee Service

oyee Service

18 23 28

ngth of Service


47/131

Service

15.5 20.5 25.5 30.5

gth of Service


48/131

207.5 210.5 213.5 216.5 219.5

LPGA Scores

ores

212 215 218

LPGA Scores


49/131

45.85 48.85 51.85 54.85 57.85

ores

NFL Salaries

210.5 213.5 216.5 219.5

LPGA Scores


50/131

aries

50.35 53.35 56.35

NFL Salaries

NFL Salaries


51/131

17.55 22.55 27.55 32.55

Automobile Fuel Efficiency

aries

48.85 51.85 54.85 57.85

uel Efficiency


52/131

14

5

5

0

ency

iency

iency

20 25 30

22.55 27.55 32.55

l efficiency


53/131

0

1

0

2

1563.5 2061.5 2559.5 3057.5 3555.5 4053.5

Midpoints

14 318.5

5 816.5

5 1314.5

0 1812.5

0 2310.5

1 2808.5

0 3306.5

2 3804.5

ency

Speed and fatalities

talities


54/131

ies

fatalities

2808.5 3306.5 3804.5

1563.5 2061.5 2559.5 3057.5 3555.5 4053.5

Speed and Fatalities


55/131

3.65 4.35 5.05 5.75 6.45

Reaction Time of Dogs

8 4 2

eaction Time


56/131

Math.

Reading

Frequency

7

6

11

16

8

1 20

18

e of Dogs

e of Dogs

4.35 5.05 5.75 6.45

eaction Time


57/131

16

14

12

10Reading

Frequency 8

6

4

2

0

37.5 42.5 47.5 17.5 22.5 27.5 32.5

Percentage of Schools

Polygon Di

17.5

22.5

27.5

32.537.5

42.5

Class

Math Frequency

30 35 40 45

on For Math Frequency


58/131

Ogive Distri

17.5 22.5

22.5 27.5

27.5 32.5

32.5 37.537.5 42.5

42.5 47.5

47.5

Tally Freq

l 1

lllll- 5lllll-lllll-lllll-lllll 20

lllll-lllll-lllll-lllll 22

lllll-lllll-ll 12

lllll 5

llll 4

l 1

Math Frequency

Class Limits

27.5 32.5 37.5 42.5 47.5

ve For Math Frequency


59/131

Tally Freq

ll 2

lllll-lllll-lllll-lll 18lllll-lll 8

lllll-lllll-lllll-llll 19

lllll-lllll-lll 13

ll 2

lll 3

l 1

24

22

20

18

Sosa

Frequency 16

14

12

10

8

6

4

2

433.5 465.5 497.5 529.5 561.5 0 339.5



60/131

17.5 22.5

22.5 27.5

27.5 32.5

32.5 37.5

37.5 42.5

42.5 47.5

Frequency


Salaries

17.5 22.522.5 27.5

27.5 32.5

32.5 37.5

37.5 42.5

42.5 47.5

47.5

Cummulati

Frequency

Class Limits

ire

Class Limits

35 40 45

r McGwire

r McGwire


61/131

10.5 15.5 20.5 25.5 30.5

75

Length of Employee Service

ire

32.5 37.5 42.5 47.5

ngth of Service


62/131

oyee Service

Service

18 23 28

15.5 20.5 25.5 30.5

gth of Service


63/131

27.15 34.75 42.35 49.95 57.55

40

Protein in Fast food

tein in Fast Food


64/131

ast food

ast food

38.55 46.05 53.75

34.75 42.35 49.95 57.55

in for Fast Food


65/131

3.65 4.35 5.05 5.75 6.45

42

Dogs are

How Fast the Dogs are

4.7 5.4 6.1

quick the dogs are


66/131

Dogs are

4.35 5.05 5.75 6.45

uick the dogs are


67/131


68/131


69/131


70/131


71/131


72/131


73/131


74/131


75/131


76/131


77/131


78/131


79/131


80/131

37.5 42.5 47.5

tribution :

Midpoints Frequency

22.5 20 7

27.5 25 6

32.5 30 11

37.5 35 1642.5 40 8

47.5 45 1

Frequency

Limits

Reading Frequency

0

2

4

6

8

10

12

14

16

18

20 25 30 35 40 45

Polygon For Reading Frequency


81/131

ibution :


7 0

6 7

11 13

16 248 40

1 48

49

Cummulative

Frequency

Reading Frequency

0

10

20

30

40

50

60

17.5 22.5 27.5 32.5 37.5 42.5 47.5

Ogive For Reading Frequency


82/131

360.5 381.5 402.5 423.5 444.5 465.5 486.5 507.5

Distance


83/131

Midpoints Frequency

20 7

25 6

30 11

35 16

40 8

45 1

Frequency Cumulative

7 06 7

11 13

16 24

8 40

1 48

49

ve

Sosa

0

2

4

6

8

10

12

14

16

18

20 25 30 35 40 45

Polygon For Sosa

10

20

30

40

50

60

Ogive For Sosa


84/131

Sosa

0

17.5 22.5 27.5 32.5 37.5 42.5 47.5


85/131

Exercis 2.4

1) Federal Prison Population

Offenses % contribution 70.00%

Drug Offenses 60.20%

Violent Offenses 12.60% 60.00%

Property Offenses 8.50%Weapons 8.20% 50.00%

Others 5.60%

Immigration 4.90% 40.00%

Public Order Offfenses

100.00% 30.00%

20.00%

10.00%

0.00%

Most of the money for rehabilitation should be alloted to Drug Offenses as top one offense fol

3) Internet Connections

Location No. of Computers

homes 240 300large companies 148

small companies 102 250

schools 47

government agencies 33 # of 200

Computers

150

100

50

0

homes

5) World Energy Use

Fuel Contribution

Drug

Offenses


86/131

Petroleum 39.80% 40

Coal 23.20%

Dry Natural Gas 22.40% 35

Hydroelectric 7.00%

Nuclear 6.40% 30

Others 1.20%

% Contribution 25

20

15

10

5

0

Petroleum

7) Tobacco Consumption

Year Amount

1996 7.9

1997 9.9

1998 10.5

1999 10.9

2000 11

2001 9.82002 10.1

Consumption increased from 1996 until 2000 and slight decrease in 2001. Generally the Trend

9) Do Voters Vote?

Year % Voters

1964 95.83%

1968 89.65%

1972 79.85%


87/131

1976 77.64%

1980 76.53%

1984 74.63%

1988 72.48%

1992 78.01%

1996 65.97%

2000 67.50%

Generally the number of voters decreased in time..

11) Distribution of Assets

Distribution Percentages

Business / Real Estates 46.90%

Stock/Mutual Funds/ Trusts 31.60%

Principal Residences 7.80%

Pension accounts 6.90%

Liquid Assets 5.00%

Miscellaneous 1.80%

13) Workers Switch Jobs

What to do Percent

Career Change 34.00%

New Job in same industry 29.00%

Start a Business 21.00%

Retire 16.00%

Pe

What to do Co

s


88/131

40.00%

35.00%

% Contribution 30.00%

25.00%

20.00%

15.00%

10.00%

0.00%

Pie Chart would represent the contribution on a certain population while pareto chart would s

Both Chart represent the same data but it will depend on the purpose of processing the data a

determines which chart represents better.

15) Presidents' age in Inauguration

Leading Digit (stem)

Most of the Presidents were inaugurated at the peak of 50-59 age Class. Not much variation

for it involves only 3 age classes.

17) Twenty Days of Plant Growth

Career

Change

New Job in

same

industry

Trailing Digit (leaf)


89/131

The Contribution of both varieties are almost the same having the peak at 50-59 cm. V2 has m

height in cm.V1 basically averages smaller having greater numbers on the 30-39 cm class.

19) Non Stop Flights

21) Meat Production (M lbs)

Year Veal Lamb

1960 1109 769

1970 588 551

1980 400 3181990 327 358

2000 225 234

M lbs

Both Meat Production is decreasing thru time.

Year

0

200

400

600

800

1000

1200

1960 1970 1980 1990 20


90/131

23) Nobel Prizes in Physiology or Medicine

Country # of Prizes

USA 80UK 24

Germany 16

Sweden 8

France 7

Switzerland 6

Denmark 5

Austria 4

Belgium 4

Italy 3

Australia 3

Most Appropriate Graph is the Pareto Chart to show the country with the highest number of a

90

80 80

70

60

50

40

30

24

20

16

10

0

USA UK Germany


91/131

lowed by Violence and Property offenses.

large

companies

small

companiesschools

government

agencies

Violent

Offenses

Property

Offenses Others

Public Order

Offenses

(Immigration)

Public Order

Offenses

(Weapons)


92/131

CoalDry Natural

GasHydroelectric Nuclear Others

is increasing..


93/131

rcentagesBusiness / Real Estates

Stock/Mutual Funds/

Trusts

Principal Residences

Pension accounts

Liquid Assets

Miscellaneous

ntribution on 3 of 10

rveyed

Career Change

New Job in same industry

Start a Business

Retire


94/131

how the highest move contribution.

nd what you would want to show

Start a

BusinessRetire


95/131

ore variation in the

00

Veal

Lamb


96/131

wards and their ranking

8 76 5 4 4 3

Sweden France Switzerland Denmark Austria Belgium Italy


97/131


98/131


99/131


100/131


101/131


102/131

3

Australia


103/131

True or False

1) False

2) False

3) False

4) True

5) True

6) False7) False

Select the Best Answer:

8) C

9) C

10) B

11) B

Complete the Statements

12) Categorical, grouped and ungrouped

13) 5 and 20

14) Categorical

15) Time Series graph

16) Stem and Leaf Plot

17) Vertical or Y-axis

18) Freq

House lllll-l 6

Apartment lllll- 5

Mobile Home lllll-l 6

Condominium lllll-lll 8

19) Pie Chart

Freq Deg % contribution

House 6 86.4 24.00%

Apartment 5 72 20.00%

Mobile Home 6 86.4 24.00%

Condominium 8 115.2 32.00%

25 100.00%


104/131

20) Items Purchased at a convenience store

No of Items Count Frequency Cumm. Freq. Limits

1 l 1 0 0.5

2 lllll 5 1 1.53 lll 3 6 2.5

4 llll 4 9 3.5

5 ll 2 13 4.5

6 lllll-l 6 15 5.5

7 ll 2 21 6.5

8 lll 3 23 7.5

9 llll 4 26 8.5

30 9.5

21) Items Purchased 7

6

5

Frequency

4

3

2

1

0

1 2

1

2

3

4

5

6

7

Frequency Polygon Frequency

5

10

15

20

25

30

35


105/131

22-23) Murders in selected City Data Skewed to the Right.

Max 598

Min 27

Classes 63.4444444 65

Lower Upper Lower Limit Upper Limit Midpoint Frequency

1 27 92 26.5 92.5 59.5 lllll-lllll-lll

2 93 158 92.5 158.5 125.5 ll

3 159 224 158.5 224.5 191.5

4 225 290 224.5 290.5 257.5 lllll-

5 291 356 290.5 356.5 323.5 l

6 357 422 356.5 422.5 389.5 l

7 423 488 422.5 488.5 455.5

8 489 554 488.5 554.5 521.5 l

9 555 620 554.5 620.5 587.5 ll

14

12

10

Frequency

8

6

4

2

026.5 92.5 158.5

Classes

0

1 2 3 4 5 6 7 8 9

0

0

14

Frequency Pol


106/131

24) Recycled Trash Pareto chart

Type Amount (M Tons)

Paper 320

Iron / Steel 292

Aluminum 276

Yard waste 242.4

Glass 196

Plastics 41.6

25) Tresspasser Fatalities

0

2

4

6

8

10

59.5 125.5 191.5 257.

0

5

10

15

20

25

30

26.5 92.5 158.5 2

Ogive f

0

50

100

150

200

250

300

350

Paper Iron / Steel Aluminum

Pareto Chart for Re


107/131

Year No. of Fatalities

1998 536

1999 463

2000 511

2001 540

There is no Trend for no. of Fatalities on Tresspassers .

26) Museum Visitors The no. of visitors for the Museum is widely spread amd varied.

27) Travel and Sales

Miles Travelled Sales (y)

50 25250 175

120 100

300 210

200 150

There is a relationship between no. of miles

travelled and sales. It is Directly Proportional.

420

440

460

480

500

520

540

560

1998 1999

Trend o

100

150

200

250


108/131

0

50

0 50


109/131

House

Apartment

Mobile Home

Condominium


110/131

3 4 5 6 7 8 9

No. of Items

Histogram

Ogive for Items Purchased

Cumm. Freq.


111/131

Count Cummulative Ogive Limit

13 0 26.5

2 13 92.5

0 15 158.5

5 15 224.5

1 20 290.5

1 21 356.5

0 22 422.5

1 22 488.5

2 23 554.5

25 620.5

224.5 290.5 356.5 422.5 488.5 554.5 620.5

.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5

gon for Murders in Selected City


112/131

5 323.5 389.5 455.5 521.5 587.5

Count

24.5 290.5 356.5 422.5 488.5 554.5 620.5

r Murders in selected CityCummulative

ard waste Glass Plastics

cycled trash

Amount (M Tons)


113/131

2000 2001

No. of Fatalities No. of Fatalities

Sales (y) Sales (y)


114/131

100 150 200 250 300 350


115/131

Exercise 3-2

1) 3.8 3.77 3.7 3.74 3.7

3.86 3.76 3.68 3.67 3.57

3.83 3.7 3.8 3.74 3.67

3.78 3.74 3.73 3.65 3.66

3.75 3.64 3.78 3.73 3.64

a) Mean =(sumX/n) =93.09/25 3.724

b) median = 3.73

3.86 3.83 3.8 3.8 3.78 3.78

3.73 3.7 3.7 3.7 3.68 3.67

c) mode Bimodal on 3.74 and 3.70

3.86 3.83 3.8 3.8 3.78 3.78

3.73 3.7 3.7 3.7 3.68 3.67

d) midrange (Highest Value + Lowest value ) / 2

=(3.57 + 3.86) / 2

Midrange 3.715

2) Heights of the Highest waterfall (ft)

3212 1650 2425 2151

1904 2540 1170 1198

2800 1612 1388 1182

1841 2499 1215 2123

2625 1536 2307 2000

a) Mean 1968.9

b) median 1952 in between the values 1904 and 2000 thus

=(2000 + 1904) / 2

3212 2800 2625 2540 2499 24251904 1841 1650 1612 1536 1388

c) mode the data set has no mode

d) midrange 2191


116/131

3) Burglaries at Pennsylvania University

The most appropriate measure of average is the Mean for it varies less than the mode

especially on varied data such as this.

61 3 18 Mean 15.111 2 3

1 30 7

4) Public School suspension

Beaver Butler

67 56

12 12

11 18

92 21

13 There is a significant Difference in the A

Mean 39 26.75

Median 11 15

Mode None None

Midrange 40 38.5

5) Identity theft

574 229 663 372 102

117 239 465 136 189

Mean 270.75

Median 205 The researcher has 10% er

Mode None and 23% error against the

Midrange 369

7) Earthquake Strengths

The Mean, Median and Midrange should be used to measure the most typical case of

7 6.2 7.7 8 6.4 6.27.2 5.4 6.4 6.5 7.2 5.4

The Dataset showed multi-modal case of 7.2, 6.4, 5,4 and 6.2.

Mean = 6.633

Median = 6.7

Midrange = 6.7


117/131

8) Top Paid CEO

47.7 29.1 24.3 20.1 17.5

41.7 28.6 24.1 20 17.4

38.5 26.8 24 19.8 17.337.6 25.9 24 19.7 17.2

36.8 25.5 23.7 19.3 17.2

35.4 25.4 23.2 19.1 17

35.2 25.2 22.9 19.1 16.9

31.7 25.2 21.6 18.2 16.9

31.7 25.1 21.4 18 16.8

31.4 25 20.4 18 16.5

15) Murders in Cities

Class Frequency Midpoint f.Xm

34-96 13 65 845

97-159 2 128 256

160-222 0 191 0

223-285 5 254 1270

286-348 1 317 317

249-411 1 380 380

412-474 0 443 0

475-537 1 506 506

538-600 2 569 113825 4712.0

The Mean doesn't represent the dataset average since the mean represent

the class with no occurrence. The best representative of the average is the Modal sinc

it is the most typical situation to happen which is the 34-96 class. (Mode = 65)

Mean = 188.48

20) Commissions Earned

Frequency Midpoint f.Xm

150 158 5 154 770

159 167 16 163 2608168 176 20 172 3440

177 185 21 181 3801

186 194 20 190 3800

195 203 15 199 2985

204 212 3 208 624

100 18028.0

Mean = 180.28

Class


118/131

Mode= 181 (Class 177-185)

21) Copier Service Calls

Frequency Midpoint f.Xm15.5 18.5 14 17 238

18.5 21.5 12 20 240

21.5 24.5 18 23 414

24.5 27.5 10 26 260

27.5 30.5 15 29 435

30.5 33.5 6 32 192

75 1779

Mean= 23.72

Mode= 23 (Class 21.5-24.5)

27)Fat Grams

Meat or Fish Fat(g/oz) Weight

Fried Shrimp 3 3.33 9.99

Veal cutlet 3 3 9

Roast Beef 2 2.5 5

Fried Chicken 2 4.4 8.8Tuna 4 1.75 7

14 39.79

Average meat or fish a person ate in 5 days = 2.842

28) Diet Cola Preference

Area % Favored Number of Surveyed Weight

1 40 1000 400002 30 3000 90000

3 50 800 40000

120 170000.0

Weighted Mean = 1416.7

29) Costs of Helicopters

Class


119/131

Model Number Sold Cost Weight

Sunscraper 9 427,000 3843000

Skycoaster 6 365,000 2190000

High-flyer 12 725,000 8700000

27 14733000

Weighted Mean of Cost = $545,666.67

30) Final Grade

Grade Weight

20 83 1660

30 72 2160

50 90 4500

100 8320

Final Grade = 83.2

31) Final Grade

Exam Grade Weight

1 62 62

1 83 83

1 97 97

1 90 90

2 82 164

6 496

Final Grade = 82.7

32 ) Situational 33) Situational

a) Mode a) Median

b) Median b) Mean

c) Median c) Mode

d) Median d) Mode

e) Mean e) Mode

f) Median f) Mean

34) Symbols

Greek Symbols Sigma shows summation

Roman Letters such as X and n which shows data value and frequency respectively.

35) Both Could be true if one is basing on the mean and the other is basing on the mode of the

datasets.

Percent of final Grade


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Median

3.77 3.76 3.75 3.74 3.74 3.74 3.73

3.67 3.66 3.65 3.64 3.64 3.57

3.77 3.76 3.75 3.74 3.74 3.74 3.73

3.67 3.66 3.65 3.64 3.64 3.57

2307 2151 2123 20001215 1198 1182 1170


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r median

erage.

88

75

ror on his estimate against the Mean, 30% against the Median

Midrange.

agnitude..


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Mean = 24.422 24.422

Mode= Multi Modal on 31.7, 25.2, 24, 17.2, 18, 19.1 and 16.9.

Midrange= 32.1Median = 23.45

The Midrange shows the best measure for average.


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11) Heights of tall bldgs

n=11

St Paul X-u (x-u)2

32 3.55 12.6025

36 7.55 57.0025

46 17.55 308.0025

20 -8.45 71.402532 3.55 12.6025

18 -10.45 109.2025

16 -12.45 155.0025

34 5.55 30.8025

26 -2.45 6.0025

27 -1.45 2.1025

26 -2.45 6.0025

Mean 28.45 770.7275

Chicago has more variable than St Paul. Std Deviation is at 14.70 vs 8.371 for St. Paul.

Chicago dataset is more variable graphically.

12) Fuel Costs n=7

Cost/gal X-u (x-u)2 (x-u)2/n

3.8 0.168571 0.028416 Std Dev =

3.8 0.168571 0.0284163.2 -0.43143 0.186131

3.57 -0.06143 0.003774

3.62 -0.01143 0.000131

3.74 0.108571 0.011788

3.69 0.058571 0.003431

3.631428571 0.262086

The datasets is a representation of the prices of Fuel in all foreign countries

since its standard deviation is at 0.19 only.

13) HARDCOVER BESTSELLERS

Range Highest-Lowest

Range = 21

The Range Rule of Thumb Showed high variability on the datasets at 21.

n=15


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Data X-u (x-u)2 (x-u)2/n 35.52889

22 16.066667 258.1377885 Std Dev = 5.960611

18 12.066667 145.6044525

10 4.066667 16.53778049

6 0.066667 0.004444489 The dataset has an actual Std Dev

5 -0.933333 0.871110489 Both measure showed with variati

5 -0.933333 0.8711104894 -1.933333 3.737776489

4 -1.933333 3.737776489

3 -2.933333 8.604442489

3 -2.933333 8.604442489

2 -3.933333 15.47110849

2 -3.933333 15.47110849

2 -3.933333 15.47110849

2 -3.933333 15.47110849

1 -4.933333 24.33777449

5.933333333 532.9333333

22) Reaction times

Freq Midpoint F*Xm (f*Xm)2

2.1 2.7 12 2.4 28.8 69.12

2.8 3.4 13 3.1 40.3 124.93

3.5 4.1 7 3.8 26.6 101.08

4.2 4.8 5 4.5 22.5 101.25

4.9 5.5 2 5.2 10.4 54.085.6 6.2 1 5.9 5.9 34.81

40 134.5 485.27

(sum(f*Xm))2 18090.25

n= 40

((sum(f*Xm))2)/n= 452.25625

s2= 0.84650641

s= 0.92005783

23) Lightbulb Lifetimes


52.5 63.5 6 58 348 20184

63.5 74.5 12 69 828 57132

74.5 85.5 25 80 2000 160000

Class

Class


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85.5 96.5 18 91 1638 149058

96.5 107.5 14 102 1428 145656

107.5 118.5 5 113 565 63845

80 6807 595875

(sum(f*Xm))2 46335249n= 80

((sum(f*Xm))2)/n= 579190.6125

s2= 211.1947785

s= 14.53254205

24) Murder Rates


5 11 8 8 64 512

12 18 5 15 75 1125

19 25 7 22 154 3388

26 32 1 29 29 841

33 39 1 36 36 1296

40 46 3 43 129 5547

25 487 12709

(sum(f*Xm))2 237169n= 25

((sum(f*Xm))2)/n= 9486.76

s2= 134.26

s= 11.58706175

Page 170

6) Fuel Capacity


10 12 6 11 66 726

13 15 4 14 56 784

16 18 14 17 238 4046

19 21 15 20 300 6000

22 24 8 23 184 4232

Class

Class


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25 27 2 26 52 1352

28 30 1 29 29 841

50 925 17981

a) Mean Mean = 18.5

(sum(f*Xm))2 855625

n= 50((sum(f*Xm))2)/n= 17112.5

b) Modal Class Class 19-21

c) Variance s2= 17.7244898

d) Std Dev s= 4.210046294

7) Number of Cavities

Number of Students No. of Cavities Weight

12 0 0

8 1 8

5 2 10

5 3 15

30 33

Weighted Mean = 1.1


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(x-u)2/n 70.06614 Chicago X-u (x-u)2 (x-u)2/n 216.2314

Std Dev = 8.370552 100 27.64 763.9696 Std Dev = 14.70481

100 27.64 763.9696

83 10.64 113.2096

60 -12.36 152.769664 -8.36 69.8896

65 -7.36 54.1696

66 -6.36 40.4496

74 1.64 2.6896

60 -12.36 152.7696

67 -5.36 28.7296

57 -15.36 235.9296

72.36 2378.546

0.037441

0.193496


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of 5.961 compared to 21 from the Range Rule of thumb.

on though.


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True or False Best Answer Complete the sentence

1 TRUE 10 C 16 statistic

2 TRUE 11 C 17 parameters , statisitics

3 FALSE 12 B 18 standard deviation

4 FALSE 13 B 19 lower case sigma

5 FALSE 14 D 20 midrange6 FALSE 15 B 21 Positively

7 FALSE 22 Outlier

8 FALSE

9 FALSE

23) Miles per Gallon 29) Newspaper for sale

a) Mean 15.3 The Age of the Pilots d

b) Median 15,5

c) Mode 15, 16, 17

d) Midrange 15

e) Range 6

f) Variance 3.57

g) Std Deviation 1.9

24) Errors on a Typing Test

a) Mean 6.4

b) Modal Class 6.8

c) Variance 11.6e) Std Deviation 3.4

25) Inches of Rain

a) Mean 51.4

b) Modal Class 35.5-50.5

c) Variance 451.5

d) Std Deviation 21.2

26) Shipment Times

a) Mean 8.2

b) Modal Class 9-Jul

c) Variance 21.6

d) Std Deviation 4.6


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27)Best Friends of Students

Weighted Mean = 1.6

28) Employee Years of Service

Weighted Mean = 4.5


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atasets has more variable.

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Final Assignment on Statistics