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
b. Descriptive
c. Descriptive
d. Descriptive

e. Inferential
f. Inferential
g. Descriptive
h. Inferential

7. a. Ratio level
b. Ordinal level
c. Ratio level
d. Interval level
e. Rato level

f. Ordinal level
g. Ratio level
h. Ratio level
i. Nominal leve
j. Ratio level

8. a. Quantitative
b. Qualitative
c. Quantitative
d. Quantitative

e. Quantitative
f. Quantitative
g. Quantitative

9. a. Discrete
b. Continuous
c. Continuous
d. Continuous

e. Discrete
f. Discrete
g. Continuous

10. Give boundaries of each value:

a. 42.8 miles
b. 1.6 milliliters
c. 5.36 ounces
d. 18 tons
e. 93.8 tons
f. 40 inches

Boundaries
42.75 - 42.85
1.55 - 1.65
5.355 - 5.365
17.5 - 18.5
93.7 - 93.85
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 means
such as geographic area or schools in a large district

12. a. Cluster sampling

b. Systematic sampling
c. Random sampling

d. Systematic sampling
e. Stratified sampling

13. Examples
Nominal
1. Religion
2. Political Party
3. Marital Status

Ordinal
1. Grade
2. Rating Scale
3. Ranking

Interval
1. Temperature
2. Score
3. IQ

Ratio
1. Age
2. Height
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 day
Sampling 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.

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 burning capability.
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 considered properly.

fect of 74% calories burning capability.

bles are not considered properly.

1. True
2. True
3. False. The highest level is the Ratio Scale.
4. True
5. False. Quantitave variable for it has a numerical value
6. 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 Method
22. 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. Continuous
b. 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

e. 6.5 - 7.5 ft

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 = (18-12) / 6 = 1
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=18.5;
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
698.5
698.5
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
0.1
Classes
Boundaries
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

14.3
14.4
14.5
14.6
14.7

14.25
14.35
14.45
14.55
14.65

14.35
14.45
14.55
14.65
14.75

4. There Should be between 5 to 20 classes to have enough classes though there is no hard rule on
number of classes.
The class width is preferably an odd number to ensure that the midpoint of each class has the same
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 considerable loss
of information in putting them in one class at the end with a closed class interval. In such situations
the best procedure would be to specify the open end class interval and all the values of the observations
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
M
H
S

llll
lllll-lllll-lllll-lllll-lllll-lll
lllll-l
ll

8. Common Herb Heigths (6 classes)

7
Xm
No of Classes
Width
Classes
7
12
17
22
27
32
9. Charging Elephant Speeds (5 classes)
19
Xm
No of Classes

4
28
6
2

36
21.5
6 classes
5
11
16
21
26
31
36

32
25.5
5 classes

Boundaries
6.5
11.5
16.5
21.5
26.5
31.5

11.5
16.5
21.5
26.5
31.5
36.5

Width

2.6
Classes
19
22
25
28
31

10. Energy Consumption (10 classes)

164
Xm
No of Classes
Width
Classes
164
1307
2450
3593
4736
5879
7022
8165
9308
10451

21
24
27
30
33

11588
5876
10 classes
1142.4
1306
2449
3592
4735
5878
7021
8164
9307
10450
11593

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

746
780
Xm
763
No of Classes
6 classes
Width
5.666666667
Classes
746
751
752
757
758
763
764
769
770
775
776
781
12. Unhealthy Days in Cities (7 classes)
0
Xm
No of Classes
Width
Classes
0
14
28

93
46.5
7 classes
13.28571429
13
27
41

3
Boundaries
18.5
21.5
24.5
27.5
30.5

21.5
24.5
27.5
30.5
33.5

1143
Boundaries
163.5
1306.5
2449.5
3592.5
4735.5
5878.5
7021.5
8164.5
9307.5
10450.5

1306.5
2449.5
3592.5
4735.5
5878.5
7021.5
8164.5
9307.5
10450.5
11593.5

6
Boundaries
745.5
751.5
757.5
763.5
769.5
775.5

751.5
757.5
763.5
769.5
775.5
781.5

14
Boundaries
-0.5
13.5
27.5

13.5
27.5
41.5

42
56
70
84

55
69
83
97

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

27
70
Xm
48.5
No of Classes
7 classes
Width
6.142857143
Classes
27
33
34
40
41
47
48
54
55
61
62
68
69
75

14. Speed Limits and Fatalities (8 classes)

70
Xm
No of Classes
Width
Classes
70
568
1066
1564
2062
2560
3058
3556

4040
2055
8 classes
496.25
567
1065
1563
2061
2559
3057
3555
4053

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

31
90
Xm
60.5
No of Classes
7 classes
Width
8.428571429
Classes
31
40
41
50
51
60
61
70

41.5
55.5
69.5
83.5

55.5
69.5
83.5
97.5

7
Boundaries
26.5
33.5
40.5
47.5
54.5
61.5
68.5

33.5
40.5
47.5
54.5
61.5
68.5
75.5

497
Boundaries
69.5
567.5
1065.5
1563.5
2061.5
2559.5
3057.5
3555.5

567.5
1065.5
1563.5
2061.5
2559.5
3057.5
3555.5
4053.5

9
Boundaries
30.5
40.5
50.5
60.5

40.5
50.5
60.5
70.5

71
81
91

80
90
100

70.5
80.5
90.5

80.5
90.5
100.5

Peak age of wealthy people in the US is from 61 to 70 years old, extreme values at 41 t0 50 class.

16. US National Park Acreage (8 classes)

5

775
390
8 classes
96.25

Xm
No of Classes
Width
Classes
5
103
201
299
397
495
593
691

102
200
298
396
494
592
690
788

97
Boundaries
4.5
102.5
200.5
298.5
396.5
494.5
592.5
690.5

102.5
200.5
298.5
396.5
494.5
592.5
690.5
788.5

1127
Boundaries
149.5
1277.5
2405.5
3533.5
4661.5
5789.5
6917.5
8045.5
9173.5
10301.5

1277.5
2405.5
3533.5
4661.5
5789.5
6917.5
8045.5
9173.5
10301.5
11429.5

17. Heights of Alaskan Volcanoes (10 classes)

150

11413
5781.5
10 classes
1126.3

Xm
No of Classes
Width
Classes
150
1278
2406
3534
4662
5790
6918
8046
9174
10302

1277
2405
3533
4661
5789
6917
8045
9173
10301
11429

18. Homerun Records (8 classes)

McGwire

306
Xm

550
428

No of Classes
Width

8 classes
30.5
Classes

Sosa

306
338
370
402
434
466
498
530

337
369
401
433
465
497
529
561

340

500
420
8 classes
20

Xm
No of Classes
Width
Classes
340
361
382
403
424
445
466
487

360
381
402
423
444
465
486
507

31
Boundaries
305.5
337.5
369.5
401.5
433.5
465.5
497.5
529.5

337.5
369.5
401.5
433.5
465.5
497.5
529.5
561.5

20
Boundaries
339.5
360.5
381.5
402.5
423.5
444.5
465.5
486.5

360.5
381.5
402.5
423.5
444.5
465.5
486.5
507.5

Width = (18-12) / 6 = 1
5; 17.5=18.5;

e.

hard rule on

ass has the same

tions falling
s considerable loss
n such situations
s of the observations

Tally
ll
lllll
lllllllll
ll
l

Freq
2
5
9
2
0
1

Tally
ll
lllll-lllll-lll
lllll-lllll-lll
lll
l

Freq

Tally
lllll-lllll-lllll-lllll-lllll
lllll-lllll-ll
lllll
lllll
l

Freq

2
13
11
3
1

25
12
5
5
1
0
0
1
0
1

l
l

Tally
llll
llll
lllll-ll
lllll-l
lllll-l
lll

Freq

Tally
lllll-lllll-llll
lllll-llll
lllll

Freq

4
4
7
6
6
3

14
9
5

l
l
l
ll

1
1
1
2

Tally
lllll-ll
lllll-lllll-lll
lllll-lllll-lllll
lllll-lllll-l
lll
llll
ll

Freq

Tally
lllll-lllll-llll
lllll
lllll

Freq

7
13
15
11
3
4
2

14
5
5
0
0
1
0
2

l
ll

Tally

Freq
6
3
9
12

11
4
0

alues at 41 t0 50 class.

Tally
lllll-lllll-lllll-ll
lllll-l
lllll-l
ll
ll
lll
l
ll

Freq

Tally
ll
ll
llllllllll-lll
lllll-ll
lll
lllll-ll
lll
lll
ll

Freq

17
6
6
2
2
3
1
2

2
2
5
8
7
3
7
3
3
2

Tally
l
llllllllll-lllll-lllll-llllllllll-lllll-lllll-lllll-ll
lllll-lllll-ll
lllll
llll
l

Freq

Tally
ll
lllll-lllll-lllll-lll
lllll-lll
lllll-lllll-lllll-llll
lllll-lllll-lll
ll
lll
l

Freq

1
5
20
22
12
5
4
1

2
18
8
19
13
2
3
1

Chapter 2-3

1) Do students need summer Development

Exam Scores
90-98
99-107
108-116
117-125
126-134

Frequency
6
22
43
28
9

Histogram :
45
40
35
Frequency

30
25
20
15
10
5
0
89.5

98.5

107.5
Entrance Exam Scores

Polygon Distribution :
Exam Scores Midpoints
90-98
94
99-107
103
108-116
112
117-125
111
126-134
130

Frequency
6
22
43
28
9

Polygon For Entrance Exam Scores

50
45

Frequency

45
40
35
30
25
20
15
10
5
0
94

103

112

Entrance Exam Scores

Ogive Distribution :
Exam Scores
89.5
98.5
107.5
116.5
125.5
134.5

Frequency
0
6
22
43
28
9

Cumulative
0
6
28
71
99
108

Ogive For Entrance Exam Scores

120

Cummulative
Frequency

100
80
60
40
20
0
89.5

98.5

107.5

Entrance Exam Scores

2) Length of Employee Service

Class Limits
1-5
6-10
11-15

Frequency

Class Boundary
21
25
15

0.5
5.5
10.5

116.5

16-20
21-25
26-30

0
8
6

15.5
20.5
25.5
30.5

Histogram :
30
25
Frequency
20
15
10
5
0
0.5

Polygon Distribution :
Length
1-5
6-10
11-15
16-20
21-25
26-30

Midpoints
3
8
13
18
23
28

5.5

Frequency
21
25
15
0
8
6

Polygon For Length of Servic

30
25

Frequency

20
15
10
5
0
3

13

Length of Employee Service

Ogive Distribution :
Length

Frequency

0.5
5.5
10.5
15.5
20.5
25.5
30.5

0
21
25
15
0
8
6

Cumulative
0
21
46
61
61
69
75

Ogive For Length of Service

80

Cummulative
Frequency

70
60
50
40
30
20
10
0
0.5

5.5

10.5

15.5

Length of Service

3) LPGA Scores

Data are Skewed to the left.

Class Limits
Frequency
Class Boundary
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

15
10
5
0
201.5

Polygon Distribution :
Length
202-204
205-207
208-210
211-213
214-216
217-219

Midpoints
203
206
209
212
215
218

204.5

Frequency
2
7
16
26
18
4

Polygon For LPGA Scores

30
25

Frequency

20
15
10
5
0
203

206

209

LPGA Scores

Ogive Distribution :
Length
Length
202-204
201.5
205-207
204.5
208-210
207.5
211-213
210.5
214-216
213.5
217-219
216.5
219.5

Frequency
0
2
7
16
26
18
4

Cumulative
0
21
28
44
70
88
92

Ogive For LPGA Scores

Cummulative
Frequency

100
90
80
70
60
50
40
30
20
10
0
201.5

204.5

207.5

210.5

LPGA Scores

4) NFL Salaries

Data are Skewed to the left.

Class Limits
Frequency
Class Boundary
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

Polygon Distribution :

42.85

Salaries
39.9-42.8
42.9-45.8
45.9-48.8
48.9-51.8
51.9-54.8
54.9-57.8

Midpoints
41.35
44.35
47.35
50.35
53.35
56.35

Frequency
2
2
5
5
12
5

Polygon For NFL Salaries

14
12

Frequency

10
8
6
4
2
0
41.35

44.35

47.35

NFL Salaries

Ogive Distribution :
Frequency
Salaries
39.9-42.8
39.85
42.9-45.8
42.85
45.9-48.8
45.85
48.9-51.8
48.85
51.9-54.8
51.85
54.9-57.8
54.85
57.85

Frequency
0
2
2
5
5
12
5

Cumulative
0
2
4
9
14
26
31

Ogive For NFL Salaries

35

Cummulative
Frequency

30
25
20
15
10
5

5
0
39.85

42.85

45.85

48.85

NFL Salaries

5) Automobile Fuel Efficiency

Class Limits
7.5-12.5
12.5-17.5
17.5-22.5
22.5-27.5
27.5-32.5

Frequency
3
5
15
5
2

Class Boundary
7.45
12.55
17.55
22.55
27.55
32.55

Histogram :

Frequency

15
10
5
0
7.45

Polygon Distribution :
Efficiency
7.5-12.5
12.5-17.5
17.5-22.5
22.5-27.5
27.5-32.5

Midpoints
10
15
20
25
30

12.55

Frequency
3
5
15
5
2

Polygon For Fuel Efficiency

16
14
12

14
12

Frequency

10
8
6
4
2
0
10

15

Fuel Efficiency

Ogive Distribution :
Class
Efficiency
7.5-12.5
7.45
12.5-17.5
12.55
17.5-22.5
17.55
22.5-27.5
22.55
27.5-32.5
27.55
32.55

Frequency
0
3
5
15
5
2

Cumulative
0
3
8
23
28
30

Ogive For Fuel efficiency

35

Cummulative
Frequency

30
25
20
15
10
5
0
7.45

12.55

17.55

Fuel Efficiency
6) Speed Limits and Fatalities

Skewed to the Right.

Class
70
568
1066
1564

567
1065
1563
2061

Boundaries
69.5
567.5
1065.5
1563.5

Frequency
567.5 lllll-lllll-llll
1065.5 lllll
1563.5 lllll
2061.5

2062
2560
3058
3556

2559
3057
3555
4053

2061.5
2559.5
3057.5
3555.5
4053.5

2559.5
3057.5 l
3555.5
4053.5 ll

Histogram :
16
14
12
Frequency
10
8
6
4
2

Polygon Distribution :
Class
70
568
1066
1564
2062
2560
3058
3556

567
1065
1563
2061
2559
3057
3555
4053

69.5

567.5

Boundaries
69.5
567.5
1065.5
1563.5
2061.5
2559.5
3057.5
3555.5
4053.5

567.5
1065.5
1563.5
2061.5
2559.5
3057.5
3555.5
4053.5

1065.5

Frequency
lllll-lllll-llll
lllll
lllll

l
ll

Polygon For Speed vs Fatalities

16
14

Frequency

12
10
8

8
6
4
2
0
318.5

816.5

1314.5

1812.5

2310.5

2808.5

Speed and fatalities

Ogive Distribution :
Class
69.5
567.5
1065.5
1563.5
2061.5
2559.5
3057.5
3555.5
4053.5

Frequency
14
5
5
0
0
1
0
2

Cumulative
0
14
19
24
24
24
25
25
27

Ogive For Speed and Fa

30

Cummulative
Frequency

25
20
15
10
5
0
69.5

567.5

1065.5

1563.5

Speed and fatalities

8) How Quick are Dogs ?

Class Limits
2.3
3.0
3.7
4.4

2.9
3.6
4.3
5.0

Frequency
10
12
6
8

Class Boundaries
2.25
2.95
2.95
3.65
3.65
4.35
4.35
5.05

5.1
5.8

5.7
6.4

4
2

5.05
5.75
6.45

5.75
6.45

2.25

2.95

Histogram:
14
12
10
Frequency
8
6
4
2
0

Polygon Distribution :
Class Limits
2.3
2.9
3.0
3.6
3.7
4.3
4.4
5.0
5.1
5.7
5.8
6.4

Midpoints
2.6
3.3
4
4.7
5.4
6.1

Frequency
10
12
6
8
4
2

Polygon For Reaction Time

14
12

Frequency

10
8
6
4
2
0
10

12

10

12

Reaction Time of Dogs

2.3
3.0
3.7
4.4
5.1
5.8

Ogive Distribution :
Class Limits
Salaries
2.25
2.9
2.95
3.6
3.65
4.3
4.35
5.0
5.05
5.7
5.75
6.4
6.45

Frequency
10
12
6
8
4
2

Cumulative
0
10
22
28
36
40
42

Ogive For Reaction Time

45

Cummulative
Frequency

40
35
30
25
20
15
10
5
0
2.25

2.95

3.65

4.35

Reaction Time of Dogs

10) Making the Grade : No substantive Difference on the performance of the students on Reading and Math.
Class Limits
17.5
22.5
27.5
32.5
37.5
42.5
47.5

MathFrequency
22.5
27.5
32.5
37.5
42.5
47.5

5
9
11
16
8
1

Class Boundaries

16
14
12
Math Frequency
10
8
6
4
2
0
17.5

22.5

27.5

32.5

Percentage of Schools

Polygon Distribution :
Class Limits
17.5
22.5
22.5
27.5
27.5
32.5
32.5
37.5
37.5
42.5
42.5
47.5

Midpoints
20
25
30
35
40
45

Frequency
5
9
11
16
8
1

Polygon For Math F

18
16
14

Frequency

12
10
8
6
4
2
0
20

25

Math Frequency

Ogive Distribution :
Class Limits
Salaries
17.5
22.5
22.5
27.5
27.5
32.5
32.5
37.5
37.5
42.5
42.5
47.5
47.5

Frequency Cumulative
0
5
5
9
14
11
25
16
41
8
49
1
50

Ogive For Math F

60

Cummulative
Frequency

50
40
30
20
10
0
17.5

22.5

Math Frequency

12) Home Run Record Breakers

McGwire

306
Xm
No of Classes
Width
Classes
306
338
370
402
434
466
498
530

550
428
8 classes
30.5
31
Boundaries
337
305.5
369
337.5
401
369.5
433
401.5
465
433.5
497
465.5
529
497.5
561
529.5
561.5

337.5
369.5
401.5
433.5
465.5
497.5
529.5
561.5

Sosa

340
Xm
No of Classes
Width
Classes
340
361
382
403
424
445
466
487

500
420
8 classes
20
20
Boundaries
360
339.5
381
360.5
402
381.5
423
402.5
444
423.5
465
444.5
486
465.5
507
486.5
507.5

360.5
381.5
402.5
423.5
444.5
465.5
486.5
507.5

24
22
20
18
McGwire
Frequency

16
14
12
10
8
6
4
2
0

305.5

337.5

369.5
Distance

Polygon Distribution :

401.5

Class Limits
17.5
22.5
22.5
27.5
27.5
32.5
32.5
37.5
37.5
42.5
42.5
47.5

Midpoints
20
25
30
35
40
45

Frequency
5
9
11
16
8
1

Polygon For McGwire

18
16
14

Frequency

12
10
8
6
4
2
0
20

25

30

McGwire

Ogive Distribution :
Class Limits
Salaries
17.5
22.5
22.5
27.5
27.5
32.5
32.5
37.5
37.5
42.5
42.5
47.5
47.5

Frequency
5
9
11
16
8
1

Cumulative
0
5
14
25
41
49
50

Ogive For McGwire

60

Cummulative
Frequency

50
40
30
20
10

0
17.5

22.5

27.5

32.5

McGwire

14) Length of Employee Service

Class Limits
1-5
6-10
11-15
16-20
21-25
26-30

Frequency

Class Boundary
21
25
15
0
8
6
75

0.5
5.5
10.5
15.5
20.5
25.5
30.5

Relative Freq
28.00%
33.33%
20.00%
0.00%
10.67%
8.00%

Histogram :
60%
50%
Frequency
40%
30%
20%
10%
0
0.5

Polygon Distribution :
Length

Midpoints

1-5
6-10
11-15
16-20
21-25
26-30

3
8
13
18
23
28

5.5

Rel
Frequency Frequency
28.00%
21
33.33%
25
20.00%
15
0.00%
0
10.67%
8
8.00%
6

Polygon For Length of Servic

35.00%
30.00%

30.00%
25.00%

Frequency

20.00%
15.00%
10.00%
5.00%
0.00%
3

13

Length of Employee Service

Ogive Distribution :
Length
0.5
5.5
10.5
15.5
20.5
25.5
30.5

Rel Frequency Cumulative

0.00%
0
28.00%
21
61.33%
46
81.33%
61
81.33%
61
92.00%
69
100.00%
75

Ogive For Length of Service

120.00%

Cummulative
Frequency

100.00%
80.00%
60.00%
40.00%
20.00%
0.00%
0.5

5.5

10.5

Length of Service

16) Protein Grams in Fast Food

Class Limits
12-19.5
19.6-27.1
27.2-34.7

Frequency

Class Boundary
7
11.95
17
19.55
6
27.15

Relative Freq
17.50%
42.50%
15.00%

34.8-42.3
42.4-49.9
50-57.5

7
2
1
40

34.75
42.35
49.95
57.55

17.50%
5.00%
2.50%

50%
40%
Histogram :
30%
25%
Frequency
20%
15%
10%
5%
0
11.95

19.55

Polygon Distribution :
Class Limits
12-19.5
19.6-27.1
27.2-34.7
34.8-42.3
42.4-49.9
50-57.5

Midpoints
15.75
23.35
30.95
38.55
46.05
53.75

Rel
Frequency Frequency
17.50%
7
42.50%
17
15.00%
6
17.50%
7
5.00%
2
2.50%
1

Polygon For Protein in Fast Fo

45.00%
40.00%
35.00%

Frequency

30.00%
25.00%
20.00%
15.00%
10.00%
5.00%

5.00%
0.00%
15.75

23.35

30.95

Protein in Fast food

Ogive Distribution :
Length
11.95
19.55
27.15
34.75
42.35
49.95
57.55

Rel Frequency Frequency Cumm Freq

0.00%
0
0
17.50%
7
7
60.00%
17
24
75.00%
6
30
92.50%
7
37
97.50%
2
39
100.00%
1
40
40

Ogive For Protein for Fast Fo

120.00%

Cummulative
Frequency

100.00%
80.00%
60.00%
40.00%
20.00%
0.00%
11.95

19.55

27.15

Protein in Fast food

18) How Quick are Dogs

Class Limits
2.3-2.9
3.0-3.6
3.7-4.3
4.4-5.0
5.1-5.7
5.8-6.4

Frequency
1
3
4
16
14
4
42

Class Boundary
2.25
2.95
3.65
4.35
5.05
5.75
6.45

Histogram :
60%

Relative Freq
2.38%
7.14%
9.52%
38.10%
33.33%
9.52%

50%
Frequency
40%
30%
20%
10%
0
2.25

2.95

Polygon Distribution :
Class Limits
2.3-2.9
3.0-3.6
3.7-4.3
4.4-5.0
5.1-5.7
5.8-6.4

Midpoints
2.6
3.3
4
4.7
5.4
6.1

Rel
Frequency Frequency
2.38%
1
7.14%
3
9.52%
4
38.10%
16
33.33%
14
9.52%
4

Polygon For how quick the dog

40.00%
35.00%
30.00%

Frequency

25.00%
20.00%
15.00%
10.00%
5.00%
0.00%
2.6

3.3

How Fast the Dogs are

Ogive Distribution :
Length
2.25
2.95
3.65

Rel Frequency Frequency Cumm Freq

0.00%
0
0
2.38%
1
1
9.52%
3
4

4.35
5.05
5.75
6.45

19.05%
57.14%
90.48%
100.00%

4
16
14
4
42

8
24
38
42

Ogive For how quick the dogs

120.00%

Cummulative
Frequency

100.00%
80.00%
60.00%
40.00%
20.00%
0.00%
2.25

2.95

3.65

How Fast the Dogs are

20) From the result of Exercise 19
a) 0 zero
b) 14 fourteen
c) 10 ten
d) 16 sixteen

116.5
Entrance Exam Scores

ance Exam Scores

125.5

134.5

111

130

Scores

nce Exam Scores

Scores

116.5

125.5

134.5

10.5

15.5

20.5

25.5

Length of Employee Service

n For Length of Service

18

gth of Employee Service

23

28

30.5

For Length of Service

15.5

Length of Service

20.5

25.5

30.5

207.5

210.5

213.5

216.5

LPGA Scores

gon For LPGA Scores

212

LPGA Scores

215

218

219.5

ve For LPGA Scores

210.5

213.5

216.5

219.5

LPGA Scores

45.85

48.85

NFL Salaries

51.85

54.85

57.85

gon For NFL Salaries

50.35

NFL Salaries

ive For NFL Salaries

53.35

56.35

48.85

51.85

54.85

57.85

NFL Salaries

17.55

22.55

27.55

Automobile Fuel Efficiency

on For Fuel Efficiency

32.55

20

25

30

Fuel Efficiency

For Fuel efficiency

22.55

Fuel Efficiency

Frequency
14
5
5
0

27.55

32.55

0
1
0
2

1563.5

2061.5

Speed and fatalities

Frequency
14
5
5
0
0
1
0
2

ed vs Fatalities

Midpoints
318.5
816.5
1314.5
1812.5
2310.5
2808.5
3306.5
3804.5

2559.5

3057.5

3555.5

4053.5

2808.5

3306.5

3804.5

d and fatalities

ive For Speed and Fatalities

1563.5

Speed and fatalities

2061.5

2559.5

3057.5

3555.5

4053.5

3.65

4.35

5.05

5.75

Reaction Time of Dogs

on For Reaction Time

6.45

Reaction Time of Dogs

ve For Reaction Time

4.35

5.05

5.75

6.45

Reaction Time of Dogs

Reading and Math.

Reading
Frequency
7
6
11
16
8
1

20
18

16
14
12
10
Reading
Frequency

8
6
4
2
0

37.5

42.5

47.5

17.5

22.5

27.5

32.5

Percentage of Schools

Polygon Distribution :
Class Limits
17.5
22.5
27.5
32.5
37.5
42.5

Polygon For Math Frequency

30

Math Frequency

35

40

45

Ogive Distribution :
Class Limits
17.5
22.5
22.5
27.5
27.5
32.5
32.5
37.5
37.5
42.5
42.5
47.5
47.5

Ogive For Math Frequency

27.5

32.5

37.5

Math Frequency

Tally
Freq
l
llllllllll-lllll-lllll-llllllllll-lllll-lllll-lllll-ll
lllll-lllll-ll
lllll
llll
l

1
5
20
22
12
5
4
1

42.5

47.5

Tally
Freq
ll
lllll-lllll-lllll-lll
lllll-lll
lllll-lllll-lllll-llll
lllll-lllll-lll
ll
lll
l

2
18
8
19
13
2
3
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

339.5

Polygon Distribution :

Class Limits
17.5
22.5
22.5
27.5
27.5
32.5
32.5
37.5
37.5
42.5
42.5
47.5

ygon For McGwire

18
16
14

Frequency 12
10

35

40

45

McGwire

Ogive Distribution :
Class Limits
Salaries
17.5
22.5
22.5
27.5
27.5
32.5
32.5
37.5
37.5
42.5
42.5
47.5
47.5

give For McGwire

Cummulative
Frequency

32.5

37.5

42.5

47.5

McGwire

10.5

15.5

20.5

Length of Employee Service

75

n For Length of Service

25.5

30.5

13

18

23

28

gth of Employee Service

For Length of Service

15.5

Length of Service

20.5

25.5

30.5

27.15

34.75

Protein in Fast food

40

For Protein in Fast Food

42.35

49.95

57.55

30.95

38.55

46.05

53.75

Protein in Fast food

or Protein for Fast Food

34.75

Protein in Fast food

42.35

49.95

57.55

3.65

4.35

5.05

5.75

How Fast the Dogs are

42

or how quick the dogs are

How Fast the Dogs are

4.7

5.4

6.1

6.45

r how quick the dogs are

4.35

How Fast the Dogs are

5.05

5.75

6.45

37.5

42.5

47.5

Polygon Distribution :
Class Limits
Midpoints Frequency
20
7
22.5
25
6
27.5
30
11
32.5
35
16
37.5
40
8
42.5
45
1
47.5

Polygon For Reading Frequency

18
16
14

Frequency 12
10
8
6
4
2
0
20

25

30

Reading Frequency

35

40

45

Ogive Distribution :
Salaries Frequency Cumulative
7
0
6
7
11
13
16
24
8
40
1
48
49

Ogive For Reading Frequency

60

Cummulative50
Frequency
40
30
20
10
0
17.5

22.5

27.5

32.5

Reading Frequency

37.5

42.5

47.5

360.5

381.5

402.5

423.5
Distance

444.5

465.5

486.5

507.5

Midpoints Frequency
20
7
25
6
30
11
35
16
40
8
45
1

Polygon For Sosa

18
16
14
12
10
8
6
4
2
0
20

25

30

35

Sosa

Frequency Cumulative
7
0
6
7
11
13
16
24
8
40
1
48
49

Ogive For Sosa

60

Cummulative50
40
30
20
10

40

45

0
17.5

22.5

27.5

Sosa

32.5

37.5

42.5

47.5

Exercis 2.4
1) Federal Prison Population
Offenses
Drug Offenses
Violent Offenses
Property Offenses
Weapons
Others
Immigration
Public Order Offfenses

% contribution
60.20%
12.60%
8.50%
8.20%
5.60%
4.90%

70.00%

100.00%

30.00%

60.00%
50.00%
40.00%

20.00%
10.00%
0.00%
Drug
Offenses

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

3) Internet Connections
Location
homes
large companies
small companies
schools
government agencies

No. of Computers
240
148
102
47
33

300
250
# of
Computers

200
150
100
50
0
homes

5) World Energy Use

Fuel

Contribution

Petroleum
Coal
Dry Natural Gas
Hydroelectric
Nuclear
Others

39.80%
23.20%
22.40%
7.00%
6.40%
1.20%

40
35
30
% Contribution

25
20
15
10
5
0
Petroleum

7) Tobacco Consumption
Year
1996
1997
1998
1999
2000
2001
2002

Amount
7.9
9.9
10.5
10.9
11
9.8
10.1

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

9) Do Voters Vote?
Year
1964
1968
1972

% Voters
95.83%
89.65%
79.85%

1976
1980
1984
1988
1992
1996
2000

77.64%
76.53%
74.63%
72.48%
78.01%
65.97%
67.50%

Generally the number of voters decreased in time..

11) Distribution of Assets

Distribution
Business / Real Estates
Stock/Mutual Funds/ Trusts
Principal Residences
Pension accounts
Liquid Assets
Miscellaneous

Percentages
46.90%
31.60%
7.80%
6.90%
5.00%
1.80%

Percentages

13) Workers Switch Jobs

What to do
Career Change
New Job in same industry
Start a Business
Retire

Percent
34.00%
29.00%
21.00%
16.00%

What to do Contribution
surveyed

40.00%
35.00%
% Contribution

30.00%
25.00%
20.00%
15.00%
10.00%
0.00%
Career
Change

New Job in
same
industry

Pie Chart would represent the contribution on a certain population while pareto chart would show the highest
Both Chart represent the same data but it will depend on the purpose of processing the data and what you wou
determines which chart represents better.

15) Presidents' age in Inauguration

Leading Digit (stem)

Trailing Digit (leaf)

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

The Contribution of both varieties are almost the same having the peak at 50-59 cm. V2 has more variation in th
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
1960
1970
1980
1990
2000

Veal
1109
588
400
327
225

Lamb
769
551
318
358
234

1200
1000

M lbs

800
600
400
200
0
1960

1970

1980

Year
Both Meat Production is decreasing thru time.

1990

2000

23) Nobel Prizes in Physiology or Medicine

Country
USA
UK
Germany
Sweden
France
Switzerland
Denmark
Austria
Belgium
Italy
Australia

# of Prizes
80
24
16
8
7
6
5
4
4
3
3

Most Appropriate Graph is the Pareto Chart to show the country with the highest number of awards and their r

90
80

80

70
60
50
40
30
24
20
16
10
0
USA

UK

Germany

Violent
Offenses

Property
Offenses

Public Order
Offenses
(Weapons)

Others

offense followed by Violence and Property offenses.

large
companies

small
companies

schools

government
agencies

Public Order
Offenses
(Immigration)

Coal

y the Trend is increasing..

Dry Natural
Gas

Hydroelectric

Nuclear

Others

Percentages
Business / Real Estates
Stock/Mutual Funds/
Trusts
Principal Residences
Pension accounts
Liquid Assets
Miscellaneous

o do Contribution on 3 of 10
surveyed

Career Change
New Job in same industry
Start a Business
Retire

Start a
Business

Retire

hart would show the highest move contribution.

g the data and what you would want to show

m. V2 has more variation in the

Veal
Lamb

2000

number of awards and their ranking

8
Sweden

7
France

6
Switzerland

5
Denmark

4
Austria

4
Belgium

3
Italy

3
Australia

True or False
1) False
2) False
3) False
4) True
5) True
6) False
7) 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)
House
Apartment
Mobile Home
Condominium

Freq
lllll-l
llllllllll-l
lllll-lll

6
5
6
8

19) Pie Chart

Freq
House
Apartment
Mobile Home
Condominium

Deg
6
5
6
8
25

86.4
72
86.4
115.2

% contribution
24.00%
20.00%
24.00%
32.00%
100.00%

20) Items Purchased at a convenience store

No of Items
1
2
3
4
5
6
7
8
9

Count
l
lllll
lll
llll
ll
lllll-l
ll
lll
llll

Frequency
1
5
3
4
2
6
2
3
4

Cumm. Freq.
0
1
6
9
13
15
21
23
26
30

21) Items Purchased

Limits
0.5
1.5
2.5
3.5
4.5
5.5
6.5
7.5
8.5
9.5

7
6
5
Frequency
4
3
2
1
0
1

Frequency Polygon

Frequency

35

30

25

20

15

10

0
1

22-23) Murders in selected City

Data Skewed to the Right.

Max
Min
Classes

65

598
27
63.4444444

Lower
1
2
3
4
5
6
7
8
9

Upper
27
93
159
225
291
357
423
489
555

92
158
224
290
356
422
488
554
620

0.5

Lower Limit
Upper Limit
Midpoint
Frequency
26.5
92.5
59.5 lllll-lllll-lll
92.5
158.5
125.5 ll
158.5
224.5
191.5
224.5
290.5
257.5 lllll290.5
356.5
323.5 l
356.5
422.5
389.5 l
422.5
488.5
455.5
488.5
554.5
521.5 l
554.5
620.5
587.5 ll

14
12
10
Frequency
8
6
4
2
0
26.5

92.5

158.5
Classes

Frequency Polygon for Mu

14
12

12
10
8
6
4
2
0
59.5

125.5

191.5

257.5

Ogive for Murders i

30
25
20
15
10
5
0
26.5

92.5

158.5

224.5

24) Recycled Trash Pareto chart

Pareto Chart for Recycled trash

Type
Paper
Iron / Steel
Aluminum
Yard waste
Glass
Plastics

Amount (M Tons)
320
292
276
242.4
196
41.6

350
300
250
200
150
100
50
0
Paper

Iron / Steel

Aluminum

Yard waste

25) Tresspasser Fatalities

Trend of No. of Fata

Year
1998
1999
2000
2001

No. of Fatalities
536
463
511
540

Trend of No. of Fata

560
540
520
500
480
460
440
420
1998

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
250
120
300
200

25
175
100
210
150

There is a relationship between no. of miles

travelled and sales. It is Directly Proportional.

250
200
150
100

1999

50
0
0

50

100

House
Apartment
Mobile Home
Condominium

Histogram

No. of Items

Ogive for Items Purchased

Cumm. Freq.

0.5

1.5

2.5

Count

3.5

4.5

Cummulative

5.5

6.5

13
2
0
5
1
1
0
1
2

0
13
15
15
20
21
22
22
23
25

Ogive Limit
26.5
92.5
158.5
224.5
290.5
356.5
422.5
488.5
554.5
620.5

224.5

290.5

356.5

7.5

422.5

ncy Polygon for Murders in Selected City

8.5

9.5

488.5

554.5

620.5

Count

257.5

323.5

389.5

455.5

521.5

587.5

Ogive for Murders in selected City

Cummulative

224.5

290.5

356.5

422.5

t for Recycled trash

Amount (M Tons)

Yard waste

Glass

Trend of No. of Fatalities

Plastics

488.5

554.5

620.5

Trend of No. of Fatalities

1999

2000

Sales (y)

No. of Fatalities

2001

Sales (y)

100

150

200

250

300

350

Exercise 3-2
1)

3.8
3.86
3.83
3.78
3.75
a) Mean

3.77
3.76
3.7
3.74
3.64
=(sumX/n)

b) median = 3.73
3.86
3.73

c) mode

3.7
3.68
3.8
3.73
3.78
=93.09/25

3.83
3.7

3.74
3.67
3.74
3.65
3.73

3.7
3.57
3.67
3.66
3.64

3.724

3.8
3.7

3.8
3.7

3.78
3.68

3.78
3.67

Bimodal on 3.74 and 3.70

3.86
3.83
3.8
3.73
3.7
3.7

3.8
3.7

3.78
3.68

3.78
3.67

d) midrange

(Highest Value + Lowest value ) / 2

=(3.57 + 3.86) / 2
3.715

Midrange

2) Heights of the Highest waterfall (ft)

3212
1904
2800
1841
2625
a) Mean

1650
2540
1612
2499
1536

2425
1170
1388
1215
2307

2151
1198
1182
2123
2000

1968.9

b) median

1952 in between the values 1904 and 2000 thus

=(2000 + 1904) / 2
3212
2800
2625
2540
2499
1904
1841
1650
1612
1536

c) mode

d) midrange

the data set has no mode

2191

2425
1388

3) Burglaries at Pennsylvania University

The most appropriate measure of average is the Mean for it varies less than the mode or median
especially on varied data such as this.
61
11
1

3
2
30

4) Public School suspension

Beaver
Butler
67
12
11
92
13
Mean
39
26.75
Median
11
15
Mode
None
None
Midrange
40
38.5

18
3
7

Mean

15.1

56
12
18
21
There is a significant Difference in the Average.

5) Identity theft
574
117
Mean
Median
Mode
Midrange

229
239
270.75
205
None
369

663
465

372
136

102
189

The researcher has 10% error on his estimate a

and 23% error against the Midrange.

7) Earthquake Strengths
The Mean, Median and Midrange should be used to measure the most typical case of magnitude..
7
6.2
7.7
8
6.4
6.2
7.2
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 =
Median =
Midrange =

6.633
6.7
6.7

8) Top Paid CEO

47.7
41.7
38.5
37.6
36.8
35.4
35.2
31.7
31.7
31.4

29.1
28.6
26.8
25.9
25.5
25.4
25.2
25.2
25.1
25

24.3
24.1
24
24
23.7
23.2
22.9
21.6
21.4
20.4

20.1
20
19.8
19.7
19.3
19.1
19.1
18.2
18
18

17.5
17.4
17.3
17.2
17.2
17
16.9
16.9
16.8
16.5

15) Murders in Cities

Class
34-96
97-159
160-222
223-285
286-348
249-411
412-474
475-537
538-600

Frequency

Midpoint

f.Xm

13
65
845
2
128
256
0
191
0
5
254
1270
1
317
317
1
380
380
0
443
0
1
506
506
2
569
1138
25
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 since
it is the most typical situation to happen which is the 34-96 class. (Mode = 65)
Mean =
188.48
20) Commissions Earned
Class
150
159
168
177
186
195
204

Mean =

Frequency
158
167
176
185
194
203
212

5
16
20
21
20
15
3
100
180.28

Midpoint
154
163
172
181
190
199
208

f.Xm
770
2608
3440
3801
3800
2985
624
18028.0

Mode=

181 (Class 177-185)

21) Copier Service Calls

Class
15.5
18.5
21.5
24.5
27.5
30.5

Mean=
Mode=

18.5
21.5
24.5
27.5
30.5
33.5

Frequency
14
12
18
10
15
6
75

Midpoint
17
20
23
26
29
32

f.Xm
238
240
414
260
435
192
1779

23.72
23 (Class 21.5-24.5)

27)Fat Grams

Fried Shrimp
Veal cutlet
Roast Beef
Fried Chicken
Tuna

Meat or Fish Fat(g/oz)

Weight
3
3.33
9.99
3
3
9
2
2.5
5
2
4.4
8.8
4
1.75
7
14
39.79
Average meat or fish a person ate in 5 days =

2.842

28) Diet Cola Preference

Area

29) Costs of Helicopters

% Favored

Number of Surveyed
Weight
1
40
1000
40000
2
30
3000
90000
3
50
800
40000
120
170000.0
Weighted Mean =
1416.7

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

Percent of final Grade

Grade
20
30
50
100
Final Grade = 83.2

Weight
83
72
90

1660
2160
4500
8320

31) Final Grade

Exam

Grade
1
1
1
1
2
6

Weight
62
83
97
90
82

Final Grade =

32 ) Situational

62
83
97
90
164
496
82.7

33) Situational
a) Mode
b) Median
c) Median
d) Median
e) Mean
f) Median

a) Median
b) Mean
c) Mode
d) Mode
e) Mode
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.

3.77
3.67

3.76
3.66

3.75
3.65

3.74
3.64

3.74
3.64

Median
3.74
3.73
3.57

3.77
3.67

3.76
3.66

3.75
3.65

3.74
3.64

3.74
3.64

3.74
3.57

2307
1215

2151
1198

2123
1182

2000
1170

3.73

n the mode or median

ce in the Average.

88
75

has 10% error on his estimate against the Mean, 30% against the Median
against the Midrange.

cal case of magnitude..

Mean =
24.422
24.422
Mode=
Multi Modal on 31.7, 25.2, 24, 17.2, 18, 19.1 and 16.9.
Midrange=
32.1
Median =
23.45

The Midrange shows the best measure for average.

Modal since

11) Heights of tall bldgs

n=11
St Paul
32
36
46
20
32
18
16
34
26
27
26
28.45

Mean

X-u
3.55
7.55
17.55
-8.45
3.55
-10.45
-12.45
5.55
-2.45
-1.45
-2.45

(x-u)2
12.6025
57.0025
308.0025
71.4025
12.6025
109.2025
155.0025
30.8025
6.0025
2.1025
6.0025
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
3.8
3.8
3.2
3.57
3.62
3.74
3.69
3.631428571

X-u
0.168571
0.168571
-0.43143
-0.06143
-0.01143
0.108571
0.058571

(x-u)2
0.028416
0.028416
0.186131
0.003774
0.000131
0.011788
0.003431
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

(x-u)2/n
Std Dev =

Data

X-u
16.066667
12.066667
4.066667
0.066667
-0.933333
-0.933333
-1.933333
-1.933333
-2.933333
-2.933333
-3.933333
-3.933333
-3.933333
-3.933333
-4.933333

22
18
10
6
5
5
4
4
3
3
2
2
2
2
1
5.933333333

(x-u)2
258.1377885
145.6044525
16.53778049
0.004444489
0.871110489
0.871110489
3.737776489
3.737776489
8.604442489
8.604442489
15.47110849
15.47110849
15.47110849
15.47110849
24.33777449
532.9333333

(x-u)2/n
Std Dev =

35.52889
5.960611

The dataset has an actual Std Dev of 5.961 com

Both measure showed with variation though.

22) Reaction times

Class

Freq

2.1
2.8
3.5
4.2
4.9
5.6

2.7
3.4
4.1
4.8
5.5
6.2

12
13
7
5
2
1
40

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

Midpoint F*Xm
(f*Xm)2
2.4
28.8
69.12
3.1
40.3
124.93
3.8
26.6
101.08
4.5
22.5
101.25
5.2
10.4
54.08
5.9
5.9
34.81
134.5
485.27

18090.25
40
452.25625

s2=

0.84650641
0.92005783

s=

23) Lightbulb Lifetimes

Class
52.5
63.5
74.5

Freq
63.5
74.5
85.5

Midpoint F*Xm
(f*Xm)2
6
58
348
20184
12
69
828
57132
25
80
2000
160000

85.5
96.5
107.5

96.5
107.5
118.5

18
14
5
80

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

46335249
80
579190.6125

s2=

211.1947785
14.53254205

s=

91
102
113

1638
1428
565
6807

149058
145656
63845
595875

24) Murder Rates

Class
5
12
19
26
33
40

Freq
11
18
25
32
39
46

8
5
7
1
1
3
25

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

Midpoint F*Xm
(f*Xm)2
8
64
512
15
75
1125
22
154
3388
29
29
841
36
36
1296
43
129
5547
487
12709

237169
25
9486.76

s2=

134.26
11.58706175

s=

Page 170

6) Fuel Capacity
Class
10
13
16
19
22

Freq
12
15
18
21
24

6
4
14
15
8

Midpoint F*Xm
(f*Xm)2
11
66
726
14
56
784
17
238
4046
20
300
6000
23
184
4232

25
28

a)

Mean

b)
c)
d)

Modal Class
Variance
Std Dev

27
30

Mean =
(sum(f*Xm))2
n=
((sum(f*Xm))2)/n=
Class 19-21
s2=

2
1
50

26
29

18.5
855625
50
17112.5

s=

17.7244898
4.210046294

7) Number of Cavities
Number of Students

No. of Cavities
12
8
5
5
30

Weighted Mean =

Weight
0
1
2
3

1.1

0
8
10
15
33

52
29
925

1352
841
17981

(x-u)2/n
Std Dev =

0.037441
0.193496

70.06614
8.370552

Chicago
100
100
83
60
64
65
66
74
60
67
57
72.36

X-u
27.64
27.64
10.64
-12.36
-8.36
-7.36
-6.36
1.64
-12.36
-5.36
-15.36

(x-u)2
763.9696
763.9696
113.2096
152.7696
69.8896
54.1696
40.4496
2.6896
152.7696
28.7296
235.9296
2378.546

(x-u)2/n
Std Dev =

216.2314
14.70481

ual Std Dev of 5.961 compared to 21 from the Range Rule of thumb.
with variation though.

True or False
1
2
3
4
5
6
7
8
9

Best Answer
TRUE
TRUE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE

23) Miles per Gallon

a) Mean
b) Median
c) Mode
d) Midrange
e) Range
f) Variance
g) Std Deviation

10
11
12
13
14
15

15.3
15,5
15, 16, 17
15
6
3.57
1.9

24) Errors on a Typing Test

a) Mean
b) Modal Class
c) Variance
e) Std Deviation

6.4
6.8
11.6
3.4

25) Inches of Rain

a) Mean
b) Modal Class
c) Variance
d) Std Deviation

51.4
35.5-50.5
451.5
21.2

26) Shipment Times

a) Mean
b) Modal Class
c) Variance
d) Std Deviation

8.2
9-Jul
21.6
4.6

C
C
B
B
D
B

Complete the sentence

16
17
18
19
20
21
22

statistic
parameters , statisitics
standard deviation
lower case sigma
midrange
Positively
Outlier

29) Newspaper for sale

The Age of the Pilots datasets has more varia

27)Best Friends of Students

Weighted Mean =

1.6

28) Employee Years of Service

Weighted Mean =

4.5

s , statisitics

the Pilots datasets has more variable.