Lecture Probability & statistics: Chapter 2

LECTURE 2 – TABLES & CHARTS LECTURE 2 – TABLES & CHARTS

 [1] Chapter 2, pp. 33 – 79

 Frequency, relative frequency, cumulative table  Pie chart  Bar chart, Column chart  Histogram  Line chart, Radar chart  Scatter plot, bubble chart

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Raw data Raw data

 Data from a customer survey, n = 50 observations

No. Sex (Male /

Age (year) 43

Waiting time (Minute) 15 to 20

Evaluation (VG, G, F, B) Bad

Female) Female

1 0 to 5

Good

Male

2

23 5 to 10

Very Good

Female

3

36 …

50

28 Female

10 to 15

Fair

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Frequency & Relative frequency Frequency & Relative frequency

 Frequency table of Gender

Sex

Male

Female

Frequency

 Relative frequency (proportion): =

()

Sex

Male

Female

Relative frequency Proportion, percent

0.4 40%

0.6 60%

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Pie chart Pie chart

Gender

Sex

Male

Female

Male

Freq.

Female

40%

60%

[VAL UE] [PER CE…

Evaluation

Very Good

Good Fair Bad

Good

Evalua tion

Very Good

Fair

Freq.

Bad

[VALUE ] [PERCE NTAGE]

20% 50% 18% 12%

[VALUE [VALUE ] ] [PERCE [PERCE NTAGE] [VALUE NTAGE] ] [PERCE NTAGE]

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Column chart Column chart

Evaluation

Evaluation Freq.

%

25

Very Good

20%

50%

Good

18%

Fair

10

9 12% 100%

6 50

Bad TOTAL

6

Very Good Good

Fair

Bad

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Cross frequency table – Column chart Cross frequency table – Column chart

Evaluation

Very Good Good

Fair

Bad

Sum

11 14

2 7

1 5

20 30

6 4

Male Female

25

9

6

50

10 Sum

Evaluation by Gender

Gender by Evaluation

16 14 14 14 11 12

10 11

7 8 6 5 6 7 4 6 4 5 2 4 1 2 2 1 0

MALE FEMALE VERY GOOD GOOD FAIR BAD

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Very Good Good Fair Bad Male Female

Contingency table – Stacked column Contingency table – Stacked column

Evaluation

Very Good Good

Fair

Bad

Sum

Male Female

6 4

11 14

2 7

1 5

20 30

Sum

10

25

9

6

50 Evaluation by Gender

Gender by Evaluation

30 5 14 25

7 20 1 2 15

11 14 11 10 4 7 5 6 5 6 4 0

2 FAIR 1 BAD MALE FEMALE VERY GOOD GOOD

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Very Good Good Fair Bad Male Female

Cross tab: grand-percent Cross tab: grand-percent

Evaluation

Very Good Good

Fair

Bad

Sum

Male Female

12% 8%

22% 28%

4% 14%

2% 10%

40% 60%

Sum

20%

50%

18%

12%

100%

Evaluation by Gender

Gender by Evaluation

70%

60% 28% 10% 50% 22% 14% 40% 2% 4% 30% 14% 22% 12% 28% 20% 10% 8% 10% 12% 4% 2% 8% 0%

MALE FEMALE VERY GOOD GOOD FAIR BAD

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Very Good Good Fair Bad Male Female

Cross tab: Column-percent Cross tab: Column-percent

Evaluation

Very Good

Good

Fair

Bad

TOTAL

Male Female

60% 40%

44% 56%

22% 78%

17% 83%

40% 60%

Sum

100%

Gender by Evaluation

Gender by evaluation

100% 40% 56% 78% 83% 83% 78% 80%

60% 56% 60% 60% 44% 40% 40% 44% 22% 17% 20% 22% 17%

0% VERY GOOD GOOD FAIR BAD Very Good Good Fair Bad

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Male Female Male Female

Cross tab: Row-percent Cross tab: Row-percent

Evaluation

Very Good Good

Fair

Bad

Sum

Male Female

55% 47%

30% 13%

10% 23%

5% 17%

100% 100%

GRAND

50%

20%

18%

12%

100%

Evaluation by Gender

60% 55% 17% 5% 10% 47% 50%

23% 40%

30% 55% 30% 23%

47% 17% 20% 13% 10% 10% 5% 30% 13% 0% MALE FEMALE MALE FEMALE

PROBABILITY & STATISTICS – Bui Duong Hai – NEU – www.mfe.edu.vn/buiduonghai

Very Good Good Fair Bad Very Good Good Fair Bad

Scale variable: Column chart Scale variable: Column chart

Age

23 26

38 40 43

54 58 63 Sum

Freq.

2% 4% 4% 4% 8% 6% 10% 16% 14% 8% 10% 8% 4% 2% 100%

Age of customer

8 8 7 7 6

5 5 5 4 4 4 4 3 3 2 2 2 2 2 1 1 1 0

PROBABILITY & STATISTICS – Bui Duong Hai – NEU – www.mfe.edu.vn/buiduonghai

23 26 28 32 35 36 38 40 43 47 50 54 58 63

Scale variable: Column chart Scale variable: Column chart

Age

23 26

38 40 43

54 58 63 Sum

Freq.

2% 4% 4% 4% 8% 6% 10% 16% 14% 8% 10% 8% 4% 2% 100%

Age of customer

8 8 7 7 6

5 5 5 4 4 4 4 3 3 2 2 2 2 2 1 1 1 0

PROBABILITY & STATISTICS – Bui Duong Hai – NEU – www.mfe.edu.vn/buiduonghai

23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63

Column chart: Grouped data Column chart: Grouped data

Age

Sum

Freq.

20 – 24 1

25 – 29 4

30 – 34 2

35 – 39 12

40 – 44 15

45 – 49 4

55 – 59 2

60 – 64 1

50 – 54 9

24%

30%

100%

18%

Age of customer

30%

24%

18%

8%

2%

4%

2%

PROBABILITY & STATISTICS – Bui Duong Hai – NEU – www.mfe.edu.vn/buiduonghai

20-24 25-29 30-34 35-39 40-44 45-49 50-54 55-59 60-64

Column chart: Histogram Column chart: Histogram

Age

20 – 29

30 – 39

40 – 49

50 – 59

60 – 69

Sum

Freq.

10%

28%

38%

22%

100%

Age of customer

38%

28%

22%

10%

2%

PROBABILITY & STATISTICS – Bui Duong Hai – NEU – www.mfe.edu.vn/buiduonghai

20-29 30-39 40-49 50-59 60+

Histogram – Cumulative chart Histogram – Cumulative chart

Customer’s Age

Age

Freq.

Cumula tive

40% 100% 100% 38%

98% 90% 35%

20-29

10%

80% 76% 30% 28% 70%

30-39

28%

38%

25% 60% 22%

20% 50%

40-49

38%

76%

40% 38% 15%

50-59

22%

98%

30% 10% 10% 20%

60+

100%

5% 10% 10% 2%

0% 0%

20-29 30-39 40-49 50-59 60+

 Also called: Ogive,

% Cumulative %

Pareto chart

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Histogram Histogram

Waiting time (minute)

Freq

25 100% 100%

Waiting time

Cumula tive

96% 90%

20 86% 20 80%

[0 – 5)

30%

70% 70% 15 15 60%

[5 – 10)

40%

70%

50%

10 40%

[10 – 15)

16%

86%

30% 30%

5 5 20%

[15 – 20)

10%

96%

2 10%

20+

100%

0 0%

0 - 5 5 - 10 10 -15 15 - 20 20 +

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Freq. Cummulative %

Distribution shape Distribution shape

 Symmetric and Asymmetric distribution

Positively skewed Right skewed

Negatively skewed Left skewed

Symmetrical distribution (Bell shaped)

Asymetrical / Skewed distribution

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Line chart for Time series Line chart for Time series

Sales of product A and B over time

A B

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Combined chart Combined chart

 VN Index and Volume of transaction

VIETNAM STOCK EXCHANGE

700 1060

1040 600 1020

500 1000

980 400 960 300 940

920 200

900 100 880

0 860

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Volume (VND. Bil.) VN Index

Radar (Spider web) chart Radar (Spider web) chart

 Same scale variables (multi-dimension)

Employee Evaluation

Staff

Dimension

A

B

Knowledge 80

85

50 Loyalty

Skill 90

50

30

60

80

65 Harmony

Learning

90

60

65

80 Attitude

75 Discipline

Knowledge Skill Learning Discipline Attitude Harmony Loyalty

50 50 60 65 80 90 85

80 90 80 75 60 65 30

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Scatter plot Scatter plot

 Using for pair sample (dependent sample)

Output – Labor relationship

Labor Output

250

300

130

220

250

150

210

200

t u p t u O

110

240

150

200

100

200

260

170

240

Labor

180

280

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10 12 14 16 18 20

Relationship Relationship

 Between two scale variable, there is

r = 0.5

Positively

Week

r = 0.8

Strong

r = 0

Negatively

No correlated

r = – 0.5

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Bubble chat Bubble chat

Profit vs R&D and Advertising

Project R&D Adv. Profit

C, [BUBBLE SIZE]

D, [BUBBLE SIZE]

A, [BUBBLE SIZE]

F, [BUBBLE SIZE]

g n i s i t r e v d A

B, [BUBBLE SIZE]

E, [BUBBLE SIZE]

0 10 20 40 50 60

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30 R&D

Exercise Exercise

 [1] Chapter 2  (p39) 2, 10  (p51) 12, 13, 19, 20, 21  (p60) 32  (p68) 36, 39, 42, 50

Case Problem 1 (p.84) Pelican Stores Case Problem 2 (p.85) Motion Picture Industry

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Lecture Probability & statistics: Chapter 2 - Bùi Dương Hải