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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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
PROBABILITY & STATISTICS– Bui Duong Hai – NEU – www.mfe.edu.vn/buiduonghai 1
Raw data
No. Sex (Male /
Female)
Age
(year)
Waiting time
(Minute)
Evaluation
(VG, G, F, B)
1 Female 43 15 to 20 Bad
2 Male 23 0 to 5 Good
3 Female 36 5 to 10 Very Good
50 Female 28 10 to 15 Fair
PROBABILITY & STATISTICS – Bui Duong Hai – NEU – www.mfe.edu.vn/buiduonghai 2
Data from a customer survey, n = 50 observations
Frequency & Relative frequency
Frequency table of Gender
Relative frequency (proportion): =
( )
PROBABILITY & STATISTICS – Bui Duong Hai – NEU – www.mfe.edu.vn/buiduonghai 3
Sex Male Female
Frequency 20 30
Sex Male Female
Relative frequency
Proportion, percent
0.4
40%
0.6
60%
Pie chart
[VAL
UE]
[PER
CE
[VAL
UE]
[PER
CE
Gender
Male
Female
PROBABILITY & STATISTICS – Bui Duong Hai – NEU – www.mfe.edu.vn/buiduonghai 4
Sex Male Female
Freq. 20 30
% 40% 60%
Evalua
tion
Very
Good
Good Fair Bad
Freq. 10 25 9 6
% 20% 50% 18% 12%
[VALUE
]
[PERCE
NTAGE][VALUE
]
[PERCE
NTAGE]
[VALUE
]
[PERCE
NTAGE]
[VALUE
]
[PERCE
NTAGE]
Evaluation
Very Good
Good
Fair
Bad
Column chart
PROBABILITY & STATISTICS – Bui Duong Hai – NEU – www.mfe.edu.vn/buiduonghai 5
Evaluation Freq. %
Very Good 10 20%
Good 25 50%
Fair 9 18%
Bad 6 12%
TOTAL 50 100%
10
25
9
6
0
5
10
15
20
25
30
Very Good Good Fair Bad
Evaluation
Cross frequency table – Column chart
PROBABILITY & STATISTICS – Bui Duong Hai – NEU – www.mfe.edu.vn/buiduonghai 6
Evaluation Very Good Good Fair Bad Sum
Male 6 11 2 1 20
Female 4 14 7 5 30
Sum 10 25 9 6 50
6
4
11
14
2
7
1
5
0
2
4
6
8
10
12
14
16
MALE FEMALE
Evaluation by Gender
Very Good Good Fair Bad
6
11
2 1
4
14
7
5
VERY GOOD GOOD FAIR BAD
Gender by Evaluation
Male Female
Contingency table – Stacked column
PROBABILITY & STATISTICS – Bui Duong Hai – NEU – www.mfe.edu.vn/buiduonghai 7
Evaluation Very Good Good Fair Bad Sum
Male 6 11 2 1 20
Female 4 14 7 5 30
Sum 10 25 9 6 50
6 4
11 14
2
7
1
5
0
5
10
15
20
25
30
35
MALE FEMALE
Evaluation by Gender
Very Good Good Fair Bad
6
11
2 1
4
14
7
5
VERY GOOD GOOD FAIR BAD
Gender by Evaluation
Male Female
Cross tab: grand-percent
PROBABILITY & STATISTICS – Bui Duong Hai – NEU – www.mfe.edu.vn/buiduonghai 8
Evaluation Very Good Good Fair Bad Sum
Male 12% 22% 4% 2% 40%
Female 8% 28% 14% 10% 60%
Sum 20% 50% 18% 12% 100%
12% 8%
22% 28%
4%
14%
2%
10%
0%
10%
20%
30%
40%
50%
60%
70%
MALE FEMALE
Evaluation by Gender
Very Good Good Fair Bad
12%
22%
4% 2%
8%
28%
14%
10%
VERY GOOD GOOD FAIR BAD
Gender by Evaluation
Male Female
Cross tab: Column-percent
PROBABILITY & STATISTICS – Bui Duong Hai – NEU – www.mfe.edu.vn/buiduonghai 9
Evaluation Very Good Good Fair Bad TOTAL
Male 60% 44% 22% 17% 40%
Female 40% 56% 78% 83% 60%
Sum 100% 100% 100% 100% 100%
60%
44%
22%
17%
40% 56% 78% 83%
VERY GOOD GOOD FAIR BAD
Gender by Evaluation
Male Female
60%
44%
22%
17%
40%
56%
78%
83%
0%
20%
40%
60%
80%
100%
Very Good Good Fair Bad
Gender by evaluation
Male Female
Cross tab: Row-percent
PROBABILITY & STATISTICS – Bui Duong Hai – NEU – www.mfe.edu.vn/buiduonghai 10
Evaluation Very Good Good Fair Bad Sum
Male 30% 55% 10% 5% 100%
Female 13% 47% 23% 17% 100%
GRAND 20% 50% 18% 12% 100%
30%
13%
55%
47%
10%
23%
5%
17%
0%
10%
20%
30%
40%
50%
60%
MALE FEMALE
Evaluation by Gender
Very Good Good Fair Bad
30%
13%
55%
47%
10%
23%
5%
17%
MALE FEMALE
Evaluation by Gender
Very Good Good Fair Bad
Scale variable: Column chart
Age 23 26 28 32 35 36 38 40 43 47 50 54 58 63 Sum
Freq. 1 2 2 2 4 3 5 8 7 4 5 4 2 1 50
% 2% 4% 4% 4% 8% 6% 10% 16% 14% 8% 10% 8% 4% 2% 100%
PROBABILITY & STATISTICS – Bui Duong Hai – NEU – www.mfe.edu.vn/buiduonghai 11
1
2 2 2
4
3
5
8
7
4
5
4
2
1
0
1
2
3
4
5
6
7
8
9
23 26 28 32 35 36 38 40 43 47 50 54 58 63
Age of customer
Scale variable: Column chart
Age 23 26 28 32 35 36 38 40 43 47 50 54 58 63 Sum
Freq. 1 2 2 2 4 3 5 8 7 4 5 4 2 1 50
% 2% 4% 4% 4% 8% 6% 10% 16% 14% 8% 10% 8% 4% 2% 100%
PROBABILITY & STATISTICS – Bui Duong Hai – NEU – www.mfe.edu.vn/buiduonghai 12
1
2 2 2
4
3
5
8
7
4
5
4
2
1
0
1
2
3
4
5
6
7
8
9
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
Age of customer
Column chart: Grouped data
Age
20 –
24
25 –
29
30 –
34
35 –
39
40 –
44
45 –
49
50 –
54
55 –
59
60 –
64
Sum
Freq. 1 4 2 12 15 4 9 2 1 50
% 2% 8% 4% 24% 30% 8% 18% 4% 2% 100%
PROBABILITY & STATISTICS – Bui Duong Hai – NEU – www.mfe.edu.vn/buiduonghai 13
2%
8%
4%
24%
30%
8%
18%
4% 2%
20-24 25-29 30-34 35-39 40-44 45-49 50-54 55-59 60-64
Age of customer
Column chart: Histogram
Age 20 – 29 30 – 39 40 – 49 50 – 59 60 – 69 Sum
Freq. 5 14 19 11 1 50
% 10% 28% 38% 22% 2% 100%
PROBABILITY & STATISTICS – Bui Duong Hai – NEU – www.mfe.edu.vn/buiduonghai 14
10%
28%
38%
22%
2%
20-29 30-39 40-49 50-59 60+
Age of customer
Histogram – Cumulative chart
10%
28%
38%
22%
2%10%
38%
76%
98%
100%
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
0%
5%
10%
15%
20%
25%
30%
35%
40%
20-29 30-39 40-49 50-59 60+
Customer’s Age
% Cumulative %
PROBABILITY & STATISTICS – Bui Duong Hai – NEU – www.mfe.edu.vn/buiduonghai 15
Age Freq. %
Cumula
tive
20-29 5 10% 10%
30-39 14 28% 38%
40-49 19 38% 76%
50-59 11 22% 98%
60+ 1 2% 100%
Also called: Ogive,
Pareto chart
Histogram
PROBABILITY & STATISTICS – Bui Duong Hai – NEU – www.mfe.edu.vn/buiduonghai 16
Waiting
time
Freq %
Cumula
tive
[0 – 5) 15 30% 30%
[5 – 10) 20 40% 70%
[10 – 15) 8 16% 86%
[15 – 20) 5 10% 96%
20+ 2 4% 100%
15
20
8
5
2
30%
70%
86%
96%
100%
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
0
5
10
15
20
25
0 - 5 5 - 10 10 -15 15 - 20 20 +
Waiting time (minute)
Freq. Cummulative %
Distribution shape
Symmetric and Asymmetric distribution
PROBABILITY & STATISTICS – Bui Duong Hai – NEU – www.mfe.edu.vn/buiduonghai 17
Symmetrical
distribution
(Bell shaped)
Positively skewed
Right skewed
Negatively skewed
Left skewed
Asymetrical / Skewed distribution
Line chart for Time series
10
20
30
40
50
60
70
Sales of product A and B over time
A B
PROBABILITY & STATISTICS – Bui Duong Hai – NEU – www.mfe.edu.vn/buiduonghai 18
Combined chart
VN Index and Volume of transaction
PROBABILITY & STATISTICS – Bui Duong Hai – NEU – www.mfe.edu.vn/buiduonghai 19
860
880
900
920
940
960
980
1000
1020
1040
1060
0
100
200
300
400
500
600
700
VIETNAM STOCK EXCHANGE
Volume (VND. Bil.) VN Index
Radar (Spider web) chart
Same scale variables (multi-dimension)
PROBABILITY & STATISTICS – Bui Duong Hai – NEU – www.mfe.edu.vn/buiduonghai 20
50
50
60
65
80
90
85
80
90
80
75
60
65
30
Knowledge
Skill
Learning
DisciplineAttitude
Harmony
Loyalty
Employee Evaluation
Dimension
Staff
A B
Knowledge 50 80
Skill 50 90
Learning 60 80
Discipline 65 75
Attitude 80 60
Harmony 90 65
Loyalty 85 30
Scatter plot
0
50
100
150
200
250
300
10 12 14 16 18 20
O
u
tp
u
t
Labor
Output – Labor relationship
PROBABILITY & STATISTICS – Bui Duong Hai – NEU – www.mfe.edu.vn/buiduonghai 21
Labor Output Labor Output
11 80 15 250
11 130 16 220
12 150 17 210
13 110 18 240
13 150 18 200
13 200 17 260
15 170 19 240
14 180 19 280
Using for pair sample (dependent sample)
Relationship
Between two scale variable, there is
PROBABILITY & STATISTICS – Bui Duong Hai – NEU – www.mfe.edu.vn/buiduonghai 22
Positively
Week
Strong
Negatively
No
correlated
r = 0.5
r = – 0.5
r = 0.8
r = 0
Bubble chat
PROBABILITY & STATISTICS – Bui Duong Hai – NEU – www.mfe.edu.vn/buiduonghai 23
Project R&D Adv. Profit
A 30 35 50
B 40 25 40
C 45 50 18
D 15 45 22
E 50 10 15
F 10 30 20
A, [BUBBLE
SIZE]
B, [BUBBLE
SIZE]
C, [BUBBLE
SIZE]D, [BUBBLE
SIZE]
E, [BUBBLE
SIZE]
F, [BUBBLE
SIZE]
0
10
20
30
40
50
60
0 10 20 30 40 50 60
A
d
ve
rt
is
in
g
R&D
Profit vs R&D and Advertising
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
PROBABILITY & STATISTICS – Bui Duong Hai – NEU – www.mfe.edu.vn/buiduonghai 24