Matakuliah
Tahun
Versi
: I0272 – Statistik Probabilitas
: 2005
: Revisi
Pertemuan 02
Analisis Data
1
Learning Outcomes
Pada akhir pertemuan ini, diharapkan mahasiswa
akan mampu :
• Mahasiswa akan dapat menjelaskan cara
menentukan data pencilan dengan
diagram kotak - garis
2
Outline Materi
•
•
•
•
•
Kuantil suatu sebaran
Kuantil sebaran empiris
Statistik urutan dan kuartil
Diagram kotak-garis
Ukuran pemusatan dan variabilitas
3
Descriptive Statistics:
Tabular and Graphical Methods
•
•
•
•
Summarizing Qualitative Data
Summarizing Quantitative Data
Exploratory Data Analysis
Crosstabulations
and Scatter Diagrams
4
Summarizing Qualitative Data
•
•
•
•
•
Frequency Distribution
Relative Frequency
Percent Frequency Distribution
Bar Graph
Pie Chart
5
Contoh Soal: Marada Inn
• Frequency Distribution
Rating
Frequency
Poor
2
Below Average
3
Average
5
Above Average
9
Excellent
1
Total
20
6
Contoh Soal: Marada Inn
• Relative Frequency and Percent Frequency
Distributions
Relative
Percent
Rating
Frequency Frequency
Poor
.10
10
Below Average
.15
15
Average
.25
25
Above Average
.45
45
Excellent
.05
5
Total
1.00
100
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Contoh Soal: Marada Inn
• Bar Graph
9
Frequency
8
7
6
5
4
3
2
1
Poor
Below Average Above Excellent
Average
Average
Rating
8
Summarizing Quantitative
Data
• Frequency Distribution
• Relative Frequency and Percent
Frequency Distributions
• Dot Plot
• Histogram
• Cumulative Distributions
• Ogive
9
Contoh Soal: Hudson Auto Repair
The manager of Hudson Auto would like to get a
better picture of the distribution of costs for engine
tune-up parts. A sample of 50 customer invoices has
been taken and the costs of parts, rounded to the
nearest dollar, are listed below.
91
71
104
85
62
78
69
74
97
82
93
72
62
88
98
57
89
68
68
101
75
66
97
83
79
52
75
105
68
105
99
79
77
71
79
80
75
65
69
69
97
72
80
67
62
62
76
109
74
73
10
Contoh Soal: Hudson Auto Repair
Cumulative Percent Frequency
• Ogive with Cumulative Percent Frequencies
100
80
60
40
20
50
60
70
80
90
100
110
Parts
Cost ($)
11
Contoh Soal: Hudson Auto Repair
• Stem-and-Leaf Display
5 2 7
6 2 2 2 2 5 6 7 8 8 8 9 9 9
7 1 1 2 2 3 4 4 5 5 5 6 7 8 9 9
8 0 0 2 3 5 8 9
9 1 3 7 7 7 8 9
10 1 4 5 5 9
12
Contoh Soal: Hudson Auto Repair
• Stretched Stem-and-Leaf Display
5 2
5 7
6 2 2 2 2
6 5 6 7 8 8 8 9 9 9
7 1 1 2 2 3 4 4
7 5 5 5 6 7 8 9 9 9
8 0 0 2 3
8 5 8 9
9 1 3
9 7 7 7 8 9
10 1 4
10 5 5 9
13
Scatter Diagram
• A Positive Relationship
y
x
14
Scatter Diagram
• A Negative Relationship
y
x
15
Tabular and Graphical Procedures
Data
Qualitative Data
Tabular
Methods
•Frequency
Distribution
•Rel. Freq. Dist.
•% Freq. Dist.
•Crosstabulation
Graphical
Methods
•Bar Graph
•Pie Chart
Quantitative Data
Tabular
Methods
•Frequency
Distribution
•Rel. Freq. Dist.
•Cum. Freq. Dist.
•Cum. Rel. Freq.
Distribution
•Stem-and-Leaf
Display
•Crosstabulation
Graphical
Methods
•Dot Plot
•Histogram
•Ogive
•Scatter
Diagram
16
Measures of Location
•
•
•
•
•
Mean
Median
Mode
Percentiles
Quartiles
17
Mean
• The mean of a data set is the average
of all the data values.
x
• If the data are from a sample, the mean
is denoted by
 xi
x
.
n
• If the data are from a population, the
mean is denoted by m (mu).
 xi

N
18
Quartiles
• Quartiles are specific percentiles
• First Quartile = 25th Percentile
• Second Quartile = 50th Percentile =
Median
• Third Quartile = 75th Percentile
19
Measures of Variability
•
•
•
•
•
Range
Interquartile Range
Variance
Standard Deviation
Coefficient of Variation
20
Variance
• The variance is the average of the
squared differences between each data
value and the mean.
• If the data set is a sample, the variance
is denoted by s2. 2  ( x  x ) 2
s 
i
n 1
• If the data set is a population, the
variance is denoted by  2.
 ( xi   ) 2
 
N
2
21
Coefficient of Variation
• The coefficient of variation indicates how
large the standard deviation is in relation
to the mean.
• If the data set is a sample, the coefficient
of variation is computed as follows:
s
(100)
x
• If the data set is a population, the
coefficient of variation is computed as
follows:  (100)

22
• Selamat Belajar Semoga Sukses.
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