Matakuliah
Tahun
: I0272 - STATISTIK PROBABILITAS
: 2009
PENGOLAHAN DAN ANALISIS DATA
Pertemuan 2
Materi



Penyajian data
Ukuran pemusatan dan letak
Ukuran penyebaran
Bina Nusantara University
3
 Penyajian data
Tujuan penyajian data adalah menampilkan kumpulan data
menjadi lebih informatif, dengan menggunakan: tabel,
grafik, diagram.
Data dapat terdiri variabel kategorik dan numerik (kualitatif
dan kuantitatif) mempengaruhi cara penyajian data.
Data
Categorical
(Qualitative)
Numerical
(Quantitative)
Discrete
Bina Nusantara University
Continuous
4
Data Numerik:
Numerical Data
Ordered Array
21, 24, 24, 26, 27, 27, 30, 32, 38, 41
Stem and Leaf
Display
Bina Nusantara University
Frequency Distributions
Cumulative Distributions
2 144677
3 028
4 1
41, 24, 32, 26, 27, 27, 30, 24, 38, 21
Histograms
Tables
Ogive
Polygons
5
Distribusi Frekuensi: data diurutkan
12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58
Class
10 but under 20
20 but under 30
30 but under 40
40 but under 50
50 but under 60
Total
Bina Nusantara University
Frequency
3
6
5
4
2
20
Relative
Frequency
Percentage
.15
.30
.25
.20
.10
1
15
30
25
20
10
100
6
Histogram (Dari distribusi frekuensi):
12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58
Frequency
Histogram
7
6
5
4
3
2
1
0
5
4
3
2
0
5
Class Boundaries
Bina Nusantara University
No Gaps
Between
Bars
6
0
15
25
35
45
55
More
Class Midpoints
7
Data kategorik:
Categorical Data
Graphing Data
Tabulating Data
The Summary Table
Pie Charts
Bar Charts
Bina Nusantara University
Pareto Diagram
8
x
 Ukuran Pemusatan dan letak
• Mean (populasi: parameter μ; sampel: statistik x )
• Modus
: pengamatan yg frekuensinya terbanyak
• Letak
: data harus diurutkan terlebih dahulu:
–
–
–
–
Median
Quartil
Desil
Presentil
: membagi data menjadi dua bagian yg sama (Me)
: membagi data menjadi 4 bag yg sama (Q1, Q2, Q3)
: membagi data menjadi 10 bag yg sama (D5 = Me)
: membagi data menjadi 100 bag yg sama (P50=Me)
Mean = Median =Mode
Symmetric
Contoh: Distribusi Normal
Bina Nusantara University
9
• Mean (Arithmetic Mean) :
– Sample mean
Sample Size
n
X
X1  X 2 
n
n
– Population mean
X
i 1
i

Population Size
N

Bina Nusantara University
X
i 1
N
 Xn
i
X1  X 2 

N
 XN
10
Mean (Arithmetic Mean):
•
•
•
c
The Most Common Measure of
Central Tendency
Affected by Extreme Values (Outliers)
Approximating the Arithmetic Mean
Used when raw data are not available
X
m f
j 1
j j
n
n  sample size
c  number of classes in the frequency distribution
m j  midpoint of the jth class
f j  frequencies of the jth class
0 1 2 3 4 5 6 7 8 9 10
Mean = 5
Bina Nusantara University
0 1 2 3 4 5 6 7 8 9 10 12 14
Mean = 6
11
 Ukuran Penyebaran
Variation
Variance
Range
Population
Variance
Sample
Variance
Interquartile Range
Bina Nusantara University
Standard Deviation
Coefficient of
Variation
Population
Standard
Deviation
Sample
Standard
Deviation
12
Range  X Largest  X Smallest
Range:
Range = 12 - 7 = 5
7
8
9
10
11
Range = 12 - 7 = 5
12
7
8
9
10
11
12
Inter Quartil Range:
Data in Ordered Array: 11 12 13 16 16 17
17 18 21
Interquartile Range  Q3  Q1  17.5  12.5  5
Bina Nusantara University
13
Variance (ragam):
• Important Measure of Variation
• Shows Variation about the Mean
– Sample Variance:
n
S2 
 X
i 1
i
X
2
n 1
– Population Variance:
N
2 
Bina Nusantara University
 X
i 1
i

2
N
14
Standard deviation (standar deviasi/ simpangan baku):
n
2
var ian
standard deviation =
–Sample Standard Deviation:
S
 X
i 1
i
X
n 1
N
–Population Standard Deviation:

 X
i 1
i

2
N
Membandingkan penyebaran (homogenitas) beberapa data:
• Jika mean sama, maka digunakan s (yg nilai kecil=homogen)
• Jika mean tidak sama, maka digunakan CV (coefficient of variation)
Bina Nusantara University
15
Perbandingan penyebaran data: (mean sama, gunakan s)
Data A
Mean = 15.5
s = 3.338
11 12 13 14 15 16 17 18 19 20 21
Data B
Mean = 15.5
s = .9258
11 12 13 14 15 16 17 18 19 20 21
Data C
11 12 13 14 15 16 17 18 19 20 21
Bina Nusantara University
Mean = 15.5
s = 4.57
16
Perbandingan penyebaran data (mean tidak sama,
gunakan CV)
Coefficient of variation (CV):
S
CV  
X
Bina Nusantara University

100%

17