Pengantar Ilmu
Statistika
By : Ratih Rahmahwati
Hal. 1
SUB POKOK BAHASAN

Definisi ilmu statistik
Klasifikasi statistik dan Klasifikasi
data

Materi besar :




Statistik deskriptif
Statistik inferensi
Statistik multivariate
Hal. 2
Definisi ilmu statistik

DEFINISI menurut The random House Collage
Dictionary
“Ilmu (science) yang berkaitan
dengan pengumpulan (collection),
analisis, dan interpretasi suatu fakta
numerik atau data”
 statistik merupakan the science of data.
Hal. 3
Peran Statistik




Problem : informasi yang tidak lengkap 
derajat ketidakpastian (level of uncertainty)
Statistik menjadi unique karena
kemampuannya untuk menyatakan (quantify)
ketidakpastian.
Kontribusi utama statistik adalah
memungkinkan kita membuat inferensi/dugaan
– mengestimasi dan membuat keputusan
tentang parameter populasi – dengan ukuran
ketidakpastian tertentu  untuk mengevaluasi
dugaan berdasarkan data sampel
Experimental research dalam engineering
melibatkan penggunaan data eksperimen – yaitu
sample – untuk menduga perilaku dari populasi
Hal. 4
Klasifikasi statistik
Statistical
Methods
Descriptive
Statistics
Inferential
Statistics
Berdasarkan banyaknya data yang dianalisis :
•Univariate data analysis : satu data
•Bivariate data analysis : dua data
•Multivariate data analysis : lebih dari dua data
Hal. 5
Klasifikasi data
Data
Qualitative (Categorical):
possess no quantitative interpretation
Quantitative (Numerical):
represent the quantity/amount of something
Measured on a numerical scale
Examples:



Marital Status
Political Party
Eye Color
(Defined categories)
Discrete
Examples:


Continuous
Examples:
Number of Children  Weight
Defects per hour

Voltage
(Counted items)
(Measured
characteristics)
Hal. 6
Macam Data

Berdasarkan nilai (value) dari data/variabel tersebut:
 Scale : Data values are numeric values on an interval or
ratio scale (e.g., age, income). Scale variables must be
numeric.
 Ordinal : Data values represent categories with some
intrinsic order (e.g., low, medium, high; strongly agree,
agree, disagree, strongly disagree).
Ordinal
variables can be either string (alphanumeric) or numeric
values that represent distinct categories (e.g., 1=low,
2=medium, 3=high). In general, it is more reliable to use
numeric codes to represent ordinal data.
Note: for
ordinal string variables, the alphabetic order of string
values is assumed to reflect the true order of the
categories.
 Nominal : Data values represent categories with no
intrinsic order (e.g., job category or company division).
Nominal variables can be either string (alphanumeric) or
numeric values that represent distinct categories (e.g.,
1=Male, 2=Female).
Hal. 7
Macam Data

Berdasarkan sumber data :




Data Primer : data yang pengambilannya dilakukan sendiri
Data sekunder : data yang didapatkan dari apa yang sudah
dikumpulkan pihak lain
Berdasarkan sifatnya

Data Kuantitatif : menyatakan kuantitas / jumlah dari sesuatu,
diukur dalam skala numerik tertentu. Contoh : waktu tunggu
(dalam menit) sebelum proses komputer dimulai,

Data kualitatif / kategorikal : tidak menunjukkan interpretasi
kuantitatif, hanya bisa diklasifikasikan. Contoh : bidang / bagian
pekerjaan yang ditempati oleh lulusan perguruan tinggi
Berdasarkan cara mendapatkannya :


Data diskrit : data yang tertentu nilainya, didapatkan dengan
jalan menghitung (countable). Contoh : jumlah pelanggan per jam
Data kontinu : data yang tidak tertentu nilainya, didapatkan
dengan jalan mengukur (measurale). Contoh : waktu untuk
melayani pelanggan
Hal. 8
Teknik Sampling
Samples
Probability Samples
Non-Probability
Samples
kuota
purposive
Simple
Random
accidental
Systematic
Stratified
Cluster
jenuh
snowball
Hal. 9
Statistical Sampling

Items of the sample are chosen based
on known or calculable probabilities
Probability Samples
Simple
Stratified
Systematic
Cluster
Random
Teknik sampling yang memberikan peluang yang sama bagi setiap anggota
populasi untuk dipilih menjadi anggota sampel
Hal. 10
Simple Random Samples

Every individual or item from the
population has an equal chance of being
selected

Selection may be with replacement or
without replacement

Samples can be obtained from a table of
random numbers or computer random
number generators
populasi
sampel
Hal. 11
Stratified Samples

Population divided into subgroups (called strata) according to
some common characteristic

Simple random sample selected from each subgroup

Samples from subgroups are combined into one
Population
Divided
into 4
strata
Sample
Populasi berstrata
Proportionated
atau
disproportionated
sampel
Hal. 12
Systematic Samples

Decide on sample size: n

Divide frame of N individuals into groups of k individuals:
k=N/n

Randomly select one individual from the 1st group

Select every kth individual thereafter
N = 64
n=8
First Group
k=8
Hal. 13
Cluster Samples

Population is divided into several “clusters,” each
representative of the population

A simple random sample of clusters is selected

All items in the selected clusters can be used,
or items can be chosen from a cluster using
another probability sampling technique
Population
divided into 16
clusters.
Randomly selected clusters for sample
B
A
B
A
C
D
E
D
Hal. 14
Nonprobability sampling
Non-Probability
Samples
kuota
purposive
accidental
jenuh
snowball
–Teknik sampling yang tidak memberikan peluang yang
sama pada semua anggota populasi untuk dipilih menjadi
anggota sampel.
–Berdasarkan jugdement dan convenience
Hal. 15
Nonprobability sampling

Sampling kuota
pengambilan sampel dari populasi yang mempunyai ciri-ciri
tertentu sampai jumlah (kuota) yang diinginkan
contoh : sekelompok peneliti yang terdiri dari 5 orang
melakukan penelitian terhadap pegawai golongan II.
Jumlah sampel ditentukan 100. sehingga setiap anggota
peneliti dapat memilih sampel secara bebas sesuai denga
karakteristik yang ditentukan (golongan II) sebanyak 20
orang

Sampling aksidental
pengambilan sampel berdasarkan kebetulan, yaitu siapa
saja yang secara kebetulan bertemu dengan peneliti dapat
digunakan sebagai sampel bila dipandang orang tersebut
cocok sebagai sumber data
Hal. 16
Nonprobability sampling



Sampling purposive
pengambilan sampel dengan pertimbangan tertentu
contoh : penelitian tentang disiplin pegawai, maka sampel
yang dipilih adalah orang yang ahli dalam bidang
kepegawaian saja
Sampling jenuh
pengambilan sampel dengan mengambil semua anggota
populasi sebagai sampel (bila jumlah populasi relatif
sedikit, kurang dari 30, sama dengan sensus)
Snowball sampling
pengambilan sampel yang mula-mula jumlahnya sedikit,
kemudian sampel itu diminta memilih teman-temannya
untuk dijadikan sampel, begitu seterusnya sehingga jumlah
sampel semakin banyakb
Hal. 17
STATISTIK DESKRIPTIF
Hal. 18
Statistik Deskriptif
1.Involves



Collecting Data
Presenting Data
Characterizing Data
2.Purpose




Describe Data
Preserve in useful
ways
Know data patern
Summary basic shape
of data
50
$
25
0
Q1
Q2
Q3
Q4
X = 30.5 S2 = 113
Hal. 19
STATISTIK DESKRIPTIF
Deskripsi statistik dapat dilakukan
dengan dua cara :
-
-
Metode grafik
Metode numerik
Mendeskripsikan suatu data sangat
tergantung pada jenis data apakah
kuantitatif atau kualitatif
Hal. 20
Bar Chart Solution*
Mfg.
Lotus
Microsoft
Wordperf.
Others
0%
20%
40%
Market Share
(%)
60%
Hal. 21
Pie Chart Solution*
Market Share
Wordperf.
10%
Others
15%
Lotus
15%
Microsoft
60%
Hal. 22
Dot Chart Solution*
Mfg.
Lotus
Microsoft
Wordperf.
Others
0%
20%
40%
Market Share
(%)
60%
Hal. 23
Stem-and-Leaf Display
1. Divide Each
Observation into Stem
Value and Leaf Value
 Stem Value Defines
Class
 Leaf Value Defines
Frequency (Count)
2 144677
3 028
26
4 1
2. Data: 21, 24, 24, 26, 27, 27, 30, 32,
38, 41
Hal. 24
Numerical Data Properties
Central
Tendency
(Location)
Variation
(Dispersion)
Shape
Hal. 25
Numerical Data Properties &
Measures
Numerical Data
Properties
Central
Tendency
Variation
Shape
Mean
Range
Median
Interquartile Range
Mode
Variance
Skew
Standard Deviation
Hal. 26
Central Tendency
Statistik Industri
Hal. 27
Numerical Data Properties &
Measures
Numerical Data
Properties
Central
Tendency
Variation
Shape
Mean
Range
Median
Interquartile Range
Mode
Variance
Skew
Standard Deviation
Hal. 28
Mean
1.
2.
3.
4.
5.
Measure of Central Tendency
Most Common Measure
Acts as ‘Balance Point’
Affected by Extreme Values (‘Outliers’)
Formula (Sample Mean)
n
X
 Xi
i 1
n

X1  X 2    X n
n
Hal. 29
Mean Example

Raw Data: 10.3 4.98.9 11.7 6.3 7.7
n
X

 Xi
i 1
n

X1  X 2  X 3  X 4  X 5  X 6
6
103
.  4.9  8.9  117
.  6.3  77
.
6
 8.30
Hal. 30
Numerical Data Properties & Mea
Numerical Data
Properties
Central
Tendency
Variation
Shape
Mean
Range
Median
Interquartile Range
Mode
Variance
Skew
Standard Deviation
Hal. 31
Median
1. Measure of Central Tendency
2. Middle Value In Ordered Sequence
If Odd n, Middle Value of Sequence
If Even n, Average of 2 Middle Values
3.
Position of Median in Sequence
Positioning Point
n1
2
4. Not Affected by Extreme Values
Hal. 32
Median Example Odd-Sized
Sample
Raw Data:24.122.6 21.5 23.7 22.6
Ordered: 21.5 22.6 22.6 23.7 24.1
Position:
1
2
3
4
5
n1 51

 3.0
Positioning Point
2
2
Median 226
.
Hal. 33
Median Example Even-Sized Sample
Raw Data: 10.3 4.9 8.9 11.7 6.3 7.7
Ordered:
4.9 6.3 7.7 8.9 10.3 11.7
Position:
1
2
3
4
5
6
n1 61

 3.5
Positioning Point
2
2
77
.  8.9
 8.30
Median
2
Hal. 34
Numerical Data Properties &
Measures
Numerical Data
Properties
Central
Tendency
Variation
Shape
Mean
Range
Median
Interquartile Range
Mode
Variance
Skew
Standard Deviation
Hal. 35
Mode
1. Measure of Central Tendency
2. Value That Occurs Most Often
3. Not Affected by Extreme Values
4. May Be No Mode or Several Modes
5. May Be Used for Numerical & Categorical
Data
Hal. 36
Mode Example
No Mode
Raw Data: 10.3 4.9 8.9 11.7 6.3 7.7

One Mode
Raw Data: 6.3 4.9 8.9
6.3 4.9 4.9
More Than 1 Mode
Raw Data: 21 28 28
41


43
43
Hal. 37
Thinking Challenge
You’re
a financial
analyst for PrudentialBache Securities. You
have collected the
following closing stock
prices of new stock
issues: 17, 16, 21,
18, 13, 16, 12, 11.
Describe the stock
prices
in terms of central
tendency.
Hal. 38
Central Tendency Solution*

Mean
n
X 

 Xi
i 1
n

X1  X 2    X 8
8
17  16  21 18  13  16  12  11
8
 155
.
Hal. 39
Central Tendency Solution*




Median
Raw Data:17 16 21 18 13 16 12 11
Ordered: 11 12 13 16 16 17 18 21
Position: 1 2 3 4 5 6 7 8
n1 81

 4.5
Positioning Point
2
2
16  16
 16
Median
2
Hal. 40
Central Tendency Solution*
Mode
Raw Data: 17 16 21 18 13 16 12 11
Ordered: 11 12 13 16 16 17 18 21
Hal. 41
Summary of
Central Tendency Measures
Measure
Equation
Mean
Xi / n
Median
(n+1)Position
2
Mode
none
Description
Balance Point
Middle Value
When Ordered
Most Frequent
Hal. 42
Variation
Statistik Industri
Hal. 43
Numerical Data Properties &
Measures
Numerical Data
Properties
Central
Tendency
Variation
Shape
Mean
Range
Median
Interquartile Range
Mode
Variance
Skew
Standard Deviation
Hal. 44
Range
1. Measure of Dispersion
2. Difference Between Largest & Smallest
Observations
Range X l argest  X smallest
Hal. 45
Disadvantages of the Range

Ignores the way in which data are
distributed
7
8
9
10
11
12
Range = 12 - 7 =
5

7
8
9
10
11
12
Range = 12 - 7 = 5
Sensitive to outliers
4,5
4,120
1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,
Range = 5 - 1 = 4
1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,
Range = 120 - 1 =
119
Hal. 46
Numerical Data Properties &
Measures
Numerical Data
Properties
Central
Tendency
Variation
Shape
Mean
Range
Median
Interquartile Range
Mode
Variance
Standard Deviation
Skew
Hal. 47
Variance & Standard Deviation

1.
Measures of Dispersion

2.
Most Common Measures

3.
Consider How Data Are
Distributed

4.
or )
Show Variation About Mean (X
X = 8.3
4 6
8 10 12
Hal. 48
Sample Variance Formula
n
2
S 


i 1
Xi  X
2
n - 1 in
denominator! (Use
N if Population
Variance)
n1
X1  X
2
 X2  X
2
   Xn  X
2
n1
Hal. 49
Sample Standard Deviation Formula
S S
2
n


 Xi  X
i 1
2
n1
X1  X
2
 X2  X
2
   Xn  X
2
n1
Hal. 50
Variance Example
Raw Data:10.34.9 8.9 11.7 6.3 7.7

n
2
S 

i 1
Xi  X
n
2
whereX 
n1
2
2
S 
2
 Xi
i 1
n
 8.3
103
.  8.3  4.9  8.3    77
.  8.3
2
61
 6.368
Hal. 51
Thinking Challenge
You’re
a financial
analyst for PrudentialBache Securities. You
have collected the
following closing stock
prices of new stock
issues: 17, 16, 21, 18,
13, 16, 12, 11.
What are the
variance and standard
deviation of the stock
prices?
Hal. 52
Variation Solution*
Sample Variance
Raw Data: 17 16 21 18 13 16 12 11
n
2
S 
2
S 

i 1
Xi  X
whereX 
n1
17  155
.
 1114
.
n
2
2
 16  155
.
2
 Xi
i 1
n
 155
.
   11 155
.
2
81
Hal. 53
Variation Solution*

Sample Standard Deviation
n
2
S S 

i 1
Xi  X
n1
2
 1114
.  3.34
Hal. 54
Comparing Standard Deviations
Data A
11
19
12
20
13
21
14
15
16
17
18
Mean =
15.5
18
Mean =
15.5
s =
3.338
Data B
11
19
12
20
13
21
14
15
16
17
s=
.9258
Data C
11
20
12
21
13
14
15
16
17
18
19
Mean =
15.5
s = 4.57
Hal. 55
Summary of Variation
Measures
Measure
Range
Equation
Description
Xlargest - Xsmallest Total Spread
Interquartile Range Q3 - Q1
Standard Deviation
(Sample)
 X
i
 X
n1
Spread of Middle 50%
2
Dispersion about
Sample Mean
Standard Deviation  X    2 Dispersion about
 i X Population Mean
(Population)
N
Variance
(Sample)
(Xi -X )2
n-1
Squared Dispersion
about Sample Mean
Hal. 56
Numerical Data
Properties
for grouped data
Statistik Industri
Hal. 57
Grouped Data
Raw data unavailable, but grouped into
frequency distribution
Hal. 58
Mean
k
1
X 
n i 1
dimana
f m
i
i
k
n
i 1
f
i
k= number of intervals
fi = the frequency in i th interval
mi = the midpoint in i th interval
Hal. 59
Variance and Standard
Deviation
Variance
s
2
f


Standard Deviation
k
x  nX
2
k
2
s s
2
n 1
Hal. 60
Percentiles
Xk + 1 – Xk
Qd = Xk + [( n + 1) d - k](
(73 + 1)(.25) = 18.5
h-k
)
The greatest cumulative frequency not exceeding 18.5 is 7 for
the first interval , so k = 7. Q.25 will fall in the second
interval, and its cumulative frequency is 30.
Q.25 = 100.0 + [( 18.5 - 7]
(
105.0 – 100.0
30 - 7
) = 102.5
Hal. 61
The Empirical Rule
If the data distribution is bell-shaped,
then the interval:
μ  1σ
contains about 68% of the values in
the population or the sample
X
68
%
μ
μ  1σ
Hal. 62
The Empirical Rule
μ  2σ contains about 95% of the values in
the population or the sample
μ  3σ contains about 99.7% of the values
in the population or the sample
95%
99.7
%
μ  2σ
μ  3σ
Hal. 63
Shape
Statistik Industri
Hal. 64
Numerical Data Properties &
Measures
Numerical Data
Properties
Central
Tendency
Variation
Shape
Mean
Range
Median
Interquartile Range
Mode
Variance
Skew
Standard Deviation
Hal. 65
Shape
1.
Describes How Data Are Distributed
2.
Measures of Shape
 Skew
= Symmetry
Left-Skewed
Mean MedianMode
Symmetric
Right-Skewed
Mean=Median=Mode Mode MedianMean
Hal. 66
Quartiles & Box
Plots
Statistik Industri
Hal. 67
Quartiles
1. Measure of Noncentral Tendency
2. Split Ordered Data into 4 Quarters
Q1
Q2
Q3
25
25
25
%
%
%
3. Position of i-th Quartile
25
%
i  n1
Positioning Point ofQi 
4
Hal. 68
Quartile (Q1) Example



Raw Data:10.34.9 8.9 11.7 6.3 7.7
Ordered: 4.9 6.3 7.7 8.9 10.3 11.7
Position: 1
2
3
4
5
6
1 n  1 1 6  1

 175
Q1 Position 
. 2
4
4
Q1  6.3
Hal. 69
Quartile (Q2) Example



Raw Data:10.34.9 8.9 11.7 6.3 7.7
Ordered: 4.9 6.3 7.7 8.9 10.3 11.7
Position: 1
2
3
4
5
6
2 n  1 2 6  1

 3.5
Q 2 Position
4
4
77
.  8.9
 8.3
Q2 
2
Hal. 70
Quartile (Q3) Example



Raw Data:10.34.9 8.9 11.7 6.3 7.7
Ordered: 4.9 6.3 7.7 8.9 10.3 11.7
Position: 1
2
3
4
5
6
3 n  1 3 6  1

 5.25  5
Q 3 Position
4
4
Q 3  103
.
Hal. 71
Percentiles

The pth percentile in an ordered array of
n values is the value in ith position,
where
p
i
(n  1)
100

Example: The 60th percentile in an ordered
array of 19 values is the value in 12th
position:
p
60
i
(n  1) 
(19  1)  12
100
100
Hal. 72
Numerical Data Properties &
Measures
Numerical Data
Properties
Central
Tendency
Variation
Shape
Mean
Range
Median
Interquartile
Range
Variance
Mode
Skew
Standard Deviation
Hal. 73
Interquartile Range
1. Measure of Dispersion
2. Also Called Midspread
3. Difference Between Third & First
Quartiles
Interquart
ile Range Q3  Q1
4. Spread in Middle 50%
5. Not Affected by Extreme Values
Hal. 74
Interquartile Range
Example:
X
minimum
Median
(Q2)
Q1
25%
12
Q3
25%
30
X
maximum
25%
45
25%
57
70
Interquartile
range
= 57 – 30 =
27
Hal. 75
Thinking Challenge
You’re
a financial
analyst for PrudentialBache Securities. You
have collected the
following closing stock
prices of new stock
issues: 17, 16, 21,
18, 13, 16, 12, 11.
What
are the
quartiles, Q1 and Q3,
and the interquartile
range?
Hal. 76
Quartile Solution*
Q1
Raw Data: 17 16 21 18 13 16 12 11
Ordered: 11 12 13 16 16 17 18 21
Position:
1 2 3 4 5 6 7 8
Q1 Position 
1 n  1
4

1 8  1
4
 2.5
Q1  125
.
Hal. 77
Quartile Solution*
Q3
Raw Data: 17 16 21 18 13 16 12 11
Ordered: 11 12 13 16 16 17 18 21
Position:
1 2 3 4 5 6 7 8
Q 3 Position 
3 n  1
4

3 8  1
4
 6.75  7
Q 3  18
Hal. 78
Interquartile Range Solution*
Interquartile Range
Raw Data: 17 16 21 18 13 16 12 11
Ordered: 11 12 13 16 16 17 18 21
Position:
1 2 3 4 5 6 7 8
Interquart
ile Range Q3  Q1  180
.  125
.  5.5
Hal. 79
Box Plot

1.
Graphical Display of Data Using
5-Number Summary
XsmallestQ1 Median Q3
4
6
8
10
Xlargest
12
Hal. 80
Shape of Box and Whisker Plots

The Box and central line are centered
between the endpoints if data is
symmetric around the median

A Box and Whisker plot can be shown
in either vertical or horizontal format
Hal. 81
Distribution Shape and Box and
Whisker Plot
Left-Skewed
Q1
Q2Q3
Symmetric Right-Skewed
Q1Q2Q3
Q1 Q2 Q3
Hal. 82
Box-and-Whisker Plot Example

Below is a Box-and-Whisker plot for the
following data:
Min
Max
0 2
Q1
2
Q2
2
3
Q3
3
4
5
5
10
27
2 33 55
00 2
27

27
This data is very right skewed, as the plot
Hal. 83
Methods for detecting outliers
Outlier : An observation y that is unusually
large or small relative to the other values in a
data set
Outliers typically are attributable to one of the
following causes:
The measurement is observed, recorded or
entered into computer incorrectly’
The
measurement
comes
from
different
population
The measurement is correct, but represents a
rare event
Hal. 84
Rule of thumb for detecting
Outliers
Z scores
Observation with z scores greater than
3 in absolute value

z  ( y  y) / s
Box Plot
Observation falling between the inner
and outer fences are deemed suspect
outliers
Observation falling beyond outer fences
are deemed highly suspect outliers

Hal. 85
Distorting the Truth
with Descriptive
Techniques
Statistik Industri
Hal. 86
Errors in Presenting Data
1.
Using ‘Chart Junk’
2.
No Relative Basis in
Comparing Data Batches
3.
Compressing the Vertical
Axis
4.
No Zero Point on the
Vertical Axis
Hal. 87
‘Chart Junk’
Bad Presentation
Minimum
Wage
1960:
$1.00
1970:
$1.60
1980:
$3.10
1990:
$3.80
Good Presentation
4
$
Minimum
Wage
2
0
1960 1970 1980 1990
Hal. 88
No Relative Basis
Bad Presentation
A’s by Class
Freq.
Good Presentation
%
300
30%
200
20%
100
10%
0
A’s by Class
0%
FR SO JR SR
FR SO JR SR
Hal. 89
Compressing Vertical Axis
Bad Presentation
200
$
Quarterly
Sales
Good Presentation
50
$
Quarterly
Sales
25
100
0
0
Q1 Q2 Q3 Q4
Q1 Q2 Q3 Q4
Hal. 90
No Zero Point on Vertical Axis
Bad Presentation
$
Good Presentation
Monthly Sales
$
45
60
42
40
39
20
36
0
J M M J S N
Monthly Sales
J M M J
S N
Hal. 91
STATISTIK INFERENSI
Hal. 92
Inferential Statistics
 Making
statements about a population
by examining sample results
Sample statistics
(known)
Population parameters
Inference
(unknown,
Population
but can
be estimated from
sample evidence)
Sample
Ukuran deskripsi numerik yang dihitung dari sampel disebut statistik (karakteristik sampel)
Ukuran deskripsi numerik dari populasi disebut parameter (karakteristik populasi)
Hal. 93
Inferential Statistics
Drawing conclusions and/or making decisions
concerning a population based on sample results.

Estimation


e.g.: Estimate the population mean
weight using the sample mean
weight
Hypothesis Testing

e.g.: Use sample evidence to test
the claim that the population mean
weight is 120 pounds
Hal. 94
STATISTIK
MULTIVARIATE
Hal. 95