Slide PSI 106 Materi Kuliah Statistik
Menampilkan dan Mengartikan
Data
McGraw-Hill/Irwin
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
Dot Plots
Mengelompokkan data sesederhana
mungkin identitas data secara
individual tetap ada
Data ditampilkan dalam bentuk titik
sepanjang garis horisontal sesuai
nilainya
Identik ditumpuk
4-2
Dot Plots - Contoh
Jumlah mobil yang dijual
dalam 24 bulan terakhir
4-3
Distribusi Frekuensi
Distribusi Frekuensi diguanakan untuk
mengorganisasikan data ke dalam bentuk
yang memiliki arti
Keuntungan Distribusi Frekuensi: gambaran
visual tentang bentuk penyebaran data
Kerugian Distribusi Frekuensi:
(1) Hilangnya identitas asli setiap nilai
(2) Sulit melihat penyebaran nilai tiap kelas
Cara lain untuk menggambarkan data
kuantitatif adalah stem-and-leaf display
4-4
Stem-and-Leaf
4-5
Tiap nilai dibagi dua. Digit utama menjadi
STEM dan digit sisanya menjadi LEAF. Stem
dituliskan secara vertikal, Leaf dituliskan
secara horisontal
Keuntungan: identitas setiap nilai tidak hilang
Stem-and-leaf Plot Example
4-6
Stem-and-leaf Plot Example
4-7
Quartiles, Deciles and Percentiles
4-8
Cara alternatif (selain standar deviasi) untuk
menggambarkan penyebaran data adalah
dengan menentukan LOKASI NILAI yang
membagi data menjadi beberapa bagian yang
setara
QUARTILES = KUARTIL (DIBAGI 4)
DECILES = DESIL (DIBAGI 10)
PERCENTILES = PERSENTIL ( DIBAGI 100)
Penghitungan Persentil
Lp = persentil yang dicari (misalnya Persentil 33 L33)
n = jumlah data
Median = L50
Syarat: Median data diurutkan
Rumus Persentil bisa digunakan untuk mencari Desil dan Kuartil
4-9
Percentiles - Example
Listed below are the commissions earned
last month by a sample of 15 brokers at
Salomon Smith Barney’s Oakland,
California, office.
$2,038
$2,097
$2,287
$2,406
$1,758
$2,047
$1,940
$1,471
$1,721 $1,637
$2,205 $1,787
$2,311 $2,054
$1,460
Locate the median, the first quartile, and
the third quartile for the commissions
earned.
4-10
Percentiles – Example (cont.)
Step 1: Organize the data from lowest to
largest value
$1,460
$1,758
$2,047
$2,287
4-11
$1,471
$1,787
$2,054
$2,311
$1,637
$1,940
$2,097
$2,406
$1,721
$2,038
$2,205
Percentiles – Example (cont.)
Step 2: Compute the first and third quartiles.
Locate L25 and L75 using:
L25 (15 1)
25
75
L75 (15 1)
4
12
100
100
Therefore, the first and third quartiles are located at the 4th and 12th
positions,respectively
L25 $1,721
L75 $2,205
4-12
Boxplot - Example
4-13
Boxplot Example
Step1: Create an appropriate scale along the horizontal axis.
Step 2: Draw a box that starts at Q1 (15 minutes) and ends at Q3 (22
minutes). Inside the box we place a vertical line to represent the median (18
minutes).
Step 3: Extend horizontal lines from the box out to the minimum value (13
minutes) and the maximum value (30 minutes).
4-14
Skewness
In Chapter 3, measures of central location (the
mean, median, and mode) for a set of observations
and measures of data dispersion (e.g. range and the
standard deviation) were introduced
Another characteristic of a set of data is the shape.
There are four shapes commonly observed:
–
–
–
–
4-15
symmetric,
positively skewed,
negatively skewed,
bimodal.
Commonly Observed Shapes
4-16
Skewness - Formulas for Computing
Koefisien skewness berkisar antara -3 sampai 3.
– Nilai berkisar -3 skewness negatif
– Nilai 1.63 skewness cukup positif
– Nilai 0,X (terjadi bila mean = median) berarti
distribusi simetris dan skewness tidak ada
4-17
Skewness – An Example
4-18
Following are the earnings per share for a sample of
15 software companies for the year 2007. The
earnings per share are arranged from smallest to
largest.
Compute the mean, median, and standard deviation.
Find the coefficient of skewness using Pearson’s
estimate.
What is your conclusion regarding the shape of the
distribution?
Skewness – An Example Using
Pearson’s Coefficient
X $74.26 $4.95
Step 1: Compute the Mean
X
15
n
Step 2 : Compute the Standard Deviation
XX
s
n 1
2
($0.09 $4.95) 2 ... ($16.40 $4.95) 2 )
$5.22
15 1
Step 3 : Find the Median
The middle value in the set of data, arranged from smallestto largestis 3.18
Step 3 : Compute the Skewness
sk
4-19
3( X Median ) 3($4.95 $3.18)
1.017
s
$5.22
Skewness – A Minitab Example
4-20
Describing Relationship between Two
Variables
4-21
When we study the relationship
between two variables we refer to the
data as bivariate.
One graphical technique we use to
show the relationship between
variables is called a scatter diagram.
To draw a scatter diagram we need two
variables. We scale one variable along
the horizontal axis (X-axis) of a graph
and the other variable along the vertical
axis (Y-axis).
Describing Relationship between Two
Variables – Scatter Diagram Examples
4-22
Describing Relationship between Two
Variables – Scatter Diagram Excel Example
In Chapter 2 we presented data
from AutoUSA. In this case the
information concerned the prices
of 80 vehicles sold last month at
the Whitner Autoplex lot in
Raytown, Missouri. The data
shown include the selling price
of the vehicle as well as the age
of the purchaser.
Is there a relationship between the
selling price of a vehicle and the
age of the purchaser?
Would it be reasonable to conclude
that the more expensive vehicles
are purchased by older buyers?
4-23
Describing Relationship between Two
Variables – Scatter Diagram Excel Example
4-24
Contingency Tables
4-25
A scatter diagram requires that both of the
variables be at least interval scale.
What if we wish to study the relationship
between two variables when one or both are
nominal or ordinal scale? In this case we tally
the results in a contingency table.
Contingency Tables
A contingency table is a cross-tabulation that
simultaneously summarizes two variables of interest.
Examples:
1.
Students at a university are classified by gender and class rank.
2.
A product is classified as acceptable or unacceptable and by the
shift (day, afternoon, or night) on which it is manufactured.
3.
A voter in a school bond referendum is classified as to party
affiliation (Democrat, Republican, other) and the number of children
that voter has attending school in the district (0, 1, 2, etc.).
4-26
Contingency Tables – An Example
A manufacturer of preassembled windows produced 50 windows yesterday. This
morning the quality assurance inspector reviewed each window for all quality
aspects. Each was classified as acceptable or unacceptable and by the shift
on which it was produced. Thus we reported two variables on a single item.
The two variables are shift and quality. The results are reported in the
following table.
Using the contingency table able, the quality of the three shifts can be
compared. For example:
1. On the day shift, 3 out of 20 windows or 15 percent are defective.
2. On the afternoon shift, 2 of 15 or 13 percent are defective and
3. On the night shift 1 out of 15 or 7 percent are defective.
4. Overall 12 percent of the windows are defective
4-27
URAIAN
TINGGI
SEDANG
RENDAH
F
%
F
%
F
%
1
KONFLIK
58
87,9
18
12,1
0
0
2
DURASI
64
97
2
3
0
0
3
KESUKAAN
63
95,5
3
4,5
0
0
4
PEMAIN UTAMA
66
100
0
0
0
0
5
BINTANG TAMU
65
98,5
1
1,5
0
0
6
KONSISTENSI
55
83,4
11
16,6
0
0
7
KECEPATAN CERITA
65
98,5
1
1,5
0
0
8
DAYA TARIK
47
71,2
19
28,8
0
0
9
GAMBAR YANG KUAT
63
94,5
3
5,5
0
0
10
TIMING
46
69,7
20
31,3
0
0
11
TREN
66
100
0
0
0
0
12
KOGNITIF
65
98,5
1
1,5
0
0
13
AFEKTIF
58
87,9
8
12,1
0
0
14
KEBERHASILAN
65
98,5
1
1,5
0
0
4-28
KARAKTERISTIK RESPONDEN
VARIABEL
DATA
JENIS KELAMIN
USIA
PEKERJAAN
4-29
KATEGORI
JUMLAH
PERSEN
PRIA
31
47
WANITA
35
53
12 - 19
3
4,5
20-29
18
27,3
30-39
20
30,3
40-49
15
22,7
50-59
9
13,6
>60
1
1,5
PNS
8
12,1
KARYAWAN
18
27,3
IRT
21
31,8
PELAJAR
6
9,1
WIRASWASTA
4
6,1
PEDAGANG
2
3
BURUH
3
4,5
PENSIUNAN
4
6,1
Data
McGraw-Hill/Irwin
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
Dot Plots
Mengelompokkan data sesederhana
mungkin identitas data secara
individual tetap ada
Data ditampilkan dalam bentuk titik
sepanjang garis horisontal sesuai
nilainya
Identik ditumpuk
4-2
Dot Plots - Contoh
Jumlah mobil yang dijual
dalam 24 bulan terakhir
4-3
Distribusi Frekuensi
Distribusi Frekuensi diguanakan untuk
mengorganisasikan data ke dalam bentuk
yang memiliki arti
Keuntungan Distribusi Frekuensi: gambaran
visual tentang bentuk penyebaran data
Kerugian Distribusi Frekuensi:
(1) Hilangnya identitas asli setiap nilai
(2) Sulit melihat penyebaran nilai tiap kelas
Cara lain untuk menggambarkan data
kuantitatif adalah stem-and-leaf display
4-4
Stem-and-Leaf
4-5
Tiap nilai dibagi dua. Digit utama menjadi
STEM dan digit sisanya menjadi LEAF. Stem
dituliskan secara vertikal, Leaf dituliskan
secara horisontal
Keuntungan: identitas setiap nilai tidak hilang
Stem-and-leaf Plot Example
4-6
Stem-and-leaf Plot Example
4-7
Quartiles, Deciles and Percentiles
4-8
Cara alternatif (selain standar deviasi) untuk
menggambarkan penyebaran data adalah
dengan menentukan LOKASI NILAI yang
membagi data menjadi beberapa bagian yang
setara
QUARTILES = KUARTIL (DIBAGI 4)
DECILES = DESIL (DIBAGI 10)
PERCENTILES = PERSENTIL ( DIBAGI 100)
Penghitungan Persentil
Lp = persentil yang dicari (misalnya Persentil 33 L33)
n = jumlah data
Median = L50
Syarat: Median data diurutkan
Rumus Persentil bisa digunakan untuk mencari Desil dan Kuartil
4-9
Percentiles - Example
Listed below are the commissions earned
last month by a sample of 15 brokers at
Salomon Smith Barney’s Oakland,
California, office.
$2,038
$2,097
$2,287
$2,406
$1,758
$2,047
$1,940
$1,471
$1,721 $1,637
$2,205 $1,787
$2,311 $2,054
$1,460
Locate the median, the first quartile, and
the third quartile for the commissions
earned.
4-10
Percentiles – Example (cont.)
Step 1: Organize the data from lowest to
largest value
$1,460
$1,758
$2,047
$2,287
4-11
$1,471
$1,787
$2,054
$2,311
$1,637
$1,940
$2,097
$2,406
$1,721
$2,038
$2,205
Percentiles – Example (cont.)
Step 2: Compute the first and third quartiles.
Locate L25 and L75 using:
L25 (15 1)
25
75
L75 (15 1)
4
12
100
100
Therefore, the first and third quartiles are located at the 4th and 12th
positions,respectively
L25 $1,721
L75 $2,205
4-12
Boxplot - Example
4-13
Boxplot Example
Step1: Create an appropriate scale along the horizontal axis.
Step 2: Draw a box that starts at Q1 (15 minutes) and ends at Q3 (22
minutes). Inside the box we place a vertical line to represent the median (18
minutes).
Step 3: Extend horizontal lines from the box out to the minimum value (13
minutes) and the maximum value (30 minutes).
4-14
Skewness
In Chapter 3, measures of central location (the
mean, median, and mode) for a set of observations
and measures of data dispersion (e.g. range and the
standard deviation) were introduced
Another characteristic of a set of data is the shape.
There are four shapes commonly observed:
–
–
–
–
4-15
symmetric,
positively skewed,
negatively skewed,
bimodal.
Commonly Observed Shapes
4-16
Skewness - Formulas for Computing
Koefisien skewness berkisar antara -3 sampai 3.
– Nilai berkisar -3 skewness negatif
– Nilai 1.63 skewness cukup positif
– Nilai 0,X (terjadi bila mean = median) berarti
distribusi simetris dan skewness tidak ada
4-17
Skewness – An Example
4-18
Following are the earnings per share for a sample of
15 software companies for the year 2007. The
earnings per share are arranged from smallest to
largest.
Compute the mean, median, and standard deviation.
Find the coefficient of skewness using Pearson’s
estimate.
What is your conclusion regarding the shape of the
distribution?
Skewness – An Example Using
Pearson’s Coefficient
X $74.26 $4.95
Step 1: Compute the Mean
X
15
n
Step 2 : Compute the Standard Deviation
XX
s
n 1
2
($0.09 $4.95) 2 ... ($16.40 $4.95) 2 )
$5.22
15 1
Step 3 : Find the Median
The middle value in the set of data, arranged from smallestto largestis 3.18
Step 3 : Compute the Skewness
sk
4-19
3( X Median ) 3($4.95 $3.18)
1.017
s
$5.22
Skewness – A Minitab Example
4-20
Describing Relationship between Two
Variables
4-21
When we study the relationship
between two variables we refer to the
data as bivariate.
One graphical technique we use to
show the relationship between
variables is called a scatter diagram.
To draw a scatter diagram we need two
variables. We scale one variable along
the horizontal axis (X-axis) of a graph
and the other variable along the vertical
axis (Y-axis).
Describing Relationship between Two
Variables – Scatter Diagram Examples
4-22
Describing Relationship between Two
Variables – Scatter Diagram Excel Example
In Chapter 2 we presented data
from AutoUSA. In this case the
information concerned the prices
of 80 vehicles sold last month at
the Whitner Autoplex lot in
Raytown, Missouri. The data
shown include the selling price
of the vehicle as well as the age
of the purchaser.
Is there a relationship between the
selling price of a vehicle and the
age of the purchaser?
Would it be reasonable to conclude
that the more expensive vehicles
are purchased by older buyers?
4-23
Describing Relationship between Two
Variables – Scatter Diagram Excel Example
4-24
Contingency Tables
4-25
A scatter diagram requires that both of the
variables be at least interval scale.
What if we wish to study the relationship
between two variables when one or both are
nominal or ordinal scale? In this case we tally
the results in a contingency table.
Contingency Tables
A contingency table is a cross-tabulation that
simultaneously summarizes two variables of interest.
Examples:
1.
Students at a university are classified by gender and class rank.
2.
A product is classified as acceptable or unacceptable and by the
shift (day, afternoon, or night) on which it is manufactured.
3.
A voter in a school bond referendum is classified as to party
affiliation (Democrat, Republican, other) and the number of children
that voter has attending school in the district (0, 1, 2, etc.).
4-26
Contingency Tables – An Example
A manufacturer of preassembled windows produced 50 windows yesterday. This
morning the quality assurance inspector reviewed each window for all quality
aspects. Each was classified as acceptable or unacceptable and by the shift
on which it was produced. Thus we reported two variables on a single item.
The two variables are shift and quality. The results are reported in the
following table.
Using the contingency table able, the quality of the three shifts can be
compared. For example:
1. On the day shift, 3 out of 20 windows or 15 percent are defective.
2. On the afternoon shift, 2 of 15 or 13 percent are defective and
3. On the night shift 1 out of 15 or 7 percent are defective.
4. Overall 12 percent of the windows are defective
4-27
URAIAN
TINGGI
SEDANG
RENDAH
F
%
F
%
F
%
1
KONFLIK
58
87,9
18
12,1
0
0
2
DURASI
64
97
2
3
0
0
3
KESUKAAN
63
95,5
3
4,5
0
0
4
PEMAIN UTAMA
66
100
0
0
0
0
5
BINTANG TAMU
65
98,5
1
1,5
0
0
6
KONSISTENSI
55
83,4
11
16,6
0
0
7
KECEPATAN CERITA
65
98,5
1
1,5
0
0
8
DAYA TARIK
47
71,2
19
28,8
0
0
9
GAMBAR YANG KUAT
63
94,5
3
5,5
0
0
10
TIMING
46
69,7
20
31,3
0
0
11
TREN
66
100
0
0
0
0
12
KOGNITIF
65
98,5
1
1,5
0
0
13
AFEKTIF
58
87,9
8
12,1
0
0
14
KEBERHASILAN
65
98,5
1
1,5
0
0
4-28
KARAKTERISTIK RESPONDEN
VARIABEL
DATA
JENIS KELAMIN
USIA
PEKERJAAN
4-29
KATEGORI
JUMLAH
PERSEN
PRIA
31
47
WANITA
35
53
12 - 19
3
4,5
20-29
18
27,3
30-39
20
30,3
40-49
15
22,7
50-59
9
13,6
>60
1
1,5
PNS
8
12,1
KARYAWAN
18
27,3
IRT
21
31,8
PELAJAR
6
9,1
WIRASWASTA
4
6,1
PEDAGANG
2
3
BURUH
3
4,5
PENSIUNAN
4
6,1