Bab2 Menyajikan data dalam Tabel dan Grafik
Statistika Bisnis
BAB 2
Menyajikan Data dalam Tabel dan
Grafik
Chap 2-1
Tujuan Kuliah
Pada Bab ini Anda diharapkan mempelajari:
Membangun tabel dan grafik untuk data
kategori (categorical data)
Membangun tabel dan grafik untuk data
numerik
Prinsip-prinsip yang tepat dalam menyajikan
data
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-2
Menyajikan Data
Data yang telah kita dapat biasanya tidak mudah untuk
langsung digunakan dalam pengambilan keputusan
Beberapa tipe penyajian data dibutuhkan, yaitu:
Tabel
Grafik
Teknik-teknik menyajikan data yang akan di bahas disini
adalah:
Bar charts and pie charts
Pareto diagram
Ordered array
Stem-and-leaf display
Frequency distributions, histograms and polygons
Cumulative distributions and ogives
Contingency tables
Scatter diagrams
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-3
Tabel and Grafik untuk
Categorical Data
Categorical
Data
Graphing Data
Tabulating Data
Summary
Table
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Bar
Charts
Pie
Charts
Pareto
Diagram
Chap 2-4
CONTOH
Kita melakukan investasi sebagai berikut:
(in thousands $)
Stocks 46.5, Bonds 32, CD 15.5, Savings 16
Buat summary table (tabel rekapitulasi) dan grafik
bar/pie berdasarkan frekuensi setiap kategori
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-5
The Summary Table (Tabel
Rekapitulasi)
Rekapitulasi data
berdasarkan kategori
Contoh: Portofolio Investasi
Tipe Investasi
Jumlah (dalam ribu
dollar)
Frekwensi (%)
Stocks
Bonds
Cd
savings
46.5
32
15.5
16
42.27
29.09
14.09
14.54
Total
110
100
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-6
Bar and Pie Charts
Bar charts and Pie charts digunakan
untuk categorical data
Tinggi dari dari bar atau size dari irisan
pie memperlihatkan frekuensi dari setiap
kategori
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-7
Bar Chart Example
Current Investment Portfolio
Investment
Type
Amount
(in thousands $)
Percentage
(%)
Stocks
Bonds
CD
Savings
46.5
32.0
15.5
16.0
42.27
29.09
14.09
14.55
Total
110.0
100.0
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-8
Pie Chart Example
Current Investment Portfolio
Investment
Type
Amount
(in thousands $)
Percentage
(%)
Stocks
Bonds
CD
Savings
46.5
32.0
15.5
16.0
42.27
29.09
14.09
14.55
Total
110.0
100.0
Savings
15%
Stocks
42%
CD
14%
Bonds
29%
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Percentages
are rounded to
the nearest
percent
Chap 2-9
Bar dan Pie Chart
Apa perbedaan bar dan pie chart?
Bar chart digunakan untuk melihat kategori data
mana yang terbesar/terkecil
Pie chart digunakan untuk melihat proporsi dari
setiap kategori dibanding keseluruhan
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-10
Pareto Diagram
Digunakan untuk menggambarkan categorical
data (nominal scale)
Pareto diagram digunakan pada grafik yang
sama bar chart dengan menambahkan
kumulatif frekwensi
Untuk memisahkan “vital few” dari “trivial many”
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-11
Pareto Diagram
Cummulative
percentage (%)
Tipe
Investasi
Jumlah
(in thousands $)
Percentage
(%)
Stocks
46.5
42.27
42.27
Bonds
32
29.09
71.36
CD
15.5
14.09
85.45
Savings
16. 0
14.55
100
Total
110
100
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-12
Pareto Diagram Example
45%
100%
40%
90%
80%
35%
70%
30%
60%
25%
50%
20%
40%
15%
30%
10%
20%
5%
10%
0%
0%
Stocks
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Bonds
Savings
cumulative % invested
(line graph)
% invested in each category
(bar graph)
Current Investment Portfolio
CD
Chap 2-13
Organizing
Numerical Data
Numerical Data
Ordered Array
Stem-and-Leaf
Display
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Frequency Distributions
and
Cumulative Distributions
Histogram
Polygon
Ogive
Chap 2-14
The Ordered Array
mengurutkan data kedalam tingkatan:
Memperlihatkan jarak (min to max)
Menghasilkan signal tentang variasi yang
terdapat dalam data
Bisa mengidentifikasi pencilan/outliers (unusual
observations)
tapi apabila data sangat banyak, the ordered
array susah untuk digunakan
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-15
The Ordered Array
(continued)
Data mentah yang terkumpul:
24, 26, 24, 21, 27, 27, 30, 41, 32, 38
Urutkan data memakai teknik ordered array dari
yang terkecil ke terbesar:
21 24 24 26 27 27 30 32 38 41
Range:
41-21=20
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-16
Stem-and-Leaf Diagram
Cara yang mudah untuk melihat distribusi
data
METODA: Memisahkan data menjadi yang
termasuk ke dalam leading digits (the
stem) and the trailing digits (the leaves)
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-17
CONTOH
Data in ordered array:
21, 24, 24, 26, 27, 27, 30, 32, 38, 41
Here, use the 10’s digit for the stem unit:
Stem Leaf
21 is shown as
2
1
38 is shown as
3
8
41 is shown as
4
1
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-18
CONTOH
(continued)
Data in ordered array:
21, 24, 24, 26, 27, 27, 30, 32, 38, 41
Completed stem-and-leaf diagram:
Stem
Leaves
2
1 44677
3
0 28
4
1
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-19
Using other stem units
Using the 100’s digit as the stem:
Round off the 10’s digit to form the leaves
Stem
Leaf
613 would become
6
1
776 would become
7
8
...
1224 becomes
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
12
2
Chap 2-20
Tabulating Numerical Data:
Frequency Distributions
Apakah frequency distribution?
Frequency distribution adalah list atau tabel …
Berisikan grup-grup dari kelas (class groupings)
(range/jarak berada diantara data) …
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-21
Mengapa Memakai Frequency
Distribution?
Suatu cara untuk menyusun/summarize
numerical data
Menyusun/meringkas data mentah
menjadi sesuatu yang lebih berguna dan
mudah dibaca...
Menyediakan suatu distribusi data yang
bisa diinterpretasikan
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-22
Class Intervals
and Class Boundaries
Setiap grup kelas/class grouping mempunyai lebar/jarak
yang sama
Menentukan lebar dari setiap kelas dengan
jarak/range
Lebardarikelas
jumlah kelas yang diinginkan
Biasanya sedikitnya 5 kelas tapi tidak lebih dari
15 kelas
Batas setiap kelas tidak overlap
Akhiri lebar kelas sehingga semua data masuk
ke dalam kelas
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-23
Contoh Frequency Distribution
Contoh: Suatu manufaktur penyekatan secara
acak memilih 20 musim dingin dan mencatat
termperatur tertinggi perhari sbb:
24, 35, 17, 21, 24, 37, 26, 46, 58, 30,
32, 13, 12, 38, 41, 43, 44, 27, 53, 27
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-24
Contoh Frequency Distribution
(continued)
Urutkan data:
12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58
Range: 58 - 12 = 46
Pilih jumlah kelas: 5 (biasanya antara 5 and 15)
Masukan lebar kelas/class interval (width): 10 (46/5 )
Tentukan batas setiap kelas (limits): 10, 20, 30, 40, 50, 60
Masukkan nilai tengah setiap kelas/class midpoints:
15, 25, 35, 45, 55
Buat tabel distribusi frekwensi
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-25
Contoh Frequency Distribution
(continued)
Data in ordered array:
12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58
Class
Frequency
10 but less than 20
20 but less than 30
30 but less than 40
40 but less than 50
50 but less than 60
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
3
6
Relative
Frequency
Percentage
5
0.15
0.3
0.25
15
30
25
4
2
0.2
0.1
20
10
Chap 2-26
Tabulating Numerical Data:
Cumulative Frequency
Data in ordered array:
12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58
Class
Frequency Percentage
Cumulative Cumulative
Frequency Percentage
10 but less than 20
3
15
3
15
20 but less than 30
6
30
9
45
30 but less than 40
5
25
14
70
40 but less than 50
4
20
18
90
50 but less than 60
2
10
20
100
20
100
Total
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-27
Graphing Numerical Data:
The Histogram
Grafik yang dibuat dari frequency distribution
disebut histogram
Batas setiap kelas dan class midpoints
diperlihatkan pada horizontal axis
Vertical axis digunakan untuk memperlihatkan
frequency, relative frequency, or percentage
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-28
Histogram
Class
Midpoint Frequency
Class
10 but less than 20
20 but less than 30
30 but less than 40
40 but less than 50
50 but less than 60
15
25
35
45
55
3
6
5
4
2
(No gaps
between
bars)
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Class Midpoints
Chap 2-29
Graphing Numerical Data:
The Frequency Polygon
Class
Midpoint Frequency
Class
10 but less than 20
20 but less than 30
30 but less than 40
40 but less than 50
50 but less than 60
15
25
35
45
55
3
6
5
4
2
(In a percentage
polygon the vertical axis
would be defined to
show the percentage of
observations per class)
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Class Midpoints
Chap 2-30
Graphing Cumulative Frequencies:
The Ogive (Cumulative % Polygon)
Class
Less than 10
10 but less than 20
20 but less than 30
30 but less than 40
40 but less than 50
50 but less than 60
Lower
Cumulative
class
boundary Percentage
0
10
20
30
40
50
0
15
45
70
90
100
Class Boundaries (Not Midpoints)
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-31
Bar chart dan Histogram
Apa perbedaan bar chart dan histogram?
Bar chart dipakai untuk beberapa catergorical
variabel
Histogram dipakai untuk satu variabel numerik
Polygon digunakan untuk lebih dari satu
variabel numerik
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-32
Scatter Diagrams
Scatter Diagrams digunakan untuk
menguji kemungkinan adanya
hubungan antara dua variabel
numerik
The Scatter Diagram:
Satu variabel diukur di vertical axis, dan
variabel lain di horizontal axis
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-33
Contoh Scatter Diagram
Volume
per day
Cost per
day
23
131
24
120
26
140
29
151
33
160
38
167
41
185
42
170
50
188
55
195
60
200
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-34
Contoh Scatter Diagram (Time
Series Plot
Year
Number of
Franchises
1996
43
1997
54
1998
60
1999
73
2000
82
2001
95
2002
107
2003
99
2004
95
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-35
Ringkasan
Apa aja yang dipelajari di bab ini:
Bar charts, pie charts, and Pareto diagrams
Ordered array and stem-and-leaf display
Frequency distributions, histograms and polygons
Cumulative polygon and ogives
Contingency tables and side-by-side bar charts
Scatter diagrams and time series plots
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-36
SOAL
Data berikut mewakili biaya listrik selama Juli 2006 untuk sebuah
sampel acak dari 30 kamar apartemen di kota besar:
96 171 202 178 147 102 153 197 127 82
157 185 90 116 172 111 148 213 130 165
141 149 206 175 123 128 144 168 109 167
a. Bangun sebuah frekwensi dan persentase distribusi (Sekalian
dengan cummulative percentagenya)
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-37
SOAL
b. Bangun histogram dan percentage polygon
c. Bangun grafik cummulative polygon distribution
d. Pada bulan apa aja biaya listrik terkonsentrasi?
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-38
Bab 3
Central tedency
Mean
Median
Mode
Geometric mean
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-39
Terima Kasih
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-40
Numerik
Ordered arry
Range
Tentukan byk kelas (6)
Lebar kelas : range/jumlah kelas (dibulatkan ke
atas)
Midpoints
Bikin freks dist
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-41
BAB 2
Menyajikan Data dalam Tabel dan
Grafik
Chap 2-1
Tujuan Kuliah
Pada Bab ini Anda diharapkan mempelajari:
Membangun tabel dan grafik untuk data
kategori (categorical data)
Membangun tabel dan grafik untuk data
numerik
Prinsip-prinsip yang tepat dalam menyajikan
data
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-2
Menyajikan Data
Data yang telah kita dapat biasanya tidak mudah untuk
langsung digunakan dalam pengambilan keputusan
Beberapa tipe penyajian data dibutuhkan, yaitu:
Tabel
Grafik
Teknik-teknik menyajikan data yang akan di bahas disini
adalah:
Bar charts and pie charts
Pareto diagram
Ordered array
Stem-and-leaf display
Frequency distributions, histograms and polygons
Cumulative distributions and ogives
Contingency tables
Scatter diagrams
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-3
Tabel and Grafik untuk
Categorical Data
Categorical
Data
Graphing Data
Tabulating Data
Summary
Table
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Bar
Charts
Pie
Charts
Pareto
Diagram
Chap 2-4
CONTOH
Kita melakukan investasi sebagai berikut:
(in thousands $)
Stocks 46.5, Bonds 32, CD 15.5, Savings 16
Buat summary table (tabel rekapitulasi) dan grafik
bar/pie berdasarkan frekuensi setiap kategori
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-5
The Summary Table (Tabel
Rekapitulasi)
Rekapitulasi data
berdasarkan kategori
Contoh: Portofolio Investasi
Tipe Investasi
Jumlah (dalam ribu
dollar)
Frekwensi (%)
Stocks
Bonds
Cd
savings
46.5
32
15.5
16
42.27
29.09
14.09
14.54
Total
110
100
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-6
Bar and Pie Charts
Bar charts and Pie charts digunakan
untuk categorical data
Tinggi dari dari bar atau size dari irisan
pie memperlihatkan frekuensi dari setiap
kategori
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-7
Bar Chart Example
Current Investment Portfolio
Investment
Type
Amount
(in thousands $)
Percentage
(%)
Stocks
Bonds
CD
Savings
46.5
32.0
15.5
16.0
42.27
29.09
14.09
14.55
Total
110.0
100.0
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-8
Pie Chart Example
Current Investment Portfolio
Investment
Type
Amount
(in thousands $)
Percentage
(%)
Stocks
Bonds
CD
Savings
46.5
32.0
15.5
16.0
42.27
29.09
14.09
14.55
Total
110.0
100.0
Savings
15%
Stocks
42%
CD
14%
Bonds
29%
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Percentages
are rounded to
the nearest
percent
Chap 2-9
Bar dan Pie Chart
Apa perbedaan bar dan pie chart?
Bar chart digunakan untuk melihat kategori data
mana yang terbesar/terkecil
Pie chart digunakan untuk melihat proporsi dari
setiap kategori dibanding keseluruhan
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-10
Pareto Diagram
Digunakan untuk menggambarkan categorical
data (nominal scale)
Pareto diagram digunakan pada grafik yang
sama bar chart dengan menambahkan
kumulatif frekwensi
Untuk memisahkan “vital few” dari “trivial many”
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-11
Pareto Diagram
Cummulative
percentage (%)
Tipe
Investasi
Jumlah
(in thousands $)
Percentage
(%)
Stocks
46.5
42.27
42.27
Bonds
32
29.09
71.36
CD
15.5
14.09
85.45
Savings
16. 0
14.55
100
Total
110
100
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-12
Pareto Diagram Example
45%
100%
40%
90%
80%
35%
70%
30%
60%
25%
50%
20%
40%
15%
30%
10%
20%
5%
10%
0%
0%
Stocks
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Bonds
Savings
cumulative % invested
(line graph)
% invested in each category
(bar graph)
Current Investment Portfolio
CD
Chap 2-13
Organizing
Numerical Data
Numerical Data
Ordered Array
Stem-and-Leaf
Display
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Frequency Distributions
and
Cumulative Distributions
Histogram
Polygon
Ogive
Chap 2-14
The Ordered Array
mengurutkan data kedalam tingkatan:
Memperlihatkan jarak (min to max)
Menghasilkan signal tentang variasi yang
terdapat dalam data
Bisa mengidentifikasi pencilan/outliers (unusual
observations)
tapi apabila data sangat banyak, the ordered
array susah untuk digunakan
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-15
The Ordered Array
(continued)
Data mentah yang terkumpul:
24, 26, 24, 21, 27, 27, 30, 41, 32, 38
Urutkan data memakai teknik ordered array dari
yang terkecil ke terbesar:
21 24 24 26 27 27 30 32 38 41
Range:
41-21=20
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-16
Stem-and-Leaf Diagram
Cara yang mudah untuk melihat distribusi
data
METODA: Memisahkan data menjadi yang
termasuk ke dalam leading digits (the
stem) and the trailing digits (the leaves)
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-17
CONTOH
Data in ordered array:
21, 24, 24, 26, 27, 27, 30, 32, 38, 41
Here, use the 10’s digit for the stem unit:
Stem Leaf
21 is shown as
2
1
38 is shown as
3
8
41 is shown as
4
1
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-18
CONTOH
(continued)
Data in ordered array:
21, 24, 24, 26, 27, 27, 30, 32, 38, 41
Completed stem-and-leaf diagram:
Stem
Leaves
2
1 44677
3
0 28
4
1
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-19
Using other stem units
Using the 100’s digit as the stem:
Round off the 10’s digit to form the leaves
Stem
Leaf
613 would become
6
1
776 would become
7
8
...
1224 becomes
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
12
2
Chap 2-20
Tabulating Numerical Data:
Frequency Distributions
Apakah frequency distribution?
Frequency distribution adalah list atau tabel …
Berisikan grup-grup dari kelas (class groupings)
(range/jarak berada diantara data) …
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-21
Mengapa Memakai Frequency
Distribution?
Suatu cara untuk menyusun/summarize
numerical data
Menyusun/meringkas data mentah
menjadi sesuatu yang lebih berguna dan
mudah dibaca...
Menyediakan suatu distribusi data yang
bisa diinterpretasikan
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-22
Class Intervals
and Class Boundaries
Setiap grup kelas/class grouping mempunyai lebar/jarak
yang sama
Menentukan lebar dari setiap kelas dengan
jarak/range
Lebardarikelas
jumlah kelas yang diinginkan
Biasanya sedikitnya 5 kelas tapi tidak lebih dari
15 kelas
Batas setiap kelas tidak overlap
Akhiri lebar kelas sehingga semua data masuk
ke dalam kelas
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-23
Contoh Frequency Distribution
Contoh: Suatu manufaktur penyekatan secara
acak memilih 20 musim dingin dan mencatat
termperatur tertinggi perhari sbb:
24, 35, 17, 21, 24, 37, 26, 46, 58, 30,
32, 13, 12, 38, 41, 43, 44, 27, 53, 27
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-24
Contoh Frequency Distribution
(continued)
Urutkan data:
12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58
Range: 58 - 12 = 46
Pilih jumlah kelas: 5 (biasanya antara 5 and 15)
Masukan lebar kelas/class interval (width): 10 (46/5 )
Tentukan batas setiap kelas (limits): 10, 20, 30, 40, 50, 60
Masukkan nilai tengah setiap kelas/class midpoints:
15, 25, 35, 45, 55
Buat tabel distribusi frekwensi
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-25
Contoh Frequency Distribution
(continued)
Data in ordered array:
12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58
Class
Frequency
10 but less than 20
20 but less than 30
30 but less than 40
40 but less than 50
50 but less than 60
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
3
6
Relative
Frequency
Percentage
5
0.15
0.3
0.25
15
30
25
4
2
0.2
0.1
20
10
Chap 2-26
Tabulating Numerical Data:
Cumulative Frequency
Data in ordered array:
12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58
Class
Frequency Percentage
Cumulative Cumulative
Frequency Percentage
10 but less than 20
3
15
3
15
20 but less than 30
6
30
9
45
30 but less than 40
5
25
14
70
40 but less than 50
4
20
18
90
50 but less than 60
2
10
20
100
20
100
Total
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-27
Graphing Numerical Data:
The Histogram
Grafik yang dibuat dari frequency distribution
disebut histogram
Batas setiap kelas dan class midpoints
diperlihatkan pada horizontal axis
Vertical axis digunakan untuk memperlihatkan
frequency, relative frequency, or percentage
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-28
Histogram
Class
Midpoint Frequency
Class
10 but less than 20
20 but less than 30
30 but less than 40
40 but less than 50
50 but less than 60
15
25
35
45
55
3
6
5
4
2
(No gaps
between
bars)
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Class Midpoints
Chap 2-29
Graphing Numerical Data:
The Frequency Polygon
Class
Midpoint Frequency
Class
10 but less than 20
20 but less than 30
30 but less than 40
40 but less than 50
50 but less than 60
15
25
35
45
55
3
6
5
4
2
(In a percentage
polygon the vertical axis
would be defined to
show the percentage of
observations per class)
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Class Midpoints
Chap 2-30
Graphing Cumulative Frequencies:
The Ogive (Cumulative % Polygon)
Class
Less than 10
10 but less than 20
20 but less than 30
30 but less than 40
40 but less than 50
50 but less than 60
Lower
Cumulative
class
boundary Percentage
0
10
20
30
40
50
0
15
45
70
90
100
Class Boundaries (Not Midpoints)
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-31
Bar chart dan Histogram
Apa perbedaan bar chart dan histogram?
Bar chart dipakai untuk beberapa catergorical
variabel
Histogram dipakai untuk satu variabel numerik
Polygon digunakan untuk lebih dari satu
variabel numerik
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-32
Scatter Diagrams
Scatter Diagrams digunakan untuk
menguji kemungkinan adanya
hubungan antara dua variabel
numerik
The Scatter Diagram:
Satu variabel diukur di vertical axis, dan
variabel lain di horizontal axis
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-33
Contoh Scatter Diagram
Volume
per day
Cost per
day
23
131
24
120
26
140
29
151
33
160
38
167
41
185
42
170
50
188
55
195
60
200
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-34
Contoh Scatter Diagram (Time
Series Plot
Year
Number of
Franchises
1996
43
1997
54
1998
60
1999
73
2000
82
2001
95
2002
107
2003
99
2004
95
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-35
Ringkasan
Apa aja yang dipelajari di bab ini:
Bar charts, pie charts, and Pareto diagrams
Ordered array and stem-and-leaf display
Frequency distributions, histograms and polygons
Cumulative polygon and ogives
Contingency tables and side-by-side bar charts
Scatter diagrams and time series plots
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-36
SOAL
Data berikut mewakili biaya listrik selama Juli 2006 untuk sebuah
sampel acak dari 30 kamar apartemen di kota besar:
96 171 202 178 147 102 153 197 127 82
157 185 90 116 172 111 148 213 130 165
141 149 206 175 123 128 144 168 109 167
a. Bangun sebuah frekwensi dan persentase distribusi (Sekalian
dengan cummulative percentagenya)
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-37
SOAL
b. Bangun histogram dan percentage polygon
c. Bangun grafik cummulative polygon distribution
d. Pada bulan apa aja biaya listrik terkonsentrasi?
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-38
Bab 3
Central tedency
Mean
Median
Mode
Geometric mean
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-39
Terima Kasih
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-40
Numerik
Ordered arry
Range
Tentukan byk kelas (6)
Lebar kelas : range/jumlah kelas (dibulatkan ke
atas)
Midpoints
Bikin freks dist
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 2-41