Matakuliah
Tahun
Versi
: I0134 – Metoda Statistika
: 2005
: Revisi
Pertemuan 03
Distribusi Frekuensi
1
Learning Outcomes
Pada akhir pertemuan ini, diharapkan mahasiswa
akan mampu :
• Mahasiswa dapat menjelaskan tentang
distribusi frekuensi.
2
Outline Materi
•
•
•
•
Diagram dahan dan daun
Distribusi Frekuensi
Histrogam dan Poligon
Frekuensi kumulatif dan ogif
3
Distribusi Frekuensi

Table with two columns listing:
– Each and every group or class or interval of
values
– Associated frequency of each group
• Number of observations assigned to each group
• Sum of frequencies is number of observations
– N for population
– n for sample


Class midpoint is the middle value of a group
or class or interval
Relative frequency is the percentage of total
observations in each class
– Sum of relative frequencies = 1
4
Frequency Distribution
x
Spending Class ($)
0 to less than 100
100 to less than 200
200 to less than 300
300 to less than 400
400 to less than 500
500 to less than 600
f(x)
Frequency (number of customers)
f(x)/n
Relative Frequency
30
38
50
31
22
13
0.163
0.207
0.272
0.168
0.120
0.070
184
1.000
• Example of relative frequency: 30/184 = 0.163
• Sum of relative frequencies = 1
5
Cumulative Frequency
Distribution
x
Spending Class ($)
0 to less than 100
100 to less than 200
200 to less than 300
300 to less than 400
400 to less than 500
500 to less than 600
F(x)
Cumulative Frequency
30
68
118
149
171
184
F(x)/n
Relative Cumulative Frequency
0.163
0.370
0.641
0.810
0.929
1.000
The cumulative frequency of each group is the sum of the
frequencies of that and all preceding groups.
6
Histogram

A histogram is a chart made of bars of
different heights.
– Widths and locations of bars correspond to
widths and locations of data groupings
– Heights of bars correspond to frequencies
or relative frequencies of data groupings
7
Histogram Example
Frequency Histogram
50
50
Frequency
40
30
38
31
30
22
20
13
10
100
200
300
400
500
600
Dollars
8
Histogram Example
Relative Frequency Histogram
0 .3
R e la ti ve F r e q u e n c y
0 .2 7 1 7 3 9
0 .2 0 6 5 2 2
0 .2
0. 1 6 8 4 7 8
0 .1 6 3 0 4 3
0. 1 1 9 5 6 5
0 .1
0.0 7 0 6 5 2
100
200
300
400
500
600
Dollars
9
Methods of Displaying Data

Pie Charts
– Categories represented as percentages of total

Bar Graphs
– Heights of rectangles represent group frequencies

Frequency Polygons
– Height of line represents frequency

Ogives
– Height of line represents cumulative frequency

Time Plots
– Represents values over time
10
Pie Chart
Fig. 1-8 Telecommunications Headquarters
Other (8.0%)
U.S. (30.0%)
Europe (25.0%)
Britain (8.0%)
Japan (29.0%)
11
Bar Chart
Fig. 1-9 Airline Operating Expenses and Revenues
12
Average Revenues
Average Expenses
10
8
6
4
2
0
American Continental Delta
Northwest Southwest United
USAir
A i r li n e
12
Frequency Polygon and Ogive
Ogive
Frequency Polygon
0.3
1.0
0.2
0.5
0.1
0.0
0.0
0
10
20
Sales
30
40
50
0
10
20
30
40
50
Sales
13
Time Plot
M o n thly S te e l P ro d uc tio n
(P ro b le m 1 -4 6 )
Millions of Tons
8.5
7.5
6.5
5.5
Month
J F M A M J J A S ON D J F M A M J J A S ON D J F M A M J J A S O
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• Selamat Belajar Semoga Sukses.
15