PDU 207 Basic Statistics: Frequency Distribution

PDU 207 STATISTIK DASAR
SEKSI E
SEMESTER GASAL 2016/2017
FAKULTAS PSIKOLOGI / PROGRAM STUDI S1 PSIKOLOGI
Frequency
Distribution
KULIAH III – 22 AGUSTUS 2016

Menguasai teknik-teknik statistika deskriptif dan statistika inferensial,
secara khusus terkait dengan:
• Konsep distribusi frekuensi;
• Organisasi data ke dalam tabel dan grafik distribusi, serta data dalam tabel 
dan grafik distribusi tersebut;
• Perhitungan persentil dan ranking (termasuk menggunakan interpolasi) 
serta letak data pada suatu distribusi berdasarkan hasil perhitungan tersebut.
One-Day Objectives

Introduction to
Frequency Distribution

PDU 207 STATISTIK DASAR 2016 © Ardhiati
Introduction
4
A frequency distribution is an organized tabulation 
of the number of individuals located in each category 
on the scale of measurement.
TO FREQUENCY DISTRIBUTION
TABLE GRAPH
(Gravetter & Wallnau, 2012: 39)

Introduction
5
A frequency distribution is an organized tabulation 
of the number of individuals located in each category 
on the scale of measurement.
TO FREQUENCY DISTRIBUTION
The set of categories 
that make up the original 
measurement scale
A record of the frequency, 
or number of individuals 
in each category
1 2
(Gravetter & Wallnau, 2012: 39) ICON SOURCES: Link by Joris Hoogendoorn; from the Noun Project

Tables & Graphs

7
TABLES & GRAPHS
categorized by 
the types of data
categorized by 
the scale and type of data
I RON
Singular Data Group Data
ICON SOURCES: Group by christoph robausch; 
from the Noun Project
Singular 
Data
Group 
Data
Nominal Ordinal Interval Ratio

8
TABLES & GRAPHS
categorized by 
the types of data
categorized by 
the scale and type of data
I RON
Singular Data Group Data Singular 
Data
Group 
Data

Frequency Distribution Tables
9
SINGULAR DATA
5 4 3 3
4 4 7 5
2 5 4 3
4 8 3 5
5 6 6 4
X f fX p = f/N % = p(100)
8 1 8 0,05 5%
7 1 7 0,05 5%
6 2 12 0,1 10%
5 5 25 0,25 25%
4 6 24 0,3 30%
3 4 12 0,2 20%
2 1 2 0,05 5%
highesttolowest
DATA TABLE
(Gravetter & Wallnau, 2012: 39-42)

10
There are several guidelines that help guide you 
in the construction of a grouped frequency distribution table.
GROUP DATA
G1
G2
G3
G4
Should have about 
10 class intervals
The width of each
interval should be 
a relatively simple
number
The bottom score in 
each class interval
should be a multiple 
of the width
All intervals should be
the same width

11
Steps of Creating 
GROUP DATA
85 68 67 90 59
71 82 80 60 77
83 94 70 52 87
74 99 58 71 82
72 71 64 89 76
DATA
ROWS = highest - lowest + 1
= 99 - 52 + 1
= 48
Determine the number and
width of interval
1
WIDTH NUMBER OF INTERVALS
2 23
5 10
10 5
✓
✗
✗
{ G1G2
}

12
GROUP DATA
85 68 67 90 59
71 82 80 60 77
83 94 70 52 87
74 99 58 71 82
72 71 64 89 76
DATA
Identify the lowest score 
on the interval
2
width = 5
52
the lowest score 
on the interval
= 50
G3
55 - 59
50 - 54
interval class:
G4}

13
GROUP DATA
85 68 67 90 59
71 82 80 60 77
83 94 70 52 87
74 99 58 71 82
72 71 64 89 76
DATA
X f Real Limit
95 - 99 1 94,5 - 99,5
90 - 94 2 89,5 - 94,5
85 - 89 3 84,5 - 89,5
80 - 84 4 79,5 - 84,5
75 - 79 2 74,5 - 79,5
70 - 74 6 69,5 - 74,5
65 - 69 2 64,5 - 69,5
60 - 64 2 59,5 - 64,5
55 - 59 2 54,5 - 59,5
50 - 54 1 49,5 - 54,5

Frequency Distribution Graphs
14
TYPES
I RON
Singular 
Data
Group 
Data
Bar Chart Histogram Polygon

15
TYPES
I RON
Singular 
Data
Group 
Data

16
TYPES
I RON
Singular 
Data
Group 
Data

17
TYPES
I RON
Singular 
Data
Group 
Data

18
INTERVAL & RATIO × SINGULAR DATA
Tahun f
8 19
7 12
6 24
5 55
4 69
3 40
2 11
0
10
20
30
40
50
60
70
1 2 3 4 5 6 7 8
Tahun
Frekuensi
Durasi Mengikuti 
Kursus Bahasa Jepang
real
limits
frequency
HISTOGRAM

19
INTERVAL & RATIO × SINGULAR DATA
Tahun f
8 19
7 12
6 24
5 55
4 69
3 40
2 11
0
10
20
30
40
50
60
70
1 2 3 4 5 6 7 8 9
Tahun
Frekuensi
Durasi Mengikuti 
POLYGON

20
INTERVAL & RATIO × GROUP DATA
Nilai f
95 - 99 11
90 - 94 24
85 - 89 38
80 - 84 40
75 - 79 25
70 - 74 68
65 - 69 20
60 - 64 23
55 - 59 28
50 - 54 10
Nilai
Frekuensi
Nilai Kuis I 
Statistik Dasar
HISTOGRAM
0
10
20
30
40
50
60
70
50-54 55-59 60-64 65-69 70-74 75-79 80-84 85-89 90-94 95-99

21
INTERVAL & RATIO × GROUP DATA
Nilai f
95 - 99 11
90 - 94 24
85 - 89 38
80 - 84 40
75 - 79 25
70 - 74 68
65 - 69 20
60 - 64 23
55 - 59 28
50 - 54 10
Nilai
Frekuensi
Nilai Kuis I 
Statistik Dasar
POLYGON
0
10
20
30
40
50
60
70
50 55 60 65 70 75 80 85 90 95 100

22
ORDINAL & NOMINAL × SINGULAR DATA
Angkatan f
2016 278
2015 264
2014 255
2013 213
2012 199
2011 42
2010 4
0
50
100
150
200
250
300
2016 2015 2014 2013 2012 2011 2010
Angkatan
Frekuensi
Mahasiswa Aktif 
FP Universitas Anu
BAR CHART

23
THE SHAPE
Unimodal
Bimodal
Positive 
Skew
Negative 
Skew

Percentiles, 
Percentile Ranks, &
Interpolation

Percentiles & Percentile Ranks
25
Although the primary purpose of a frequency distribution 
is to provide a description of an entire set of scores, 
it also can be used to describe the position 
of an individual within the set.
THE DEFINITION
The rank or percentile rank of a particular score 
is defined as the percentage of individuals 
in the distribution with scores equal to 
or less than the particular value.
When a score is identified by its percentile rank, 
the score is called a percentile.
PR P
(Gravetter & Wallnau, 2012: 53)

26
• Berapa persen individu yang telah
mengikuti kursus Bahasa Jepang
selama 5 tahun atau kurang?
PR5 = 76%
• Dibandingkan dengan teman-teman
yang sama-sama mengikuti kursus
Bahasa Jepang, durasi Tika mengikuti
kursus tersebut berada pada
persentil ke-22.
Berapa lama Tika sudah mengikuti
kursus Bahasa Jepang?
P22 = 3,5 tahun
THE DEFINITION
Tahun f cf c%
8 19
7 12
6 24
5 55
4 69
3 40
2 11
Durasi Mengikuti 
230
211
199
175
120
51
11
100%
92%
87%
76%
52%
22%
5%
PERCENTILE RANK
PERCENTILE

27
• Christin sudah mengikuti kursus
Bahasa Jepang selama tepat 4 tahun.
Dibandingkan dengan teman-teman
yang sama-sama mengikuti kursus
Bahasa Jelang, Christin berapa pada
persentil rank berapa?
Each cumulative percentage
in the table is associated
with the upper real limit of
its score interval.
WITH INTERPOLATION FOR SINGULAR DATA
Tahun f cf c%
8 19
7 12
6 24
5 55
4 69
3 40
2 11
Durasi Mengikuti 
230
211
199
175
120
51
11
100%
92%
87%
76%
52%
22%
5%
PERCENTILE RANK
PR4 = ?% 37%
4,5
3,5
52%
22%

28
• Tika mendapat nilai 71 pada kuis I
Statistik Dasar. Nilai tersebut berada
pada persentil rank ke-berapa?
PR71 = 37,6%
• Dibandingkan dengan teman-teman
peserta kuliah Statistik Dasar, nilai
kuis I Christin berada pada persentil
ke-90.
Berapa nilai Christin untuk kuis I
Statistik Dasar?
P90 = 91,25
WITH INTERPOLATION FOR GROUP DATA
Tahun f cf c%
95 - 99 11 287 100%
90 - 94 24 276 96%
85 - 89 38 252 88%
80 - 84 40 214 75%
75 - 79 25 174 61%
70 - 74 68 149 52%
65 - 69 20 81 28%
60 - 64 23 61 21%
55 - 59 28 38 13%
50 - 54 10 10 3%
Nilai Kuis I 
Statistik Dasar
PERCENTILE RANK
PERCENTILE
74,5
69,5
52%
28%
94,5
89,5
96%
88%

PDU 207 STATISTIK DASAR 2016 © Ardhiati 29
WANT TO KNOW MORE?
Gravetter, F.J. & Wallnau, L.B. (2012). 
Statistics for the behavioral sciences (9th ed.). 
Australia: WADSWORTH CENGAGE Learning.

PDU 207 Basic Statistics: Frequency Distribution

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