What is frequency distribution? How it helps us organizing data? (Lecture slides mostly in Bahasa Indonesia)

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

2. 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

3. Introduction to
Frequency Distribution

4. 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)

5. PDU 207 STATISTIK DASAR 2016 © Ardhiati
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

6. Frequency Distribution
Tables & Graphs

7. PDU 207 STATISTIK DASAR 2016 © Ardhiati
Frequency Distribution
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. PDU 207 STATISTIK DASAR 2016 © Ardhiati
Frequency Distribution
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
Nominal Ordinal Interval Ratio
ICON SOURCES: Group by christoph robausch;
from the Noun Project

9. PDU 207 STATISTIK DASAR 2016 © Ardhiati
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. PDU 207 STATISTIK DASAR 2016 © Ardhiati
Frequency Distribution Tables
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
(Gravetter & Wallnau, 2012: 42-45)

11. PDU 207 STATISTIK DASAR 2016 © Ardhiati
Frequency Distribution Tables
11
Steps of Creating
Frequency Distribution Tables
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
}
(Gravetter & Wallnau, 2012: 42-45)

12. PDU 207 STATISTIK DASAR 2016 © Ardhiati
Frequency Distribution Tables
12
Steps of Creating
Frequency Distribution Tables
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}
(Gravetter & Wallnau, 2012: 42-45)

13. PDU 207 STATISTIK DASAR 2016 © Ardhiati
Frequency Distribution Tables
13
Steps of Creating
Frequency Distribution Tables
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
(Gravetter & Wallnau, 2012: 42-45)

14. PDU 207 STATISTIK DASAR 2016 © Ardhiati
Frequency Distribution Graphs
14
TYPES
I RON
Nominal Ordinal Interval Ratio
Singular
Data
Group
Data
ICON SOURCES: Group by christoph robausch;
from the Noun Project
Bar Chart Histogram Polygon

15. PDU 207 STATISTIK DASAR 2016 © Ardhiati
Frequency Distribution Graphs
15
TYPES
I RON
Nominal Ordinal Interval Ratio
Bar Chart Histogram Polygon
Singular
Data
Group
Data
ICON SOURCES: Group by christoph robausch;
from the Noun Project

16. PDU 207 STATISTIK DASAR 2016 © Ardhiati
Frequency Distribution Graphs
16
TYPES
I RON
Nominal Ordinal Interval Ratio
Bar Chart Histogram Polygon
Singular
Data
Group
Data
ICON SOURCES: Group by christoph robausch;
from the Noun Project

17. PDU 207 STATISTIK DASAR 2016 © Ardhiati
Frequency Distribution Graphs
17
TYPES
I RON
Nominal Ordinal Interval Ratio
Bar Chart Histogram Polygon
Singular
Data
Group
Data
ICON SOURCES: Group by christoph robausch;
from the Noun Project

18. PDU 207 STATISTIK DASAR 2016 © Ardhiati
Frequency Distribution Graphs
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. PDU 207 STATISTIK DASAR 2016 © Ardhiati
Frequency Distribution Graphs
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
Kursus Bahasa Jepang
POLYGON

20. PDU 207 STATISTIK DASAR 2016 © Ardhiati
Frequency Distribution Graphs
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. PDU 207 STATISTIK DASAR 2016 © Ardhiati
Frequency Distribution Graphs
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. PDU 207 STATISTIK DASAR 2016 © Ardhiati
Frequency Distribution Graphs
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. PDU 207 STATISTIK DASAR 2016 © Ardhiati
Frequency Distribution
23
THE SHAPE
Unimodal
Bimodal
Positive
Skew
Negative
Skew
(Gravetter & Wallnau, 2012: 50-52)

24. Percentiles,
Percentile Ranks, &
Interpolation

25. PDU 207 STATISTIK DASAR 2016 © Ardhiati
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. PDU 207 STATISTIK DASAR 2016 © Ardhiati
Percentiles & Percentile Ranks
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
Kursus Bahasa Jepang
230
211
199
175
120
51
11
100%
92%
87%
76%
52%
22%
5%
PERCENTILE RANK
PERCENTILE

27. PDU 207 STATISTIK DASAR 2016 © Ardhiati
Percentiles & Percentile Ranks
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
Kursus Bahasa Jepang
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. PDU 207 STATISTIK DASAR 2016 © Ardhiati
Percentiles & Percentile Ranks
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%

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WANT TO KNOW MORE?
Gravetter, F.J. & Wallnau, L.B. (2012).
Statistics for the behavioral sciences (9th ed.).
Australia: WADSWORTH CENGAGE Learning.