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# PDU 207 Basic Statistics: Frequency Distribution

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

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### PDU 207 Basic Statistics: Frequency Distribution

1. 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. 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. 3. Introduction to Frequency Distribution
4. 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. 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. 6. Frequency Distribution Tables & Graphs
7. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 23. PDU 207 STATISTIK DASAR 2016 © Ardhiati Frequency Distribution 23 THE SHAPE Unimodal Bimodal Positive  Skew Negative  Skew (Gravetter & Wallnau, 2012: 50-52)
24. 24. Percentiles,  Percentile Ranks, & Interpolation
25. 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. 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. 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. 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%
29. 29. 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.