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# PDU 207 Basic Statistics: Variability

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Variability as a part of descriptive statistic
(Lecture slides mostly in Bahasa Indonesia)

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### PDU 207 Basic Statistics: Variability

1. 1. VARIABILITY PDU 207 STATISTIK DASAR SEMESTER GASAL 2014/2015 FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA KULIAH V - 11 September 2014
2. 2. ONE DAY OBJECTIVES Mahasiswa memahami tujuan umum dilakukannya perhitungan variability, serta mampu mengenali perbedaan kumpulan skor berdasarkan derajat variabilitasnya; Mahasiswa mampu memahami konsep dan melakukan perhitungan berbagai teknik variability; Mahasiswa mampu melakukan perbandingan terhadap berbagai teknik variability, sehingga dapat memilih teknik yang paling tepat sesuai tujuan pengukurannya.
3. 3. BERAPA KALI BERPACARAN? PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
4. 4. BERAPA KALI BERPACARAN? 20 kali PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
5. 5. BERAPA KALI BERPACARAN? 1 kali 20 kali 43 kali PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
6. 6. BERAPA KALI BERPACARAN? 1 kali 20 kali 43 kali VARIABILITY PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
7. 7. OVERVIEW OF VARIABILITY PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
8. 8. OVERVIEW OF VARIABILITY a quantitative measure of the differences between scores in a distribution and describes the degree to which the scores are spread out or clustered together. PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
9. 9. OVERVIEW OF VARIABILITY a quantitative measure of the differences between scores in a distribution and describes the degree to which the scores are spread out or clustered together. Usia Pertama Kali Jatuh Cinta (tahun) Usia Pertama Kali Berpacaran (tahun) PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
10. 10. OVERVIEW OF VARIABILITY a quantitative measure of the differences between scores in a distribution and describes the degree to which the scores are spread out or clustered together. 8 11 12 14 16 8 11 15 19 23 Usia Pertama Kali Jatuh Cinta (tahun) Usia Pertama Kali Berpacaran (tahun) PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
11. 11. OVERVIEW OF VARIABILITY a quantitative measure of the differences between scores in a distribution and describes the degree to which the scores are spread out or clustered together. describes the distribution PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
12. 12. OVERVIEW OF VARIABILITY a quantitative measure of the differences between scores in a distribution and describes the degree to which the scores are spread out or clustered together. describes the distribution 1 20 43 PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
13. 13. OVERVIEW OF VARIABILITY a quantitative measure of the differences between scores in a distribution and describes the degree to which the scores are spread out or clustered together. describes the distribution 1 20 43 PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
14. 14. OVERVIEW OF VARIABILITY a quantitative measure of the differences between scores in a distribution and describes the degree to which the scores are spread out or clustered together. describes the distribution measures how well an individual (or group of) score represents the entire distribution 1 20 43 PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
15. 15. OVERVIEW OF VARIABILITY a quantitative measure of the differences between scores in a distribution and describes the degree to which the scores are spread out or clustered together. describes the distribution measures how well an individual (or group of) score represents the entire distribution 43 1 20 PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
16. 16. OVERVIEW OF VARIABILITY a quantitative measure of the differences between scores in a distribution and describes the degree to which the scores are spread out or clustered together. describes the distribution measures how well an individual (or group of) score represents the entire distribution 43 1 20 PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
17. 17. OVERVIEW OF VARIABILITY a quantitative measure of the differences between scores in a distribution and describes the degree to which the scores are spread out or clustered together. RANGE STANDARD DEVIATION VARIANCE SEMI-INTERQUARTILE RANGE PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
18. 18. THE RANGE PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
19. 19. THE RANGE the distance covered by the scores in a distribution, from the smallest score to the largest score. PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
20. 20. THE RANGE the distance covered by the scores in a distribution, from the smallest score to the largest score. MEASUREMENT SCALE ☐ NOMINAL ☐ ORDINAL ☐ INTERVAL ☐ RATIO TYPES OF VARIABLES ☐ DISCRETE ☐ CONTINUOUS ACCURACY ☐ LOW ☐ MODERATE ☐ HIGH PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
21. 21. THE RANGE the distance covered by the scores in a distribution, from the smallest score to the largest score. MEASUREMENT SCALE ☐ NOMINAL ☐ ORDINAL ☐ INTERVAL ☐ RATIO TYPES OF VARIABLES ☐ DISCRETE ☐ CONTINUOUS ACCURACY ☐ LOW ☐ MODERATE ☐ HIGH range = Xmax - Xmin + 1 = URL Xmax - LRL Xmin PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
22. 22. THE RANGE the distance covered by the scores in a distribution, from the smallest score to the largest score. MEASUREMENT SCALE ☐ NOMINAL ☐ ORDINAL ☐ INTERVAL ☐ RATIO TYPES OF VARIABLES ☐ DISCRETE ☐ CONTINUOUS ACCURACY ☐ LOW ☐ MODERATE ☐ HIGH range = Xmax - Xmin + 1 = URL Xmax - LRL Xmin 5 4 3 3 4 4 8 3 5 4 2 5 7 5 4 5 6 6 4 3 PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
23. 23. THE RANGE the distance covered by the scores in a distribution, from the smallest score to the largest score. MEASUREMENT SCALE ☐ NOMINAL ☐ ORDINAL ☐ INTERVAL ☐ RATIO TYPES OF VARIABLES ☐ DISCRETE ☐ CONTINUOUS ACCURACY ☐ LOW ☐ MODERATE ☐ HIGH range = Xmax - Xmin + 1 = URL Xmax - LRL Xmin 5 4 3 3 4 4 8 3 5 4 2 5 7 5 4 5 6 6 4 3 it is completely determined by the two extreme values PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
24. 24. THE RANGE the distance covered by the scores in a distribution, from the smallest score to the largest score. MEASUREMENT ✓ ✓ ✓ SCALE ☐ NOMINAL ☐ ORDINAL ☐ INTERVAL ☐ RATIO TYPES OF VARIABLES ☐ DISCRETE ☐ CONTINUOUS ACCURACY ☐ LOW ☐ MODERATE ☐ HIGH ✓ ✓ ✓ range = Xmax - Xmin + 1 = URL Xmax - LRL Xmin 5 4 3 3 4 4 8 3 5 4 2 5 7 5 4 5 6 6 4 3 it is completely determined by the two extreme values PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
25. 25. THE INTERQUARTILE RANGE PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
26. 26. THE INTERQUARTILE RANGE the distance covered by the middle 50% of the distribution (Q3 - Q1). PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
27. 27. THE INTERQUARTILE RANGE the distance covered by the middle 50% of the distribution (Q3 - Q1). PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
28. 28. THE INTERQUARTILE RANGE the distance covered by the middle 50% of the distribution (Q3 - Q1). MEASUREMENT SCALE ☐ NOMINAL ☐ ORDINAL ☐ INTERVAL ☐ RATIO TYPES OF VARIABLES ☐ DISCRETE ☐ CONTINUOUS ACCURACY ☐ LOW ☐ MODERATE ☐ HIGH PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
29. 29. THE INTERQUARTILE RANGE the distance covered by the middle 50% of the distribution (Q3 - Q1). MEASUREMENT ✓ ✓ ✓ SCALE ☐ NOMINAL ☐ ORDINAL ☐ INTERVAL ☐ RATIO TYPES OF VARIABLES ✓ ☐ DISCRETE ✓ ☐ CONTINUOUS ACCURACY ☐ LOW ☐ MODERATE ☐ HIGH ✓ PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
30. 30. STANDARD DEVIATION & VARIANCE PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
31. 31. STANDARD DEVIATION & VARIANCE FOR POPULATION PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
32. 32. STANDARD DEVIATION & VARIANCE FOR POPULATION the average distance from the mean. PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
33. 33. STANDARD DEVIATION & VARIANCE FOR POPULATION the average distance from the mean. find the deviation (distance from the mean) for each score square each deviation find the average of the squared deviations take the square root of the variance PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
34. 34. STANDARD DEVIATION & VARIANCE FOR POPULATION the average distance from the mean. find the deviation (distance from the mean) for each score square each deviation VARIANCE take the square root of the variance PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
35. 35. STANDARD DEVIATION & VARIANCE FOR POPULATION the average distance from the mean. find the deviation (distance from the mean) for each score square each deviation VARIANCE STANDARD DEVIATION take the square root of the variance PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
36. 36. STANDARD DEVIATION & VARIANCE FOR SAMPLES the average distance from the mean. PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
37. 37. STANDARD DEVIATION & VARIANCE FOR SAMPLES the average distance from the mean. 5 4 3 3 4 2 5 7 5 4 4 8 3 5 4 5 6 6 4 3 POPULATION PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
38. 38. STANDARD DEVIATION & VARIANCE FOR SAMPLES the average distance from the mean. 5 4 3 3 4 2 5 7 5 4 4 8 3 5 4 5 6 6 4 3 POPULATION SAMPLES 4 8 3 3 2 PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
39. 39. STANDARD DEVIATION & VARIANCE FOR SAMPLES the average distance from the mean. 5 4 3 3 4 2 5 7 5 4 4 8 3 5 4 5 6 6 4 3 POPULATION SAMPLES 4 8 3 3 2 less variability PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
40. 40. STANDARD DEVIATION & VARIANCE FOR SAMPLES the average distance from the mean. 5 4 3 3 4 2 5 7 5 4 4 8 3 5 4 5 6 6 4 3 POPULATION SAMPLES 4 8 3 3 2 sample population variability variability less variability biased estimate PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
41. 41. STANDARD DEVIATION & VARIANCE FOR SAMPLES the average distance from the mean. find the deviation (distance from the mean) for each score square each deviation find the average of the squared deviations take the square root of the variance PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
42. 42. STANDARD DEVIATION & VARIANCE FOR SAMPLES the average distance from the mean. find the deviation (distance from the mean) for each score square each deviation VARIANCE STANDARD DEVIATION take the square root of the variance PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
43. 43. STANDARD DEVIATION & VARIANCE FOR SAMPLES the average distance from the mean. n = 3 M = 5 PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
44. 44. STANDARD DEVIATION & VARIANCE FOR SAMPLES the average distance from the mean. n = 3 M = 5 2 9 ? PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
45. 45. STANDARD DEVIATION & VARIANCE FOR SAMPLES the average distance from the mean. n = 3 M = 5 2 9 ? no restrictions restricted DEGREES OF FREEDOM PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
46. 46. STANDARD DEVIATION & VARIANCE the average distance from the mean. MEASUREMENT SCALE ☐ NOMINAL ☐ ORDINAL ☐ INTERVAL ☐ RATIO TYPES OF VARIABLES ☐ DISCRETE ☐ CONTINUOUS ACCURACY ☐ LOW ☐ MODERATE ☐ HIGH PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
47. 47. STANDARD DEVIATION & VARIANCE the average distance from the mean. MEASUREMENT ✓ ✓ SCALE ☐ NOMINAL ☐ ORDINAL ☐ INTERVAL ☐ RATIO TYPES OF VARIABLES ☐ DISCRETE ✓ ☐ CONTINUOUS ACCURACY ☐ LOW ☐ MODERATE ☐ HIGH ✓ PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
48. 48. COMPARING MEASURES OF VARIABILITY PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
49. 49. COMPARING MEASURES OF VARIABILITY RANGE SEMI-INTERQUARTILE RANGE STANDARD DEVIATION VARIANCE EXTREME SCORES SAMPLE SIZE STABILITY UNDER SAMPLING OPEN-ENDED DISTRIBUTION ✗ ✗ ✗ ✗ ✓ ✓ ✓ ✓ ✗ ✓ ✓ ✗ ✗ ✓ ✓ ✗ PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
50. 50. Want to Know More? Gravetter, F.J. & Wallnau, L.B. (2009). Statistics for the behavioral sciences (8th ed.). Australia: WADSWORTH CENGAGE Learning. Gravetter, F.J. & Wallnau, L.B. (2012). Statistics for the behavioral sciences (9th ed.). Australia: WADSWORTH CENGAGE Learning.