Presentasi ke-2 Statistika Untuk Ekonomi STIE Muhammadiyah Bandung

2. Ukuran Pemusatan

3. Ukuran Kecenderungan Sentral

4. Ukuran Sentral Tendensi

5. Ukuran Tendensi Sentral

6. Ukuran Gejala PusatIa Kurnia, Drs., M.Pd. 1

8. Membedakan jenis-jenis “measures of central tendency”

9. Menghitung jenis-jenis “measures of central tendency” dan menafsirkan hasilnya. Ia Kurnia, Drs., M.Pd. 2

10. Measures of Central Tendency Nilai Tunggal yang representatif bagi seluruh nilai data. Ia Kurnia, Drs., M.Pd. 3

11. Measures of Central Tendency Jenis: I Mathematical Averages Arithmetic Mean Geometric Mean Harmonic Mean Quadratic Mean (Root Mean Square) II. Positional Averages Median Mode Quartiles Deciles Percentiles Ia Kurnia, Drs., M.Pd. 4 4

12. ARITHMETIC MEAN Grouped Data Ungrouped Data Ia Kurnia, Drs., M.Pd. 5

13. ARITHMETIC MEAN Ia Kurnia, Drs., M.Pd. 6

15. Its definition is clear and precise. It corresponds to the centre of gravity of the observation

16. It is simple to understand and easy to compute.

17. It use each and every item in the data

18. It has a determinate value and is rigidly defined

19. It can be subjected to further algebraic treatment and advanced statistical theory is based on it

20. It can be found event if only the total of values is known and the individual values are not known

21. It provides a good standard of comparison since extreme values can cancel each other when the number of observation is largeIa Kurnia, Drs., M.Pd. 7 “The Arithmetic Mean is obtained by dividing the sum of values of observation by the number of observation”

23. It gives greater importance to larger and less importance to smaller values. It has an upward bias

24. It cannot be calculated if one more items in the data are missing

25. It cannot be located by inspection (like the mode and median)

26. It may conceal facts and may lead to distorted conclusions.Thus, if the performance of two students in three terms is given by (a) 30% 40% 50% marks (b) 50% 40% 30% marks Although the mean are equal we cannot know from the means alone that one students is showing improved results, and the other deteriorating. Similarly inequalities of incomes are concealed by the per capita incomes and the average result of a collage may tell nothing about the general performance of the students. Ia Kurnia, Drs., M.Pd. 8 4

27. Ia Kurnia, Drs., M.Pd. 9 GEOMETRIC MEAN Ungrouped Data (1) Untuk data yang perubahannya mengikuti atau dianggap mengikuti aturan-aturan tertentu, misalnya pertambahan penduduk, perubahan modal/tabungan, pertumbuhan bakteri dll. Pt = Keadaan pada akhir periode Po = Keadaan awal X = rata-rata t = jangka waktu atau lamanya periode (2)

28. GEOMETRICMEAN Ia Kurnia, Drs., M.Pd. 10 Grouped Data Notes Fi = Frekuensi Kelas Mdi = Mid Point Kelas

29. Ia Kurnia, Drs., M.Pd. 11 GEOMETRICMEAN

31. It has a downward bias. It gives more weight to small values than to large values

32. It is determinate. For the same data there cannot be two geometric mean

33. It balances to ratios of the values on either side of the data. It is ideally suited to average rate of change such as index numbers and ratios between measures and percentages.

35. It is determined for positive values and cannot be used for negative values or zero.Ia Kurnia, Drs., M.Pd. 12 4

37. Median (Me) = Data ke n = Banyak data Grouped Data Ia Kurnia, Drs., M.Pd. 13 LCBme = Lower Class Boundary Median terletak Ci = Panjang Class Interval FC(me-1) = Frekuensi Kumulatif sblm kelas median Fme = Frekuensi Kelas Median n = Jumlah Data Observasi

39. It can be computed even for incomplete data. It is concerned only with a few central observation

40. It balances the number of items in a distribution. It is useful in describing scores, ratios and grades

41. It is more useful in the case of skewed distributions like those of incomes and prices

42. It can be used for qualitative data

43. In the case of open end classes the median can be calculated but the Mean cannot

44. It can be easily determined graphically (see Ogives)Ia Kurnia, Drs., M.Pd. 14

46. The median is not capable of algebraic manipulation. As such it is not used in advanced studies

47. The empirical formula for the median based on interpolation may not always give correct results

48. It may ignore significant extreme values

49. Weighting cannot be used in the case of the median. The scope of operations is thus narrowed

50. It cannot be computed as exactly as the mean Ia Kurnia, Drs., M.Pd. 15 3

51. MODE Modus Nilai data yang paling sering muncul atau nilai data yang mempunyai frekuensi terbanyak. Ungrouped Data Mencari nilai data dengan kemunculan terbanyak Grouped Data LCBmo = Lower Class Boundary, modus terletak Ci = Panjan Interval Kelas Fmo = Frekuensi kelas modusbr />Fmo-1 = Frekuensi sebelum kelas modus Fmo+1 = Frekuensi setelah kelas modus Ia Kurnia, Drs., M.Pd. 16

53. It is the most popular average in the sense that is the one that most people use without being aware use without being average of it e.g. when they speak of the average number of car accident, bus breakdown etc.

54. Extreme value have no effect on the mode and it can be calculated when complete data are not available

56. It is not rigidly defined and thus cannot be called an ideal average

57. It is often indeterminate when the distribution is highly irregular

58. It is not based on all the observation in the series and hence is not an ideal measure of central tendency

59. It is not amenable to algebraic manipulation Ia Kurnia, Drs., M.Pd. 17 2

60. HUBUNGAN Xbar, Me, dan Mo Ia Kurnia, Drs., M.Pd. 18 Xbar = Me = Mo Mo Me Xbar Symmetric/Normal Curve Populasi/sampel dengan bentuk kurva ini, nilai Xbar, Me dan Mo akan sama. Skewed Negative Curve Populasi/sampel dengan bentuk kurva ini, nilai Xbar> Me > Mo

61. HUBUNGAN Xbar,, Me dan Mo Ia Kurnia, Drs., M.Pd. 19 XbarMe Mo 2 Skewed Positive Curve Populasi/sampel dengan bentuk kurva ini, nilai Xbar < Me < Mo Untuk Symmetric Curve, berlaku hubungan: Xbar – Mo = 5/4(Xbar – Me) Untuk Skewed Positive/Negative Xbar – Mo = 3(Xbar – Me)

62. CHOICE OF AN “AVERAGE” Is there such a thing as an Ideal Average? The answer is ‘probability not’ because no such ideal average has yet been computed. But what do we mean by ideal? It is generally agreed that the title should be given to that average which possesses that following characteristics: It is rigidly defined and easily computed It is simple enough to be understood by the layman It takes into account all item in the series and gives them equal weights. It is not unduly influenced by a few extreme values Its values are not greatly affected by sampling fluctuations It is amenable to algebraic manipulations. From the point listed above it obvious that all measures of central tendency discussed in the proceeding pages posses some of these characteristic and the arithmetic mean satisfies them to a greater degree than any other measure. The arithmetic mean is rigidly defined , is invariably determinate and quite easily computed. It is in common use, takes into account all items and its value is not much influenced by sampling fluctuations. Most important, it is amenable to algebraic manipulations. Its only important drawback is that it is influenced by a few high values in values in extremes. For all that is the average most often opted for when a choice has to be made. Ia Kurnia, Drs., M.Pd. 20

63. CHOICE OF AN “AVERAGE” There are three factors that have to be kept in mind when deciding what average to use: The purpose for which the average is being used The nature, characteristics and properties of the average The nature and characteristics of the data: in particular, the degree of homogeneity in the data. Ia Kurnia, Drs., M.Pd. 21 2

64. QUARTILE, DECILE, PERCENTILE QUARTILE/KUARSIL Bilangan-bilangan yang membagi sekelompok data menjadi empat bagian yang sama. Bilangan itu: Q1, Q2, Q3 Q1 : 25% dari data akan lebih kecil atau sama dengan bilangan itu. Q2 : 50% dari data akan lebih kecil atau sama dengan bilangan itu Q3 : 75% dari data akan lebih kecil atau sama dengan bilangan itu Ungrouped Data Ia Kurnia, Drs., M.Pd. 22

65. QUARTILE, DECILE, PERCENTILE Grouped Data Ia Kurnia, Drs., M.Pd. 23 DECILE/DESIL Bilangan-bilangan yang membagi sekelompok data menjadi sepuluh bagian yang sama. Bilangan itu: D1, D2, D3,….,D9 D1 : 10% dari data akan lebih kecil atau sama dengan bilangan itu. D2 : 30% dari data akan lebih kecil atau sama dengan bilangan itu D9 : 90% dari data akan lebih kecil atau sama dengan bilangan itu

66. QUARTILE, DECILE, PERCENTILE Ungrouped Data Grouped Data PERCENTILE/PERSENTIL Bilangan-bilangan yang membagi sekelompok data menjadi seratus bagian yang sama. Bilangan itu: P1, P2, P3,….,P99 Ia Kurnia, Drs., M.Pd. 24

67. QUARTILE, DECILE, PERCENTILE Ungrouped Data Grouped Data Ia Kurnia, Drs., M.Pd. 25

68. QUARTILE, DECILE, PERCENTILE Berikut ini adalah data harga Per Lembar Saham pada 20 perusahaan pilihan di Bursa Efek Jakarta Ia Kurnia, Drs., M.Pd. 26 Contoh

69. Laba bersih setahun yang diperoleh 120 perusahaan di Kota Damai Ia Kurnia, Drs., M.Pd. 27 QUARTILE, DECILE, PERCENTILE 6 Contoh

70. Ia Kurnia, Drs., M.Pd. 28