Statistika dan Luas Lingkupnya

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Statistika dan Luas Lingkupnya

  1. 1. Ia Kurnia, Drs., M.Pd 1 MEASURES OF DISPERSION VARIATION/VARIABILITY/VARIASI/ PENYIMPANGAN/PENYEBARAN/ DISPERSI Oleh: Ia Kurnia, Drs., M.Pd.
  2. 2. Ia Kurnia, Drs., M.Pd 2 MEASURES OF DISPERSION Tujuan Umum Perkuliahan: Mahasiswa diharapkan memahami perhitungan ‘measures of dispersion’ Tujuan Khusus Perkuliahan:  Dapat menjelaskan pengertian ‘measures of dispersion’  Dapat menyebutkan jenis-jenis ‘measures of dispersion’  Dapat menjelaskan pengertian ‘standard deviation’  Dapat menjelaskan fungsi ‘standard deviation’  Dapat melakukan perhitungan ‘standard deviation’ untuk memecahkan kasus yang berhubungan  Dapat menjelaskan pengertian ‘coefficient of variation ’  Dapat menjelaskan fungsi ‘coefficient of variation’  Dapat melakukan perhitungan ‘coefficient of variation’ untuk memecahkan kasus yang berhubungan  Dapat menjelaskan pengertian ‘standard score’  Dapat menjelaskan fungsi ‘standard score’  Dapat melakukan perhitungan ‘standard score’ untuk memecahkan kasus yang berhubungan  Dapat membedakan ‘standard deviation’ , ‘coefficient of variation’ dan ‘standard score’
  3. 3. Ia Kurnia, Drs., M.Pd 3 MEASURES OF DISPERSION ILUSTRASI Subject Marks of Student A Marks of Student B Statistics 75 100 Marketing 80 55 English 72 98 Taxes 75 77 Computer 72 65 Accountancy 76 55 TOTAL ?? ?? A.M ?? ?? Here the means are identical but variations in the performance of two student are large. A is definitely superior to B on the whole though B may have other commendable characteristics. An average condenses into one figure, all the characteristics of a given series. We have seen that in this process certain information about the series is concealed. A measure of variation or dispersion in any data shows the extent to which numerical values tend to spread about an average. Different series may possess different dispersions of items around the average. We may not know this by merely looking at the averages, especially if they happen to be identical
  4. 4. Ia Kurnia, Drs., M.Pd 4 MEASURES OF DISPERSION A measure of dispersion gives an idea about the extent of lack of uniformity in the sizes and qualities of the item in a series. It helps us to know the degree of uniformity and consistency in the series. If the difference between item is large the dispersion or variation is large and vice versa. If the difference between items is small, the average represents and describes the data adequately. For large difference it is proper to supplement information by calculating a measure of dispersion in addition to an average. It is useful to know the person in any data because its knowledge may serve: (1) to compare the current result with the past results, (2) to compare two or more sets of observation, (3) to suggest methods to control variations in the data. A study of variation help us in knowing the extent of uniformity or consistency in any data Uniformity in production is an essential requirement in industry. Quality control methods are based on the laws of dispersion.
  5. 5. Ia Kurnia, Drs., M.Pd 5 MEASURES OF DISPERSION Absolute Variability The Range The Quartile Deviation The Mean Deviation The Mean Difference The Standard Deviation Graphical Method Relatively Variability Relative Range Relative Quartile Deviation Relative Mean Deviation Coefficient of Variation Standard Score Jenis 4
  6. 6. Ia Kurnia, Drs., M.Pd 6 STANDARD DEVIATION Simpangan Baku Deviasi Standar Standar Deviasi Simpangan Standar It is the most important measures of dispersion. It is an improvement over the mean deviation and free from the defects of other measures of dispersion. The standard deviation or the root-mean-square deviation is the square root of the mean of the squared deviation from their mean of a set of values.
  7. 7. Ia Kurnia, Drs., M.Pd 7 STANDARD DEVIATION Ungrouped Data n xmdf s ii 2 )( − = ∑ n xx s i 2 )( − = ∑ 1 )( 2 − − = ∑ n xx s i Grouped Data 1 )( 2 − − = ∑ n xmdf s ii
  8. 8. Ia Kurnia, Drs., M.Pd 8 COEFFICIENT OF VARIATION Koefisien Variasi Koefisien Penyebaran Koefisien Standar Deviasi Angka relatif yang menunjukkan tingkat penyebaran data, digunakan untuk membandingkan dua keadaan atau lebih jika Rata-rata Hitung dan Simpangan Bakunya diketahui.
  9. 9. Ia Kurnia, Drs., M.Pd 9 COEFFICIENT OF VARIATION %100x x s CV = 2
  10. 10. Ia Kurnia, Drs., M.Pd 10 STANDARD SCORE Angka Baku Skor Baku Angka Standar Z Skor Angka yang menunjukkan kedudukan suatu individu pada kelompoknya, jika rata-rata dan simpangan baku kelompok tersebut diketahui. Fungsinya untuk membandingkan dua kedaan atau lebih.
  11. 11. Ia Kurnia, Drs., M.Pd 11 STANDARD SCORE s XX Z − = 2

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