Statistik Bisnis 1. Week 5 Variation, Shape and Exploring Numerical Data

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1 Statistik Bisnis 1 Week 5 Variation, Shape and Exploring Numerical Data

2 Agenda 15 Minutes 75 Minutes Attendance check Discussion and Exercise

3 Objectives To describe the properties of variation, and shape in numerical data To construct and interpret a boxplot

4 Numerical Descriptive Measurement Central Tendency Variation and Shape Exploring Numerical Data Numerical Descriptive Measures for a Population The Covariance and The Coefficient of Correlation

5 Variation and Shape Range Variance and Standard Deviation Coefficient of Variation Z Scores Shape

6 Review on Central Tendency Perhatikan data berikut: Hitunglah rata-rata, median, dan modus?

7 RANGE

8 Range (Rentang) Perhatikan data berikut: Berapakah rentangnya?

9 Range Range X X max min

10 Measures of Variation: Why The Range Can Be Misleading Ignores the way in which data are distributed Range = 12-7 = 5 Sensitive to outliers Range = 12-7 = 5 1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,4,5 Range = 5-1 = 4 1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,4,120 Range = = 119

11 VARIANCE AND STANDARD DEVIATION

12 Variance and Standard Deviation Variance Standard Deviation

13 Deviation Perhatikan kembali data berikut: Berapakah rata-ratanya? Mean = 162.7

14 Deviation Data Deviation Deviation X = i X

15 Variance and Standard Deviation Data Deviation (Dev)^ Sum of Squares = 594.1

16 Variance and Standard Deviation Sample size (n) = 10 Variance SD

17 Variance and Standard Deviation Sample S 2 n i 1 X i X n 1 2 Population 2 n i 1 X i N 2

18 Measures of Variation: Comparing Standard Deviations Data A Mean = 15.5 S = Data B Mean = 15.5 S = Data C Mean = 15.5 S = 4.570

19 THE COEFFICIENT OF VARIATION

20 The Coefficient of Variation Height Weight

21 The Coefficient of Variation Perhatikan kembali data berikut: Berapakah rata-rata dan simpangan baku? Mean = and SD = 8.125

22 The Coefficient of Variation Mahasiswa pada data tinggi badan sebelumnya, memiliki berat badan sebagai berikut: Berapakah rata-rata dan simpangan baku? Mean = 60.4 and SD = 7.8

23 The Coefficient of Variation Height Weight Mean SD Variabel manakah yang datanya lebih bervariasi? Coefficient of Variation: CV Height = 4.99% CV Weight = 12.92%

24 The Coefficient of Variation CV SD X.100%

25 LOCATING EXTREME OUTLIERS: Z SCORE

26 Locating Extreme Outliers: Z Score Perhatikan lagi data tinggi badan berikut: SD = SD = Mean =

27 Locating Extreme Outliers: Z Score Maka, Z Score untuk 160 adalah? SD = Z Score = 0 Z Score = -1 Z Score = Mean =

28 Locating Extreme Outliers: Z Scores Perhatikan kembali data berikut: Berapakah Z Scores dari 160, 174, 168 dan 150? Z 160 = -0.33, Z 174 = 1.39, Z 168 = 0.65, and Z 150 = -0.56

29 Locating Extreme Outliers: Z Score Z X X X SD A data value is considered an extreme outlier if its Z-score is less than -3.0 or greater than The larger the absolute value of the Z-score, the farther the data value is from the mean.

30 SHAPE

31 Shape Perhatikan kembali data berikut: Median = 161 Right-Skewed Mean =

32 Shape Bagaimana jika datanya seperti berikut: Left-Skewed Median = Mean =

33 Shape Describes how data are distributed Left-Skewed Mean < Median Symmetric Mean = Median Right-Skewed Median < Mean

34 Exploring Numerical Data Quartiles Boxplot Interquartile Range Five-Number Summary

35 QUARTILES

36 1 st Quartile 2 nd Quartile 3 rd Quartile Quartiles Q 1 Q 2 Q 3 Median

37 Quartiles Perhatikan data tinggi badan berikut: Berapakah Q 1, Q 2 dan Q 3? Q 1 = 157 Q 2 = 162 (Median) Q 3 = 170

38 Quartiles Perhatikan juga data berikut: Berapa Q 1, Q 2 dan Q 3? Q 1 = Q 2 = 162 (Median) Q 3 = 171.5

39 Quartiles Dan perhatikan pula data berikut: Berapakah Q 1, Q 2 dan Q 3? Q 1 = 157 Q 2 = 161 (Median) Q 3 = 170

40 Quartiles Median = 161 Q 1 = 157 Q 3 = % 25% 25% 25% of all data

41 INTERQUARTILE RANGE

42 Interquartile Range Q 1 = 157 Q 3 = % In the middle of all data

43 Interquartile Range Q 1 = 157 Q 3 = Berapakah rentang Interquatile? Interquartile Range = = 13

44 Interquartile Range Interquartile Range Q Q 3 1

45 FIVE-NUMBER SUMMARY

46 Five-Number Summary X min Q 1 Median Q 3 X max

47 Five-Number Summary Perhatikan data tinggi badan berikut: Apakah Five-Number Summary?

48 BOXPLOT

49 Boxplot X min Q 1 Median Q 3 X max

50 Boxplot Perhatikan data berikut: Buatlah Boxplot-nya?

51 Boxplot for the Height of Business Statistic s Student Height (cm)

52 Distribution Shape and The Boxplot Left-Skewed Symmetric Right-Skewed Q 1 Q 2 Q 3 Q 1 Q 2 Q 3 Q 1 Q 2 Q 3

53 MEASURE OF SKEWNESS

54 Karl Pearson's Measure of Skewness Median = Mean = S k 3( )

55 Karl Pearson's Measure of Skewness 3( X Median) S k S

56 Bowley's Formula for Measuring Skewness Height (cm)

57 Bowley's Formula for Measuring Skewness S k ( Q 3 Q 2 ( Q ) 3 ( Q Q 1 2 ) Q 1 )

58 EXERCISE

59 3.10 Data berikut adalah data pengeluaran yang dilakukan oleh sampel sembilan orang konsumen untuk makan siang di sebuah restoran cepat saji (dalam $): 4,20 5,03 5,86 6,45 7,38 7,54 8,46 8,47 9,87 a. Hitung variansi, simpangan baku (standard deviation), rentang, dan koefisien variasi. b. Apakah datanya menceng? Jika ya bagaimana? c. Berdasarkan hasil perhitungan diatas, apa kesimpulan yang bisa anda ambil mengenai jumlah pengeluaran konsumen untuk makan siang tersebut?

60 THANK YOU