1. 1 Pertemuan 3 Statistik Deskriptif-1 Matakuliah: A0064 / Statistik Ekonomi Tahun: 2005 Versi: 1/1

2. 2 Learning Outcomes Pada akhir pertemuan ini, diharapkan mahasiswa akan mampu : Menghitung beberapa persoalan dalam ukuran pemusatan (mean, modus, dan median) dan ukuran keragaman (renrang, jarak antar kuartil, ragam dan simpangan baku)

3. 3 Outline Materi Ukuran-ukuran Pemusatan Ukuran-ukuran Keragaman Pengelompokkan Data dan Histogram

4. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 1-4 l Measures of Variability Range Interquartile range Variance Standard Deviation l Measures of Central Tendency Median Mode Mean l Other summary measures: Skewness Kurtosis Summary Measures: Population Parameters Sample Statistics

5. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 1-5  Medianâ Middle value when sorted in order of magnitude â 50th percentile  Modeâ Most frequently- occurring value  Meanâ Average 1-3 Measures of Central Tendency or Location

6. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 1-6 SalesSorted Sales 9 6 6 9 12 10 10 12 13 15 14 16 14 14 15 14 16 16 17 16 16 17 24 17 21 18 22 18 18 19 19 20 18 21 20 22 17 24 Median 50th Percentile (20+1)50/100=10.516 + (.5)(0) = 16 The median is the middle value of data sorted in order of magnitude. It is the 50 th percentile. Example – Median (Data is used from Example 1-2) See slide # 19 for the template output

7. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 1-7...... :. : : :..... --------------------------------------------------------------- 6 9 10 12 13 14 15 16 17 18 19 20 21 22 24...... :. : : :..... --------------------------------------------------------------- 6 9 10 12 13 14 15 16 17 18 19 20 21 22 24 Mode = 16 The mode is the most frequently occurring value. It is the value with the highest frequency. Example - Mode (Data is used from Example 1-2) See slide # 19 for the template output

8. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 1-8 The mean of a set of observations is their average - the sum of the observed values divided by the number of observations. Population Mean Sample Mean    x N i N 1 x x n i n    1 Arithmetic Mean or Average

9. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 1-9 x x n i n    1 317 20 1585. Sale s 9 6 12 10 13 15 16 14 16 17 16 24 21 22 18 19 18 20 17 317 Example – Mean (Data is used from Example 1-2) See slide # 19 for the template output

10. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 1-10...... :. : : :..... --------------------------------------------------------------- 6 9 10 12 13 14 15 16 17 18 19 20 21 22 24...... :. : : :..... --------------------------------------------------------------- 6 9 10 12 13 14 15 16 17 18 19 20 21 22 24 Median and Mode = 16 Mean = 15.85 Example - Mode (Data is used from Example 1-2) See slide # 19 for the template output

11. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 1-11 l Range Difference between maximum and minimum values l Interquartile Range Difference between third and first quartile (Q 3 - Q 1 ) l Variance Average * of the squared deviations from the mean l Standard Deviation Square root of the variance   Definitions of population variance and sample variance differ slightly. 1-4 Measures of Variability or Dispersion

12. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 1-12 Sorted SalesSalesRank 9 6 1 6 9 2 1210 3 1012 4 1313 5 1514 6 1614 7 1415 8 1416 9 161610 171611 161712 241713 211814 221815 181916 192017 182118 202219 172420 First Quartile Third Quartile Q 1 = 13 + (.25)(1) = 13.25 Q 3 = 18+ (.75)(1) = 18.75 Minimum Maximum Range Maximum - Minimum = 24 - 6 = 18 Interquartile Range Q3 - Q1 = 18.75 - 13.25 = 5.5 Example - Range and Interquartile Range (Data is used from Example 1-2) See slide # 19 for the template output

13. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 1-13 ( )     2 2 1 2 1 2 2 1            ()x N x N N i N i N x i N Population Variance     s xx n x x n n s s i n i n i n 2 2 1 2 1 2 2 1 1 1              () Sample Variance Variance and Standard Deviation ( )

14. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 1-14 6-9.85 97.0225 36 9-6.85 46.9225 81 10-5.85 34.2225 100 12-3.85 14.8225 144 13-2.85 8.1225 169 14-1.85 3.4225 196 15-0.85 0.7225 225 16 0.15 0.0225 256 17 1.15 1.3225 289 18 2.15 4.6225 324 19 3.15 9.9225 361 20 4.15 17.2225 400 21 5.15 26.5225 441 22 6.15 37.8225 484 24 8.15 66.4225 576 317 0 378.5500 5403 Calculation of Sample Variance

15. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 1-15(n+1)P/100Quartiles Example: Sample Variance Using the Template Note: This is just a replication of slide #19.

16. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 1-16 l Dividing data into groups or classes or intervals l Groups should be: Mutually exclusive Not overlapping - every observation is assigned to only one group Exhaustive Every observation is assigned to a group Equal-width (if possible) First or last group may be open-ended 1-5 Group Data and the Histogram

17. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 1-17 l Table with two columns listing: Each and every group or class or interval of values Associated frequency of each group Number of observations assigned to each group Sum of frequencies is number of observations –N for population –n for sample l Class midpoint is the middle value of a group or class or interval l Relative frequency is the percentage of total observations in each class Sum of relative frequencies = 1 Frequency Distribution

18. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 1-18 xf(x)f(x)/n Spending Class ($)Frequency (number of customers) Relative Frequency 0 to less than 100300.163 100 to less than 200380.207 200 to less than 300500.272 300 to less than 400310.168 400 to less than 500220.120 500 to less than 600130.070 1841.000 xf(x)f(x)/n Spending Class ($)Frequency (number of customers) Relative Frequency 0 to less than 100300.163 100 to less than 200380.207 200 to less than 300500.272 300 to less than 400310.168 400 to less than 500220.120 500 to less than 600130.070 1841.000 Example of relative frequency: 30/184 = 0.163 Sum of relative frequencies = 1 Example 1-7: Frequency Distribution

19. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 1-19 x F(x) F(x)/n Spending Class ($)Cumulative Frequency Cumulative Relative Frequency 0 to less than 100 30 0.163 100 to less than 200 68 0.370 200 to less than 300118 0.641 300 to less than 400149 0.810 400 to less than 500171 0.929 500 to less than 600184 1.000 x F(x) F(x)/n Spending Class ($)Cumulative Frequency Cumulative Relative Frequency 0 to less than 100 30 0.163 100 to less than 200 68 0.370 200 to less than 300118 0.641 300 to less than 400149 0.810 400 to less than 500171 0.929 500 to less than 600184 1.000 cumulative frequency The cumulative frequency of each group is the sum of the frequencies of that and all preceding groups. cumulative frequency The cumulative frequency of each group is the sum of the frequencies of that and all preceding groups. Cumulative Frequency Distribution

20. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 1-20 histogram l A histogram is a chart made of bars of different heights. Widths and locations of bars correspond to widths and locations of data groupings Heights of bars correspond to frequencies or relative frequencies of data groupings Histogram

21. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 1-21 Frequency Histogram Histogram Example

22. COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002 1-22 Relative Frequency Histogram Histogram Example

23. 23 Penutup Pembahasan materi dilanjutkan dengan Materi Pokok 4 (Statistik Deskriptif-2)