1. 1 Pertemuan 2 Pendahuluan-2 Matakuliah: A0064/Statistik Ekonomi Tahun: 2005 Versi: 1/1

2. 2 Learning Outcomes Pada akhir pertemuan ini, diharapkan mahasiswa akan mampu : Menghitung beberapa persoalan yang berkaitan dengan ukuran letak seperti persentil dan kuartil

3. 3 Outline Materi Persentil Kuartil

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 Given any set of numerical observations, order them according to magnitude. l The P th percentile in the ordered set is that value below which lie P% (P percent) of the observations in the set. l The position of the P th percentile is given by (n + 1)P/100, where n is the number of observations in the set. 1-2 Percentiles and Quartiles

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 20 A large department store collects data on sales made by each of its salespeople. The number of sales made on a given day by each of 20 salespeople is shown on the next slide. Also, the data has been sorted in magnitude. Example 1-2

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 Example 1-2 (Continued) - Sales and Sorted Sales Sales Sorted 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

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 l Find the 50th, 80th, and the 90th percentiles of this data set. l To find the 50th percentile, determine the data point in position (n + 1)P/100 = (20 + 1)(50/100) = 10.5. l Thus, the percentile is located at the 10.5th position. l The 10th observation is 16, and the 11th observation is also 16. l The 50th percentile will lie halfway between the 10th and 11th values and is thus 16. Example 1-2 (Continued) Percentiles

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 l To find the 80th percentile, determine the data point in position (n + 1)P/100 = (20 + 1)(80/100) = 16.8. l Thus, the percentile is located at the 16.8th position. l The 16th observation is 19, and the 17th observation is also 20. l The 80th percentile is a point lying 0.8 of the way from 19 to 20 and is thus 19.8. Example 1-2 (Continued) Percentiles

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 l To find the 90th percentile, determine the data point in position (n + 1)P/100 = (20 + 1)(90/100) = 18.9. l Thus, the percentile is located at the 18.9th position. l The 18th observation is 21, and the 19th observation is also 22. l The 90th percentile is a point lying 0.9 of the way from 21 to 22 and is thus 21.9. Example 1-2 (Continued) Percentiles

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 l Quartiles are the percentage points that break down the ordered data set into quarters. l The first quartile is the 25th percentile. It is the point below which lie 1/4 of the data. l The second quartile is the 50th percentile. It is the point below which lie 1/2 of the data. This is also called the median. l The third quartile is the 75th percentile. It is the point below which lie 3/4 of the data. Quartiles – Special Percentiles

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 The first quartile, Q 1, (25th percentile) is often called the lower quartile. l The second quartile, Q 2, (50 th percentile) is often called median or the middle quartile. l The third quartile, Q 3, (75th percentile) is often called the upper quartile. l The interquartile range is the difference between the first and the third quartiles. Quartiles and Interquartile Range

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 SortedSales 9 6 6 9 12 10 10 12 13 13 15 14 16 14 14 15 14 16 16 16 17 16 16 17 24 17 21 18 22 18 18 19 19 20 18 21 20 22 17 24 First Quartile Median Third Quartile (n+1)P/100 (20+1)25/100=5.25 (20+1)50/100=10.5 (20+1)75/100=15.75 13 + (.25)(1) = 13.25 16 + (.5)(0) = 16 18+ (.75)(1) = 18.75 Quartiles Example 1-3: Finding Quartiles Position

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(n+1)P/100Quartiles Example 1-3: Using the Template

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(n+1)P/100Quartiles Example 1-3 (Continued): Using the Template This is the lower part of the same template from the previous slide.

15. 15 Penutup Materi Pendahuluan ini pada dasarnya merupakan pengenalan konsep-konsep dasar statistik untuk pembahasan materi- materi statistik selanjutnya