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

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

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

COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc.,  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

COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., SalesSorted Sales Median 50th Percentile (20+1)50/100= (.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

COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., :. : : : :. : : : 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

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

COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., x x n i n    Sale s Example – Mean (Data is used from Example 1-2) See slide # 19 for the template output

COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., :. : : : :. : : : Median and Mode = 16 Mean = Example - Mode (Data is used from Example 1-2) See slide # 19 for the template output

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

COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., Sorted SalesSalesRank First Quartile Third Quartile Q 1 = 13 + (.25)(1) = Q 3 = 18+ (.75)(1) = Minimum Maximum Range Maximum - Minimum = = 18 Interquartile Range Q3 - Q1 = = 5.5 Example - Range and Interquartile Range (Data is used from Example 1-2) See slide # 19 for the template output

COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., ( )                ()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              () Sample Variance Variance and Standard Deviation ( )

COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., Calculation of Sample Variance

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

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

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

COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., xf(x)f(x)/n Spending Class ($)Frequency (number of customers) Relative Frequency 0 to less than to less than to less than to less than to less than to less than xf(x)f(x)/n Spending Class ($)Frequency (number of customers) Relative Frequency 0 to less than to less than to less than to less than to less than to less than Example of relative frequency: 30/184 = Sum of relative frequencies = 1 Example 1-7: Frequency Distribution

COMPLETE 5 t h e d i t i o n BUSINESS STATISTICS Aczel/Sounderpandian McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., x F(x) F(x)/n Spending Class ($)Cumulative Frequency Cumulative Relative Frequency 0 to less than to less than to less than to less than to less than to less than x F(x) F(x)/n Spending Class ($)Cumulative Frequency Cumulative Relative Frequency 0 to less than to less than to less than to less than to less than to less than 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

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

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

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

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