1 pertemuan 3 statistik deskriptif-1 matakuliah: a0064 / statistik ekonomi tahun: 2005 versi: 1/1
Post on 20-Dec-2015
230 views
TRANSCRIPT
1
Pertemuan 3Statistik 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 nBUSINESS STATISTICS
Aczel/SounderpandianMcGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002
1-4
Measures of VariabilityRange Interquartile rangeVarianceStandard Deviation
Measures of Central TendencyMedianModeMean
Other summary measures:SkewnessKurtosis
Summary Measures: Population Parameters Sample Statistics
COMPLETE 5 t h e d i t i o nBUSINESS STATISTICS
Aczel/SounderpandianMcGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002
1-5
Median Middle value when sorted in order of magnitude 50th percentile
Mode Most frequently- occurring value
Mean Average
1-3 Measures of Central Tendency or Location
COMPLETE 5 t h e d i t i o nBUSINESS STATISTICS
Aczel/SounderpandianMcGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002
1-6
Sales Sorted Sales
9 6 6 9 12 1010 1213 1315 1416 1414 1514 1616 1617 1616 1724 1721 1822 1818 1919 2018 2120 2217 24
Median
Median50th Percentile
(20+1)50/100=10.5 16 + (.5)(0) = 16
The median is the middle value of data sorted in order of magnitude. It is the 50th percentile.
Example – Median (Data is used from Example 1-2)
See slide # 19 for the template outputSee slide # 19 for the template output
COMPLETE 5 t h e d i t i o nBUSINESS STATISTICS
Aczel/SounderpandianMcGraw-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 outputSee slide # 19 for the template output
COMPLETE 5 t h e d i t i o nBUSINESS STATISTICS
Aczel/SounderpandianMcGraw-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
xNi
N
1 xx
ni
n
1
Arithmetic Mean or Average
COMPLETE 5 t h e d i t i o nBUSINESS STATISTICS
Aczel/SounderpandianMcGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002
1-9
xx
ni
n
1 31720
1585.
Sales 9 6 12 10 13 15 16 14 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 outputSee slide # 19 for the template output
COMPLETE 5 t h e d i t i o nBUSINESS STATISTICS
Aczel/SounderpandianMcGraw-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 outputSee slide # 19 for the template output
COMPLETE 5 t h e d i t i o nBUSINESS STATISTICS
Aczel/SounderpandianMcGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002
1-11
RangeDifference between maximum and minimum values
Interquartile RangeDifference between third and first quartile (Q3 - Q1)
VarianceAverage*of the squared deviations from the mean
Standard DeviationSquare 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 nBUSINESS STATISTICS
Aczel/SounderpandianMcGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002
1-12
SortedSales Sales Rank 9 6 1 6 9 212 10 310 12 413 13 515 14 616 14 714 15 814 16 916 16 1017 16 1116 17 1224 17 1321 18 1422 18 1518 19 1619 20 1718 21 1820 22 1917 24 20
First Quartile
Third Quartile
Q1 = 13 + (.25)(1) = 13.25
Q3 = 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 outputSee slide # 19 for the template output
COMPLETE 5 t h e d i t i o nBUSINESS STATISTICS
Aczel/SounderpandianMcGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002
1-13
( )
2
2
1
2
1
2
2
1
( )x
N
xN
N
i
N
i
N xi
N
Population Variance
sx x
n
xx
nn
s s
i
n
i
ni
n
2
2
1
2
1
2
2
1
1
1
( )
Sample Variance
Variance and Standard Deviation
( )
COMPLETE 5 t h e d i t i o nBUSINESS STATISTICS
Aczel/SounderpandianMcGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002
1-14
6 -9.85 97.0225 36 9 -6.85 46.9225 8110 -5.85 34.2225 10012 -3.85 14.8225 14413 -2.85 8.1225 16914 -1.85 3.4225 196 14 -1.85 3.4225 19615 -0.85 0.7225 22516 0.15 0.0225 25616 0.15 0.0225 25616 0.15 0.0225 25617 1.15 1.3225 28917 1.15 1.3225 28918 2.15 4.6225 32418 2.15 4.6225 32419 3.15 9.9225 36120 4.15 17.2225 40021 5.15 26.5225 44122 6.15 37.8225 48424 8.15 66.4225 576
317 0 378.5500 5403
x xx ( )x x 2
x 2
sx x
n
xx
nn
s s
i
n
i
ni
n
2
2
1
2
1
2
2
2
1
378 55
20 1
378 55
1919 923684
1
5403 31720
20 1
5403100489
2019
5403 5024 45
19
378 55
1919 923684
19 923684 4 46
1
( ) .
( )
..
. ..
. .
Calculation of Sample Variance
COMPLETE 5 t h e d i t i o nBUSINESS STATISTICS
Aczel/SounderpandianMcGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002
1-15
(n+1)P/100(n+1)P/100 QuartilesQuartiles
Example: Sample Variance Using the Template
Note: This is Note: This is just a just a replication replication of slide #19.of slide #19.
COMPLETE 5 t h e d i t i o nBUSINESS STATISTICS
Aczel/SounderpandianMcGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002
1-16
Dividing data into groups or classes or intervals
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 nBUSINESS STATISTICS
Aczel/SounderpandianMcGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002
1-17
Table with two columns listing:Each and every group or class or interval of valuesAssociated frequency of each group
• Number of observations assigned to each group• Sum of frequencies is number of observations
– N for population– n for sample
Class midpoint is the middle value of a group or class or interval
Relative frequency is the percentage of total observations in each classSum of relative frequencies = 1
Frequency Distribution
COMPLETE 5 t h e d i t i o nBUSINESS STATISTICS
Aczel/SounderpandianMcGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002
1-18
x f(x) f(x)/nSpending Class ($) Frequency (number of customers) Relative Frequency
0 to less than 100 30 0.163100 to less than 200 38 0.207200 to less than 300 50 0.272300 to less than 400 31 0.168400 to less than 500 22 0.120500 to less than 600 13 0.070
184 1.000
x f(x) f(x)/nSpending Class ($) Frequency (number of customers) Relative Frequency
0 to less than 100 30 0.163100 to less than 200 38 0.207200 to less than 300 50 0.272300 to less than 400 31 0.168400 to less than 500 22 0.120500 to less than 600 13 0.070
184 1.000
• Example of relative frequency: 30/184 = 0.163 • Sum of relative frequencies = 1
Example 1-7: Frequency Distribution
COMPLETE 5 t h e d i t i o nBUSINESS STATISTICS
Aczel/SounderpandianMcGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002
1-19
x F(x) F(x)/nSpending Class ($) Cumulative Frequency Cumulative Relative Frequency
0 to less than 100 30 0.163100 to less than 200 68 0.370200 to less than 300 118 0.641300 to less than 400 149 0.810400 to less than 500 171 0.929500 to less than 600 184 1.000
x F(x) F(x)/nSpending Class ($) Cumulative Frequency Cumulative Relative Frequency
0 to less than 100 30 0.163100 to less than 200 68 0.370200 to less than 300 118 0.641300 to less than 400 149 0.810400 to less than 500 171 0.929500 to less than 600 184 1.000
The cumulative frequencycumulative frequency of each group is the sum of the frequencies of that and all preceding groups.
The cumulative frequencycumulative 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 nBUSINESS STATISTICS
Aczel/SounderpandianMcGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002
1-20
A histogram histogram is a chart made of bars of different heights.Widths and locations of bars correspond to
widths and locations of data groupingsHeights of bars correspond to frequencies or
relative frequencies of data groupings
Histogram
COMPLETE 5 t h e d i t i o nBUSINESS STATISTICS
Aczel/SounderpandianMcGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002
1-21
Frequency Histogram
Histogram Example
COMPLETE 5 t h e d i t i o nBUSINESS STATISTICS
Aczel/SounderpandianMcGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2002
1-22
Relative Frequency Histogram
Histogram Example
23
Penutup
• Pembahasan materi dilanjutkan dengan Materi Pokok 4 (Statistik Deskriptif-2)