1 pertemuan 3 statistik deskriptif-1 matakuliah: a0064 / statistik ekonomi tahun: 2005 versi: 1/1

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Pertemuan 3Statistik Deskriptif-1

Matakuliah : A0064 / Statistik Ekonomi

Tahun : 2005

Versi : 1/1

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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)

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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



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



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



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)




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



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)




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. . . . . . : . : : : . . . . . --------------------------------------------------------------- 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)




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



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)




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

( )



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



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.



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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



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



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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


184 1.000

• Example of relative frequency: 30/184 = 0.163 • Sum of relative frequencies = 1

Example 1-7: Frequency Distribution



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x F(x) F(x)/nSpending Class ($) Cumulative Frequency Cumulative Relative Frequency


x F(x) F(x)/nSpending Class ($) Cumulative Frequency Cumulative Relative Frequency


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



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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



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Frequency Histogram

Histogram Example



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Relative Frequency Histogram

Histogram Example

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Penutup

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

1 pertemuan 3 statistik deskriptif-1 matakuliah: a0064 / statistik ekonomi tahun: 2005 versi: 1/1

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