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Bab 3
Pengukuran
© 2002 Prentice-Hall, Inc.
Chap 3-1
Topik

Ukuran Pemusatan

Mean, median, mode, geometric mean, midrange

Quartile

Ukuran Keragaman


Range, interquartile range, variance and standard
deviation, coefficient of variation
Shape

Symmetric, skewed, using box-and-whisker plots
© 2002 Prentice-Hall, Inc.
Chap 3-2
Pengukuran
Pengukuran
Central Tendency
Mean
Quartile
Mode
Median
Range
Variation
Coefficient of
Variation
Variance
Geometric Mean
© 2002 Prentice-Hall, Inc.
Standard Deviation
Chap 3-3
Pengukuran Pemusatan
Central Tendency
Ratarata n
X 
Median
X
i 1
N

i 1
Geometric Mean
X G   X1  X 2 
n
X
i
Mode
 Xn 
1/ n
i
N
© 2002 Prentice-Hall, Inc.
Chap 3-4
Rata-rata (Mean)

Nilai rata-rata aritmatik

Sample mean
Sample Size
n
X

X
i 1
i
n
 Xn
Population mean
Population Size
N

© 2002 Prentice-Hall, Inc.
X1  X 2 

n
X
i 1
N
i
X1  X 2 

N
 XN
Chap 3-5
(continued)


Ukuran pemusatan yang paling sering
digunakan
Dipengaruhi oleh nilai ekstrem
0 1 2 3 4 5 6 7 8 9 10
Mean = 5
© 2002 Prentice-Hall, Inc.
0 1 2 3 4 5 6 7 8 9 10 12 14
Mean = 6
Chap 3-6
Median

Tidak dipengaruhi oleh nilai ekstrem
0 1 2 3 4 5 6 7 8 9 10
Median = 5

0 1 2 3 4 5 6 7 8 9 10 12 14
Median = 5
Dalam posisi terurut , median terletak
ditengah


If n or N is odd, the median is the middle number
If n or N is even, the median is the average of the
two middle numbers
© 2002 Prentice-Hall, Inc.
Chap 3-7
Modus (Mode)





Nilai yang sering muncul
Tidak dipengaruhi oleh nilai ekstrem
Digunakan pada data numeric atau categoric
Mungkin saja tidak terdapat modus
Atau ada beberapa modus
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Mode = 9
© 2002 Prentice-Hall, Inc.
0 1 2 3 4 5 6
No Mode
Chap 3-8
Rata-rataGeometric

Useful in the measure of rate of change of a
variable over time
X G   X1  X 2 

 Xn 
1/ n
Geometric mean rate of return

Measures the status of an investment over time
RG  1  R1   1  R2  
© 2002 Prentice-Hall, Inc.
 1  Rn  
1/ n
1
Chap 3-9
Contoh
An investment of $100,000 declined to $50,000 at the
end of year one and rebounded to $100,000 at end of
year two:
X1  $100,000
X 2  $50,000
X 3  $100,000
Average rate of return:
(50%)  (100%)
X
 25%
2
Geometric rate of return:
RG  1   50%    1  100%   
1/ 2
  0.50    2  
1/ 2
© 2002 Prentice-Hall, Inc.
1
 1  1  1  0%
1/ 2
Chap 3-10