Measures of Dispersion

MEASURES OF DISPERSION
VARIATION/VARIABILITY/VARIASI/
PENYIMPANGAN/PENYEBARAN/
DISPERSI
Oleh: Ia Kurnia
1
Tujuan Umum Perkuliahan:

Mahasiswa diharapkan memahami perhitungan ‘measures of dispersion’
Tujuan Khusus Perkuliahan:

✓ Dapat menjelaskan pengertian ‘measures of dispersion’
✓ Dapat menyebutkan jenis-jenis ‘measures of dispersion’
✓ Dapat menjelaskan pengertian ‘standard deviation’
✓ Dapat menjelaskan fungsi ‘standard deviation’
✓ Dapat melakukan perhitungan ‘standard deviation’ untuk memecahkan kasus yang
berhubungan
✓ Dapat menjelaskan pengertian ‘coefficient of variation ’
✓ Dapat menjelaskan fungsi ‘coefficient of variation’
✓ Dapat melakukan perhitungan ‘coefficient of variation’ untuk memecahkan kasus yang
berhubungan
✓ Dapat menjelaskan pengertian ‘standard score’
✓ Dapat menjelaskan fungsi ‘standard score’
✓ Dapat melakukan perhitungan ‘standard score’ untuk memecahkan kasus yang
berhubungan
✓ Dapat membedakan ‘standard deviation’ , ‘coefficient of variation’ dan ‘standard score’
2
ILUSTRASI Here the means are identical but
variations in the performance of
two student are large. A is
definitely superior to B on the
Subject Marks of Student A Marks of Student B whole though B may have other
commendable characteristics.
Statistics 75 100 An average condenses into one
figure, all the characteristics of a
Marketing 80 55 given series. We have seen that in
this process certain information
English 72 98
about the series is concealed.
75 77 A measure of variation or
Taxes dispersion in any data shows the
72 65 extent to which numerical values
Computer
tend to spread about an average.
Accountancy 76 55 Different series may possess
different dispersions of items
TOTAL ?? ?? around the average. We may not
know this by merely looking at the
A.M ?? ?? averages, especially if they happen
to be identical
3
A measure of dispersion gives an idea about the extent of lack of uniformity in the
sizes and qualities of the item in a series. It helps us to know the degree of
uniformity and consistency in the series.
If the difference between item is large the dispersion or variation is large and vice
versa. If the difference between items is small, the average represents and
describes the data adequately. For large difference it is proper to supplement
information by calculating a measure of dispersion in addition to an average.
It is useful to know the person in any data because its knowledge may serve:
(1) to compare the current result with the past results,
(2) to compare two or more sets of observation,
(3) to suggest methods to control variations in the data.
A study of variation help us in knowing the extent of uniformity or consistency in

any data
Uniformity in production is an essential requirement in industry. Quality control
methods are based on the laws of dispersion.
4
MEASURES OF DISPERSION 4
Jenis
Absolute Variability Relatively Variability
The Range Relative Range
The Quartile Deviation Relative Quartile Deviation
The Mean Deviation Relative Mean Deviation
The Mean Difference Coefficient of Variation
The Standard Deviation Standard Score
Graphical Method
5
STANDARD DEVIATION
Simpangan Baku
Deviasi Standar
Standar Deviasi
Simpangan Standar
It is the most important measures of dispersion. It is an improvement
over the mean deviation and free from the defects of other measures
of dispersion.
The standard deviation or the root-mean-square deviation is the square
root of the mean of the squared deviation from their mean of a set of
values.
6
STANDARD DEVIATION
Ungrouped Data
s =
 i
( x − x ) 2
s =
 (x i − x )2
n n −1
Grouped Data
 f (md − x )2
s =
 f (md
i i − x )2 s = i
n −1
i
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COEFFICIENT OF VARIATION
Koefisien Variasi
Koefisien Penyebaran
Koefisien Standar Deviasi
Angka relatif yang menunjukkan tingkat

penyebaran data, digunakan untuk
membandingkan dua keadaan atau lebih jika
Rata-rata Hitung dan Simpangan Bakunya
diketahui.
8
2
COEFFICIENT OF VARIATION
s
CV = x 100%
x
9
STANDARD SCORE
Angka Baku
Skor Baku
Angka Standar
Z Skor
Angka yang menunjukkan kedudukan suatu individu pada

kelompoknya, jika rata-rata dan simpangan baku kelompok tersebut
diketahui. Fungsinya untuk membandingkan dua kedaan atau lebih.
10
STANDARD SCORE 2
X − X
Z=
s
11

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MEASURES OF DISPERSION

Tujuan Umum Perkuliahan:

Tujuan Khusus Perkuliahan:

A study of variation help us in knowing the extent of uniformity or consistency in

Angka relatif yang menunjukkan tingkat

Angka yang menunjukkan kedudukan suatu individu pada

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