1. Ia Kurnia, Drs., M.Pd 1
MEASURES OF DISPERSION
VARIATION/VARIABILITY/VARIASI/
PENYIMPANGAN/PENYEBARAN/
DISPERSI
Oleh: Ia Kurnia, Drs., M.Pd.

2. Ia Kurnia, Drs., M.Pd 2
MEASURES OF DISPERSION
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’

3. Ia Kurnia, Drs., M.Pd 3
MEASURES OF DISPERSION
ILUSTRASI
Subject Marks of Student A
Marks of Student
B
Statistics 75 100
Marketing 80 55
English 72 98
Taxes 75 77
Computer 72 65
Accountancy 76 55
TOTAL ?? ??
A.M ?? ??
Here the means are identical but
variations in the performance of
two student are large. A is
definitely superior to B on the
whole though B may have other
commendable characteristics.
An average condenses into one
figure, all the characteristics of a
given series. We have seen that in
this process certain information
about the series is concealed.
A measure of variation or
dispersion in any data shows the
extent to which numerical values
tend to spread about an average.
Different series may possess
different dispersions of items
around the average. We may not
know this by merely looking at the
averages, especially if they happen
to be identical

4. Ia Kurnia, Drs., M.Pd 4
MEASURES OF DISPERSION
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.

5. Ia Kurnia, Drs., M.Pd 5
MEASURES OF DISPERSION
Absolute Variability
The Range
The Quartile Deviation
The Mean Deviation
The Mean Difference
The Standard Deviation
Graphical Method
Relatively Variability
Relative Range
Relative Quartile Deviation
Relative Mean Deviation
Coefficient of Variation
Standard Score
Jenis
4

6. Ia Kurnia, Drs., M.Pd 6
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.

7. Ia Kurnia, Drs., M.Pd 7
STANDARD DEVIATION
Ungrouped Data
n
xmdf
s ii
2
)( −
=
∑
n
xx
s
i
2
)( −
=
∑
1
)( 2
−
−
=
∑
n
xx
s i
Grouped Data
1
)( 2
−
−
=
∑
n
xmdf
s ii

8. Ia Kurnia, Drs., M.Pd 8
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.

9. Ia Kurnia, Drs., M.Pd 9
COEFFICIENT OF VARIATION
%100x
x
s
CV =
2

10. Ia Kurnia, Drs., M.Pd 10
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.

11. Ia Kurnia, Drs., M.Pd 11
STANDARD SCORE
s
XX
Z
−
=
2