Matakuliah
Tahun
Versi
: I0134 – Metoda Statistika
: 2005
: Revisi
Pertemuan 04
Ukuran Pemusatan dan Penyebaran
1
Learning Outcomes
Pada akhir pertemuan ini, diharapkan mahasiswa
akan mampu :
• Mahasiswa dapat menghitung,
mengidentifikasi penggunaan ukuran
pemusatan dan penyebaran.
2
Outline Materi
•
•
•
•
•
•
Rata-rata
Median
Modus
Kuartil
Desil Persentil
Varians dan Simpangan baku
3
Ukuran Pemusatan dan
Penyebaran
Median
 Middle value when
sorted in order of
magnitude
 50th percentile
Mode
 Most frequentlyoccurring value
Mean
 Average
4
Contoh Soal - Median
Sales
9
6
12
10
13
15
16
14
14
16
17
16
24
21
22
18
19
18
20
17
Sorted Sales
6
9
10
12
13
14
14
15
16
16
16
17
17
18
18
19
20
21
22
24
Median
50th Percentile
(20+1)50/100=10.5
16 + (.5)(0) = 16
Median
The median is the middle
value of data sorted in
order of magnitude. It is
the fiftieth percentile.
5
Contoh Soal - Mode
.
. .
.
. . : . : : : . . . .
.
--------------------------------------------------------------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.
6
Arithmetic Mean or Average
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
N
m=
x
i =1
N
n
x=
x
i =1
n
7
Contoh Soal - (Mean)
Sale
s
9
6
12
10
13
15
16
14
14
16
17
16
24
21
22
18
19
18
20
17
317
n
x=
x
i =1
n
=
317
= 1585
.
20
8
Contoh Soal - Mode
.
. .
.
. . : . : : : . . . .
.
--------------------------------------------------------------6
9 10 12 13 14 15 16 17 18 19 20 21 22 24
Mean = 15.85
Median and Mode = 16
9
Ukuran Penyebaran

Range
– Difference between maximum and minimum
values

Interquartile Range
– Difference between third and first quartile
(Q3 - Q1)

Variance
– Mean* squared deviation from the mean

Standard Deviation
– Square root of the variance

Definitions of population variance and sample variance differ slightly.
10
Contoh . Range and
Interquartile Range
Sales
9
6
12
10
13
15
16
14
14
16
17
16
24
21
22
18
19
18
20
17
Sorted
Sales
6
9
10
12
13
14
14
15
16
16
16
17
17
18
18
19
20
21
22
24
Rank
1
Minimum
2
3
4
5
6 First Quartile
7
8
9
10
11
12
13
14
15
16 Third Quartile
17
18
19
Maximum
20
Range
Maximum - Minimum =
24 - 6 =
18
Q1 = 13 + (.25)(1) = 13.25
Q3 = 18+ (.75)(1) = 18.75
Interquartile
Range
Q3 - Q1 =
18.75 - 13.25 = 5.5
11
Variance and Standard
Deviation
Population Variance
Sample Variance
2
m
(x )
s 2 = i=1
x
2
s=
( x)
-
i=1
s
s =
2
i =1
N
N
=
(x - x)
n
N
N
2
N

i =1
N
2
(n - 1)
(
)
x n
=
2
2
n
x
i =1
2
n
i =1
(n - 1)
s= s
2
12
Calculation of Sample
Variance
x
6
9
10
12
13
14
14
15
16
16
16
17
17
18
18
19
20
21
22
24
317
x-x
-9.85
-6.85
-5.85
-3.85
-2.85
-1.85
-1.85
-0.85
0.15
0.15
0.15
1.15
1.15
2.15
2.15
3.15
4.15
5.15
6.15
8.15
0
(x - x) 2
x
n
2
97.0225
46.9225
34.2225
14.8225
8.1225
3.4225
3.4225
0.7225
0.0225
0.0225
0.0225
1.3225
1.3225
4.6225
4.6225
9.9225
17.2225
26.5225
37.8225
66.4225
36
81
100
144
169
196
196
225
256
256
256
289
289
324
324
361
400
441
484
576
378.5500
5403
s =
2
=
(x - x)
i =1
(n - 1)
378.55
=
(20 - 1)
378.55
= 19.923684
19
n
=
2
x 2
i =1
 n x
 i =1 
2
n
(n - 1)
2
100489
317
5403 5403 20 =
20
=
19
(20 - 1)
5403 - 5024.45 378.55
=
= 19.923684
19
19
s = s = 19.923684 = 4.46
=
2
13
Group Data and the Histogram


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
14
• Selamat Belajar Semoga Sukses.
15