Download - Statistika Dasar (4) variasi data
UNIVERSITAS NEGERI JAKARTA
Pertemuan 4UKURAN PEMUSATAN DAN LOKASI
Hdi Nasbey, M.SiJurusan FisikaFakultas Matematika dan Ilmu Pemgetahuan Alam
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Outline
Penyajian Data Beberapa contoh daftar statistic Diagram Batang Diagram garis Diagram lingkaran dan diagram pastel Diagram lambing Diagram peta Diagram Pencar
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Learning Outcomes
Pada akhir pertemuan ini, diharapkan mahasiswa
akan mampu : Mahasiswa akan dapat menghitung ukuran-
ukuran pemusatan dan lokasi.
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Outline Materi
Rata-rata Median Modus Kuartil Desil persentil
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Measures of Center
A measure along the horizontal axis of the data distribution that locates the center center of the distribution.
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1. Arithmetic Mean or Average
The mean mean of a set of measurements is the sum of the measurements divided by the total number of measurements.
n
xx i
n
xx i
where n = number of measurementstsmeasuremen the all of sum ix
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Example
•The set: 2, 9, 1, 5, 6
n
xx i 6.6
5
33
5
651192
If we were able to enumerate the whole population, the population meanpopulation mean would be called (the Greek letter “mu”).
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Mean (Arithmetic Mean)
Approximating the Arithmetic Mean• Used when raw data are not available
• 1
sample size
number of classes in the frequency distribution
midpoint of the th class
frequencies of the th class
c
j jj
j
j
m f
Xn
n
c
m j
f j
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2. Median
• The median median of a set of measurements is the middle measurement when the measurements are ranked from smallest to largest.
• The position of the medianposition of the median is
.5(.5(nn + 1) + 1)
once the measurements have been ordered.
a. Md = X(n+1)/2 12/04/23
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Example
The set: 2, 4, 9, 8, 6, 5, 3 n = 7 Sort: 2, 3, 4, 5, 6, 8, 9 Position: .5(n + 1) = .5(7 + 1) = 4th
Median = 4th largest measurement
• The set: 2, 4, 9, 8, 6, 5 n = 6
• Sort:2, 4, 5, 6, 8, 9
• Position: .5(n + 1) = .5(6 + 1) = 3.5th Median = (5 + 6)/2 = 5.5 — average of the 3rd and 4th measurements
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b. Median Data Berkelompok
f
FnpbMe 2
1
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3. ModeUntuk menyatakan fenomena yang paling
banyak terjadi, juga untuk menentukan “rata-rata” dari data kualitatif.
a. Data tak berkelompok : Modus (Mo) dilihat dari data yang memiliki frekuensi terbanyak
The set: 2, 4, 9, 8, 8, 5, 3• The mode is 88, which occurs twice
The set: 2, 2, 9, 8, 8, 5, 3• There are two modes—88 and 22 (bimodalbimodal)
The set: 2, 4, 9, 8, 5, 3• There is no modeno mode (each value is unique).
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b. Modus Data Berkelompok
3,2,1;4
)1(
i
niXQi
4. Kuartil (Qi)Membagi kelompok data yang telah terurut menjadi 4 bagian yang sama besar.
a. Data tak berkelompok
4. Kuartil (Qi)Membagi kelompok data yang telah terurut menjadi 4 bagian yang sama besar.
a. Data tak berkelompok
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1
bb
bpbMo
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b. Kuartil Data Berkelompok
3,2,1;4
i
f
Fni
pbQi
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Example
Mean?
Median?
Mode? (Highest peak)
The number of quarts of milk purchased by 25 households:
0 0 1 1 1 1 1 2 2 2 2 2 2 2 2 2 3 3 3 3 3 4 4 4 5
2.225
55
n
xx i
2m
2mode
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Extreme Values The mean is more easily affected by extremely
large or small values than the median.
AppletApplet
•The median is often used as a measure of center when the distribution is skewed.
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Extreme Values
Skewed left: Mean < Median
Skewed right: Mean > Median
Symmetric: Mean = Median
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5. Desil Membagi kelompok data yang telah terurut
menjadi 10 bagian yang sama besar.a. Data tak berkelompok
b. Data berkelompok
9...,,2,1;10
)1( iXD nii
9,...,2,1;10
i
f
Fni
pbDi
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6. Persentil (Pi) Membagi kelompok data yang telah terurut
menjadi 100 bagian yang sama besar.a. Data tak berkelompok
b. Data berkelompok
9...,,2,1;10
)1( iXP nii
9,...,2,1;100
i
f
Fni
pbPi
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Selamat Belajar Semoga Sukses.
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