Statistik Dispersi Deviasi Variability
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Transcript of Statistik Dispersi Deviasi Variability
![Page 1: Statistik Dispersi Deviasi Variability](https://reader033.fdocuments.net/reader033/viewer/2022061601/5571f31a49795947648d7ffe/html5/thumbnails/1.jpg)
Tri CahyonoTri [email protected]@yahoo.co.id
Jurusan Kesehatan Lingkungan Jurusan Kesehatan Lingkungan PurwokertoPurwokerto
Politeknik Kesehatan Depkes SemarangPoliteknik Kesehatan Depkes Semarang
Tri CahyonoTri [email protected]@yahoo.co.id
Jurusan Kesehatan Lingkungan Jurusan Kesehatan Lingkungan PurwokertoPurwokerto
Politeknik Kesehatan Depkes SemarangPoliteknik Kesehatan Depkes Semarang
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UKURAN DISPERSI / DEVIASI / UKURAN DISPERSI / DEVIASI / VARIABILITYVARIABILITY
UKURAN DISPERSI / DEVIASI / UKURAN DISPERSI / DEVIASI / VARIABILITYVARIABILITY
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UKURAN DISPERSI / DEVIASI / VARIABILITY
• R ( Rentang )• Dr ( Deviasi Rata-rata)• V ( Variansi )• SD ( Standar Deviasi )• COV (Coefisien of Varians)• SE (Standar Error)
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RANGE / RENTANG• Range adalah jarak data terendah
sampai dengan data tertinggi, menunjukkan penyebaran data / rentang data.
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RENTANG / RANGE
DATA TUNGGAL DATA BERKELOMPOK
R= Angka tertinggi – Angka terendah
R = batas atas tidak nyata kelas tertinggi –
batas bawah tidak nyata kelas terendah
R= Angka tertinggi – Angka terendah + 1
R = batas atas tidak nyata kelas tertinggi –
batas bawah tidak nyata kelas terendah + 1
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DEVIASI RATA• Deviasi rata-rata adalah rata-rata
penyimpangan tiap angka pada suatu data terhadap meannya. Makin kecil harga deviasi ini, berarti makin kecil dispersi (pemencaran) angka pada data tersebut terhadap meannya.
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DEVIASI RATADATA
TUNGGALDATA
BERKELOMPOK
populasi
sampel
N
XXDr
i
N
XXi.fiDr
1N
XXDr
i
1N
XXi.fiDr
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VARIANSI• Variansi adalah harga deviasi yang
juga memperhitungkan deviasi tiap data terhadap meannya. Variansi untuk populasi dilambangkan , sedangkan variansi untuk sampel dilambangkan S2 atau V
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VARIANSIDATA
TUNGGALDATA
BERKELOMPOK
populasi
sampel
N
XXV
2i
1N
XX.fiV
2i
1N
XXV
2i
N
XX.fiV
2i
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STANDAR DEVIASI• Standar deviasi atau simpangan baku
merupakan akar dari variansi. • Standar deviasi dapat dipergunakan
sebagai angka yang mewakili seluruh agregate ukuran variability, dipengaruhi oleh perubahan nilai observasi.
• Standar deviasi biasa disingkat SD atau S, untuk ukuran sampel, sedangkan untuk populasi biasa dilambangkan .
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STANDAR DEVIASI
DATA TUNGGAL DATA BERKELOMPOK
VSD VSD
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COEFISIEN OF VARIANS• Coefisien of varians atau koefisien
keragaman
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COEFISIEN OF VARIANS
DATA TUNGGAL DATA BERKELOMPOK
100.X
SDCOV 100.
X
SDCOV
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STANDAR ERROR• Standar error = standar
keasalahan mean
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STANDAR ERROR
DATA TUNGGAL DATA BERKELOMPOK
Populasi sampel
N
SDSE
1N
SDSE
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CONTOH HITUNGANCONTOH HITUNGANCONTOH HITUNGANCONTOH HITUNGAN
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Contoh Data Tunggal• Kelompok I ; 35, 45, 36, 42, 38, 36, 48, 38, 40, 34, 34,
• Kelompok II ; 36, 34, 50, 32, 46, 34, 38, 44, 48, 44, 56,
• R data 1 = 48 – 34 + 1 = 15• R data 2 = 56 – 32 + 1 = 25
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73,3811
426X
4211
462X
NO KELOMPOK I KELOMPOK II
X1 Xi - X X2 Xi - X
1. 35 3,73 36 6
2. 45 6,27 34 8
3. 36 2,73 50 8
4. 42 3,27 32 10
5. 38 0,73 46 4
6. 36 2,73 34 8
7. 48 9,27 38 4
8. 38 0,73 44 2
9. 40 1,27 48 6
10. 34 4,73 44 2
11. 34 4,73 56 14
JUMLAH 426 40,19 462 72
MEAN65,3
11
19,40Dr 55,6
11
72Dr
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NOMOR Xi Xi - X Xi - X2
1. 35 -3,73 13,91
2. 45 6,27 39,31
3. 36 -2,73 7,45
4. 42 3,27 10,69
5. 38 -0,73 0,53
6. 36 -2,73 7,45
7. 48 9,27 85,93
8. 38 -0,73 0,53
9. 40 1,27 1,61
10. 34 -4,73 22,37
11. 34 -4,73 22,37
JUMLAH 426 212,18
MEAN 38,73
29,1911
18,212V
N
XXV
2
i
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39,4SD
29,19SD
VSD
33,11COV
100.73,38
39,4COV
100.X
SDCOV
32,1SE
11
39,4SE
N
SDSE
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TINGGI BADAN BALITA DI RW I DESA X
TAHUN 2000
NO TB(Cm) JML(fi)
1 70 – 79 9
2 80 – 89 15
3 90 – 99 12
4 100 – 109 10
5 110 – 119 4
JUMLAH 50
50,91X
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• R = batas atas tidak nyata kelas tertinggi – batas bawah tidak nyata kelas terendah
• R = 119,5 – 69,5• R = 50,0
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TINGGI BADAN BALITA DI RW I DESA X TAHUN 2000
No TB(Cm) JML(fi) Xi Xi - X fi.Xi-X
1 70 – 79 9 74,5 -17 153
2 80 – 89 15 84,5 -7 105
3 90 – 99 12 94,5 3 36
4 100 – 109 10 104,5 13 130
5 110 – 119 4 114,5 23 92
JUMLAH 50 516
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32,1050
516
.
Dr
Dr
N
XXifiDr
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TINGGI BADAN BALITA DI RW I DESA X TAHUN 2000
No TB(Cm) JML(fi) Xi Xi - X fi.Xi-X (Xi – X)2 fi.(Xi – X)2
1 70 – 79 9 74,5 -17 153 289 2601
2 80 – 89 15 84,5 -7 105 49 735
3 90 – 99 12 94,5 3 36 9 108
4 100 – 109 10 104,5 13 130 169 1690
5 110 – 119 4 114,5 23 92 529 2116
JUMLAH 50 516 7250
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14550
7250
.2
V
V
N
XXfiV i
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04,12
145
SD
SD
VSD
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16,13
100.5,91
04,12
100.
COV
COV
X
SDCOV
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70,1SE
50
04,12SE
N
SDSE
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USIA PENDERITA TB PARU DI KAB X TH 1996
NO USIA (Th) JUMLAH
1 35 – 39 2
2 40 – 44 5
3 45 – 49 11
4 50 – 54 21
5 55 – 59 22
6 60 – 64 25
7 65 – 69 10
8 70 – 74 4
JUMLAH 100
55,56X
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• R = batas atas tidak nyata kelas tertinggi – batas bawah tidak nyata kelas terendah
• R = 74,5 – 34,5• R = 40,0
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USIA PENDERITA TB PARU DI KAB X TH 1996
No USIA (Th) JML (fi) Xi Xi - X fi.Xi-X
1 35 – 39 2 37 -19,55 39,10
2 40 – 44 5 42 -14,55 72,75
3 45 – 49 11 47 -9,55 105,05
4 50 – 54 21 52 -4,55 95,55
5 55 – 59 22 57 0,45 9,90
6 60 – 64 25 62 5,45 136,25
7 65 – 69 10 67 10,45 104,50
8 70 – 74 4 72 15,45 61,80
JUMLAH 100 624,90
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249,6100
90,624
.
Dr
Dr
N
XXifiDr
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USIA PENDERITA TB PARU DI KAB X TH 1996
No USIA (Th) JML (fi) Xi Xi - X fi.Xi-X (Xi – X)2 fi. (Xi – X)2
1 35 – 39 2 37 -19,55 39,10 382,2025 764,41
2 40 – 44 5 42 -14,55 72,75 211,7035 1058,51
3 45 – 49 11 47 -9,55 105,05 91,2025 1003,23
4 50 – 54 21 52 -4,55 95,55 20,7025 434,75
5 55 – 59 22 57 0,45 9,90 0,2025 4,46
6 60 – 64 25 62 5,45 136,25 29,7025 742,56
7 65 – 69 10 67 10,45 104,50 109,2025 1092,03
8 70 – 74 4 72 15,45 61,80 238,7025 954,81
JUMLAH 100 624,90 6054,75
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5475,60100
75,6054
.2
V
V
N
XXfiV i
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78,7
5475,60
SD
SD
VSD
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76,13
100.55,56
78,7
100.
COV
COV
X
SDCOV
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78,0SE
100
78,7SE
N
SDSE
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TINGGI BADAN MASYARAKAT KALIMAS TAHUN 2006
NO. TINGGI BADAN JUMLAH
1. 140 – 149 6
2. 150 – 159 22
3. 160 – 169 39
4. 170 – 179 25
5. 180 – 189 7
6. 190 – 199 1
JUMLAH 100
TUGAS 1
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KADAR HB IBU – IBU DI DESA REJO TAHUN 2007
NO Hb JUMLAH
1 7,0 – 7,9 3
2 8,0 – 8,9 5
3 9,0 – 9,9 8
4 10,0 – 10,9 9
5 11,0 – 11,9 16
6 12,0 – 12,9 20
7 13,0 – 13,9 8
8 14,0 – 14,9 6
9 15,0 – 15,9 5
JUMLAH 80
TUGAS 2
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KEMIRINGAN / KEMENCENGAN / SKEWNESS KE KANAN ( + )
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KEMIRINGAN / KEMENCENGAN / SKEWNESS KE KIRI ( - )
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KURVA NORMAL
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