statistik 2.ppt
TRANSCRIPT
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STATISTIK DESKRIPTIF.
Perhitungan-perhitungan Statistik Deskriptif
dari suatu agregate ( Kumpulan Data ).
1. Nilai-nilai Central tendency = Nilai tengah.
2. Nilai-nilai Variabilitas = Sebaran.
3. Skewness = Kemiringan.
4. Kurtosis = Kerampingan.
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(1). CENTRAL TENDENCY ( NILAI TENGAH ).
1. Mean = Rerata = Rata-rata hitung = Purata.
2. Median = Rata-rata median.
3. Mode = Modus = Rata-rata mode.
4. Geometric Mean. Tidak penting.
5. Harmonic Mean.
6. Quadratic Mean.
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1. M E A N .
1. Suatu nilai yg paling dikenal, umum digunakan,
mudah dihitung, mudah difahami.
2. Semua agregate (kumpulan data) punya mean.
3. Semua angka digunakan utk menetapkan besar mean.
4. Dpt diperlakukan secara aljabar.
5. Sangat dipengaruhi angka ekstrim.
6. ∑(x-Mean) = 0
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RUMUS MEAN.
Σ x
Mean = ----------
n
x1 + x2 + x3 + …….. + xn
Mean = ---------------------------------------
n
(3). Semua angka digunakan Mean.
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(4). Dpt diperlakukan sec Aljabar.
Data : 2, 3, 4, 5, 6, 5, 6, 5, 5, 4.
Mean(1) = (2+3+4+5+6) / 5 = 4
Mean(2) = (5+6+5+5+4) / 5 = 5
Mean = (4 + 5) / 2 = 4.5
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(5). Dipengaruhi nilai Ekstrim.
Data : 2, 3, 2, 1, 2, 2
Mean(1) = (2+3+2+1+2+2) / 6 = 2
Data : 2, 3, 2, 1, 2, 2, 14 nilai ekstrim
Mean(2) = (2+3+2+1+2+2+14) / 7 = 4
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(6). Σ (x – Mean) = 0
x (x-Mean)---------------------------- 2 - 2 3 - 1 4 0 5 1 6 2--------------------------Mean = 4 0 = Σ (x-Mean)
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2. M E D I A N .
1. Suatu nilai posisi.
2. Nilai paling di tengah dari suatu array.
3. Rumus posisinya = (n+1)/2.
4. Tidak dipengaruhi oleh nilai ekstrim.
5. Dipengaruhi oleh banyaknya n.
Contoh : Kumpulan data : 2, 3, 4, 5, 6.
Posisi median = (5+1)/2 = 3.
Nilai Median = 4.
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Data : 2, 3, 4, 5, 6.
Posisi Median = (5+1) / 2 = 3
Nilai Median = 4
Data : 2, 3, 4, 5, 12 Median = 4
Data : 2, 3, 4, 5, 6, 9 Median = 4.5
( Nilai Median dipengaruhi jumlah n ).
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3. M O D U S = M O D E.
Mode ialah nilai yg paling sering muncul
dalam suatu agregate (kumpulan data).
1,2,2,2,3,5 Mode = 2
3,3,7,8,12,16
3,3,4,5,6,7,7
4,6,8,10,13,15,17
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1,2,2,2,3,5 Mode = 2
3,3,7,8,12,16 Mode = 3
3,3,4,5,6,7,7
4,6,8,10,13,15,17
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1,2,2,2,3,5 Mode = 2
3,3,7,8,12,16 Mode = 3
3,3,4,5,6,7,7 Mode = 3 dan 7
4,6,8,10,13,15,17
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1,2,2,2,3,5 Mode = 2
3,3,7,8,12,16 Mode = 3
3,3,4,5,6,7,7 Mode = 3 dan 7
4,6,8,10,13,15,17 Tidak ada Mode
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(2). V A R I A B I L I T A S.
1. Range.
2. Mean Deviation.
3. Variance = Varians
4. Standard Deviation = Simpang baku = s.
5. Standard Error = SE.
6. Coefficient of Variation = COV.
7. Quartiles, Quintiles, Deciles, Percentiles.
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1. R A N G E .Merupakan nilai Variabilitas yang paling
sederhana. Range ialah selisih antara
nilai yang ( TERBESAR - TERKECIL. )
Range sering menyesatkan, karena untuk
dua kumpulan data atau lebih dapat
mempunyai nilai Range yg SAMA.
1, 3, 2, 4, 7, 16 Range = 16 – 1 = 15
23,25,28,37,38 Range = 38 – 23 = 15
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2. MEAN DEVIATION.
Merupakan deviasi (penyimpangan) dg mean : sbb x | x-mean |-------------------------------- Dipakai harga mutlak. 2 2-4 = 2 Mengabaikan tanda (-). 3 3-4 = 1 4 4-4 = 0 5 5-4 = 1 6 6-4 = 2 n = 5------------- ------------Mean = 4 6 M.D. = 6/5 = 1.2
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3. V A R I A N C E.
Kuadrat penyimpangan x dg mean :
∑(x – Mean) 2
Var = -------------------
n - 1
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4. STANDARD DEVIATION(SIMPANG BAKU).
Merupakan ukuran Variabilitas yg terbaik.
Nilainya setaraf dg nilai sebenarnya.
Besarnya = akar dari Variance.
∑(x – mean) 2
s = √ { ---------------- } n – 1
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5. STANDARD ERROR.
SE ialah SD dibagi akar n.
SD
SE = ----------
√ n
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6. COEFFICIENT OF VARIATION.
COV ialah SD dibagi Mean x 100%.
s
COV = --------- (100%)
Mean
Suatu ukuran Variabilitas Relatif.
Membandingkan dua agregate dg unit beda.
Menetapkan apakah data Normal.
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COEFFICIENT OF VARIATION.
Varuiabel TB Mean = 160 Cm, s=8 Cm.
Variabel BB Mean = 55 Kg, s=11 Kg.
COV TB = (8/160)x100% = 5 %.
COV BB = (11/55)x100% = 20 %
Kesimpulan : BB lebih bervariasi dp TB.
COV = < 30% distribusi data NORMAL.
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7.(1). QUARTILES.
Ialah NILAI-NILAI yg membagi suatu array menjadi EMPAT bagian SAMA BESAR.
n+1 2(n+1) n+1
Posisi Q1 = -------- Q2 = --------- = ----------
4 4 2
3(n+1)
Q3 = -----------
4
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7. (2) QUINTILES.
Ialah NILAI-NILAI yg membagi sebuah array
menjadi LIMA bagian SAMA BESAR.
Ada Quintile(1), Quintile(2),
Quintile(3), Quintile(4).
n+1 2(n+1)
Posisi Quintile(1) = -------- Quin(2)= --------
5 5
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7.(3). DECILES.Ialah NILAI-NILAI yg membagi senuah arraymenjadi SEPULUH bagian SAMA BESAR.
n+1 2(n+1) Posisi D1 = ---------- D2 = ------------ 10 10
5(n+1) n+1Posisi D5 = ----------- = ----------- Ini Posisi APA? 10 2
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7. (4). PERCENTILES.Ialah NILAI-NILAI yg membagi sebuah array
Menjadi SERATUS bagian SAMA BESAR.
n+1 2(n+1)
Posisi P1 = ---------- P2 = ------------
100 100
50(n+1) n+1
P50 = -------------- = --------- Ini Posisi APA ?
100 2