Week 2 Numerical Descriptive Measures...Week 2 Numerical Descriptive Measures Agenda Time Activity...
Transcript of Week 2 Numerical Descriptive Measures...Week 2 Numerical Descriptive Measures Agenda Time Activity...
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Statistik Bisnis
Week 2
Numerical Descriptive Measures
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Agenda
Time Activity
First Session
90 minutes Central Tendency
Second Session
60 minutes Variation and Shape
30 minutes Exploring Numerical Data
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Objectives
In this chapter, you learn:
• To describe the properties of central tendency, variation,
• and shape in numerical data
• To construct and interpret a boxplot
• To compute descriptive summary measures for a population
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Numerical Descriptive Measures
Central Tendency
Variation and Shape
Exploring Numerical
Data
Numerical Descriptive
Measures for a Population
The Covariance
and The Coefficient of Correlation
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CENTRAL TENDENCY
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Central Tendency
Mean
(Arithmetic Mean)
Median
Mode Geometric
Mean
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Mean (Rata-rata Hitung)
Perhatikan data berikut:
160 157 162 170 168 174 156 173 157
Berapakah rata-rata tinggi badan?
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Mean
Sample size
n
XXX
n
X
X n21
n
1i
i
Observed values
The ith value Pronounced x-bar
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Mean
Sekarang, perhatikan data pengeluaran bulanan mahasiswa statistik bisnis berikut:
Berapakah rata-ratanya?
Pengeluaran Bulanan Frekuensi Kurang dari Rp. 500.000 2
Rp. 500.000 - kurang dari Rp. 1.000.000 7
Rp. 1.000.000 - kurang dari Rp. 1.500.000 13
Rp. 1.500.000 - kurang dari Rp. 2.000.000 5
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Mean
In this case we can only ESTIMATE the MEAN…
Keyword: “MIDPOINTS”
Pengeluaran Bulanan Frekuensi Kurang dari Rp. 500.000 2
Rp. 500.000 - kurang dari Rp. 1.000.000 7
Rp. 1.000.000 - kurang dari Rp. 1.500.000 13
Rp. 1.500.000 - kurang dari Rp. 2.000.000 5
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Estimated Mean
Midpoint Frequency Mid * f 250000 2 500000 750000 7 5250000
1250000 13 16250000 1750000 5 8750000
Total 27 30750000
𝐸𝑠𝑡𝑖𝑚𝑎𝑡𝑒𝑑 𝑀𝑒𝑎𝑛 =30750000
27= 1138888.89
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Mean
Berikut adalah data nilai “Mahasiswa A”:
Berapakah nilai rata-rata “Mahasiswa A”?
Mata Kuliah SKS Nilai
Matematika Bisnis 3 60
Bahasa Inggris 2 80
Perilaku Organisasi 3 100
Statistik 4 90
Manajemen Operasi 3 70
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Mean
Perhatikan dua data berikut ini:
A 150 152 154 155 155 155 155 155 155 157
Rata-rata?
B 150 152 154 155 155 155 155 155 155 187
Rata-rata?
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Mean
155 156 157 150 151 152 153 154 187
154.3
155 156 157 150 151 152 153 154 187
157.3 Extreme
Value
A
B
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It is DANGEROUS to ONLY use
MEAN in describing a data
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Median
dataorderedtheinposition2
1npositionMedian
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Median
Perhatikan dua data berikut ini:
A 150 152 154 155 155 155 155 155 155 157
Median?
B 150 152 154 155 155 155 155 155 155 187
Median?
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Median
155 156 157 150 151 152 153 154 187
155
155 156 157 150 151 152 153 154 187
155
A
B
154.3
157.3
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Median
Berapakah median dari data tinggi badan berikut?
160 157 162 170 168 174 156 173 157
Hitung pula median dari data berikut?
160 157 162 170 168 174 156 173 157 150
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Median
Perhatikan lagi data pengeluaran bulanan mahasiswa statistik bisnis berikut:
Berapakah mediannya?
Pengeluaran Bulanan Frekuensi Kurang dari Rp. 500.000 2
Rp. 500.000 - kurang dari Rp. 1.000.000 7
Rp. 1.000.000 - kurang dari Rp. 1.500.000 13
Rp. 1.500.000 - kurang dari Rp. 2.000.000 5
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Median
The MEDIAN group of monthly spending is Rp. 1.000.000 but less than
Rp. 1.500.000
Or ESTIMATE
the MEDIAN!!
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Estimated Median
Estimated Median = Rp. 1.173.076,92
Pengeluaran Bulanan Frekuensi Kurang dari Rp. 500.000 2
Rp. 500.000 - kurang dari Rp. 1.000.000 7
Rp. 1.000.000 - kurang dari Rp. 1.500.000 13
Rp. 1.500.000 - kurang dari Rp. 2.000.000 5
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Estimated Median
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Mode (Modus)
Berapakah modus data berikut:
160 157 162 170 168 174 156 173 157
Berapa pula modus data berikut:
160 157 162 170 168 174 156 173 150
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Mode
Perhatikan lagi data pengeluaran bulanan mahasiswa statistik bisnis berikut:
Berapakah modusnya?
Pengeluaran Bulanan Frekuensi Kurang dari Rp. 500.000 2
Rp. 500.000 - kurang dari Rp. 1.000.000 7
Rp. 1.000.000 - kurang dari Rp. 1.500.000 13
Rp. 1.500.000 - kurang dari Rp. 2.000.000 5
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Mode
The MODAL group of monthly spending is Rp. 1.000.000 but less than
Rp. 1.500.000
But the actual Mode may
not even be in that group!
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Mode
Without the raw data we don't really know…
However, we can ESTIMATE the MODE
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Estimated Mode
Pengeluaran Bulanan Frekuensi Kurang dari Rp. 500.000 2
Rp. 500.000 - kurang dari Rp. 1.000.000 7
Rp. 1.000.000 - kurang dari Rp. 1.500.000 13
Rp. 1.500.000 - kurang dari Rp. 2.000.000 5
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Estimated Mode
Estimated Mode = Rp. 1.214.285,72
Pengeluaran Bulanan Frekuensi Kurang dari Rp. 500.000 2
Rp. 500.000 - kurang dari Rp. 1.000.000 7
Rp. 1.000.000 - kurang dari Rp. 1.500.000 13
Rp. 1.500.000 - kurang dari Rp. 2.000.000 5
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Estimated Mode
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Central Tendency
Central Tendency
Arithmetic Mean
Median Mode
n
X
X
n
i
i 1
Middle value in the ordered array
Most frequently observed value
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EXERCISE
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3.10
Data berikut adalah data pengeluaran yang dilakukan oleh sampel sembilan orang konsumen untuk makan siang di sebuah restoran cepat saji (dalam $):
4,20 5,03 5,86 6,45 7,38 7,54 8,46 8,47 9,87
Tentukan rata-rata dan median!
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3.12
Berikut adalah data konsumsi bensin per kilometer dari mobil-mobil SUV tahun 2010:
24 23 22 21 22 22 18 18 26
26 26 19 19 19 21 21 21 21
21 18 29 21 22 22 16 16
Tentukan median and modus!
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GEOMETRIC MEAN
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Compounding Data
Interest Rate
Growth Rate
Return Rate
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Compounding Data
Misalkan anda telah menginvestasikan uang anda pada bursa saham selama lima tahun. Jika tingkat pengembalian tiap tahunnya adalah 90%, 10%, 20%, 30% dan -90%, berapakah rata-rata tingkat pengembalian per tahun pada periode ini?
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Compounding Data
• 90%
Year 1
• 10%
Year 2 • 20%
Year 3
• 30%
Year 4 • -90%
Year 5
If we use arithmetic mean in this case The average return during this period = 12%
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Compounding Data
• 90%
Year 1
• 10%
Year 2 • 20%
Year 3
• 30%
Year 4 • -90%
Year 5
Let say that you invest $100 in year 0 How much your stocks worth in year 5?
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Compounding Data
• 90%
Year 1
• 10%
Year 2 • 20%
Year 3
• 30%
Year 4 • -90%
Year 5
• $90
• $190
Year 1
• $19
• $209
Year 2 • $41.8
• $250.8
Year 3
• $75.24
• $326.04
Year 4 • -$293.44
• $32.6
Year 5
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Geometric Mean
This is called geometric mean rate of return
11.03.12.11.19.15 GM
%08.20GM
Well, that’s pretty bad…
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Measure of Central Tendency For The Rate Of Change Of A Variable Over Time:
The Geometric Mean & The Geometric Rate of Return
Geometric mean
Used to measure the rate of change of a variable over time
Geometric mean rate of return
Measures the status of an investment over time
Where Ri is the rate of return in time period i
n
nG XXXX /1
21 )(
1)]R1()R1()R1[(R n/1
n21G
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Geometric Mean
1 n
ValueperiodofBeginning
ValuePeriodofEndGM
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Geometric Mean
Mari perhatikan permasalahan tadi. Diketahui bahwa kita berinvestasi saham senilai $100 pada tahun ke-0. Namun, pada akhir tahun ke-5 nilai saham tersebut menjadi $32.6. Hitunglah rata-rata tingkat pengembalian tahunan!
•$100
Year 0
•$32.6
Year 5
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Geometric Mean
• This value consistent with what we found earlier
1100
6.325 GM
%08.20GM
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Example
Data penduduk Jawa Barat:
• Tahun 2000: 35.729.537 jiwa
• Tahun 2010: 43.053.732 jiwa
Tingkat pertumbuhan penduduk per tahun?
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EXERCISE
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3.22
Pada tahun 2006-2009, harga logam mulia cepat berubah. Tabel berikut menunjukkan total tingkat pengembalian (dalam persentase) untuk platina, emas, dan perak dari tahun 2006 hingga tahun 2009:
Tahun Platina Emas Perak
2009 2008 2007 2006
62.7 -41.3 36.9 15.9
25.0 4.3
31.9 23.2
56.8 -26.9 14.4 46.1
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3.22
a. Hitung rata-rata tingkat pengembalian per tahun untuk platina, emas, dan perak dari tahun 2006 hingga tahun 2009.
b. Apakah kesimpulan yang bisa kita tarik mengenai rata-rata tingkat pengembalian per tahun dari tiga logam mulia tersebut?
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VARIATION AND SHAPE
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Variation and Shape
Range
Variance and Standard Deviation
Coefficient of Variation
Z Scores
Shape
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Review on Central Tendency
Perhatikan data berikut:
160 157 162 170 168 174 156 173 157 150
Hitunglah rata-rata, median, dan modus?
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RANGE
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Range (Rentang)
Perhatikan data berikut:
160 157 162 170 168 174 156 173 157 150
Berapakah rentangnya?
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Range
minmax XXRange
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Measures of Variation: Why The Range Can Be Misleading
Ignores the way in which data are distributed
Sensitive to outliers
7 8 9 10 11 12
Range = 12 - 7 = 5
7 8 9 10 11 12
Range = 12 - 7 = 5
1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,4,5
1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,4,120
Range = 5 - 1 = 4
Range = 120 - 1 = 119
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VARIANCE AND STANDARD DEVIATION
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Variance and Standard Deviation
Variance Standard Deviation
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Deviation
Perhatikan kembali data berikut:
160 157 162 170 168 174 156 173 157 150
Berapakah rata-ratanya?
Mean = 162.7
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Deviation
Data Deviation 160 -2.7 157 -5.7 162 -0.7 170 7.3 168 5.3 174 11.3 156 -6.7 173 10.3 157 -5.7 150 -12.7
XXDeviation i
=156-162.7
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Variance and Standard Deviation
Data Deviation (Dev)^2 160 -2.7 7.29 157 -5.7 32.49 162 -0.7 0.49 170 7.3 53.29 168 5.3 28.09 174 11.3 127.69 156 -6.7 44.89 173 10.3 106.09 157 -5.7 32.49 150 -12.7 161.29
Sum of Squares = 594.1
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Variance and Standard Deviation
Sample size (n) = 10
01.661-10
594.1 Variance
125.866.01 SD
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Variance and Standard Deviation
• Sample
• Population
1
1
2
2
n
XX
S
n
i
i
N
Xn
i
i
1
2
2
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Measures of Variation: Comparing Standard Deviations
Mean = 15.5
S = 3.338 11 12 13 14 15 16 17 18 19 20 21
11 12 13 14 15 16 17 18 19 20 21
Data B
Data A
Mean = 15.5
S = 0.926
11 12 13 14 15 16 17 18 19 20 21
Mean = 15.5
S = 4.570
Data C
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Standard Deviation
Sekarang, perhatikan data pengeluaran bulanan mahasiswa statistik bisnis berikut:
Berapakah SIMPANGAN BAKU?
Pengeluaran Bulanan Frekuensi Kurang dari Rp. 500.000 2
Rp. 500.000 – kurang dari Rp. 1.000.000 7
Rp. 1.000.000 – kurang dari Rp. 1.500.000 13
Rp. 1.500.000 – kurang dari Rp. 2.000.000 5
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Standard Deviation
Sekarang, perhatikan data pengeluaran bulanan mahasiswa statistik bisnis berikut:
Berapakah SIMPANGAN BAKU?
Pengeluaran Bulanan Frekuensi Kurang dari Rp. 500.000 2
Rp. 500.000 – kurang dari Rp. 1.000.000 7
Rp. 1.000.000 – kurang dari Rp. 1.500.000 13
Rp. 1.500.000 – kurang dari Rp. 2.000.000 5
E.S.T.I.M.A.T.I.O.N
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Estimated Standard Deviation
Midpoint Frequency Dev^2 (Dev^2)*f 250000 2 790123456790.12 1580246913580.25 750000 7 151234567901.24 1058641975308.64
1250000 13 12345679012.35 160493827160.49 1750000 5 373456790123.46 1867283950617.28
Total 27 4666666666666.67
𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒 =4666666666666.67
27-1 = 179487179487.18
𝑆𝐷 = 179487179487.18 = 423659.27
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THE COEFFICIENT OF VARIATION
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The Coefficient of Variation
Height Weight
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The Coefficient of Variation
Perhatikan kembali data berikut:
160 157 162 170 168 174 156 173 157 150
Berapakah rata-rata dan simpangan baku?
Mean = 162.7 and SD = 8.125
![Page 72: Week 2 Numerical Descriptive Measures...Week 2 Numerical Descriptive Measures Agenda Time Activity First Session 90 minutes Central Tendency Second Session 60 minutes Variation and](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe2c534069a2d763a4c6ffd/html5/thumbnails/72.jpg)
The Coefficient of Variation
Mahasiswa pada data tinggi badan sebelumnya, memiliki berat badan sebagai berikut:
50 55 57 52 55
69 60 65 71 70
Berapakah rata-rata dan simpangan baku?
Mean = 60.4 and SD = 7.8
![Page 73: Week 2 Numerical Descriptive Measures...Week 2 Numerical Descriptive Measures Agenda Time Activity First Session 90 minutes Central Tendency Second Session 60 minutes Variation and](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe2c534069a2d763a4c6ffd/html5/thumbnails/73.jpg)
The Coefficient of Variation
Height Weight
Mean 162.7 60.4
SD 8.125 7.8
Variabel manakah yang datanya lebih bervariasi? Coefficient of Variation: CVHeight = 4.99% CVWeight= 12.92%
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The Coefficient of Variation
%100.
X
SDCV
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LOCATING EXTREME OUTLIERS: Z SCORE
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Locating Extreme Outliers: Z Score
Perhatikan lagi data tinggi badan berikut:
160 157 162 170 168 174 156 173 157 150
160 162 164 150 152 154 156 158
Mean = 162.7
166 168 170 172 174
SD = 8.125 SD = 8.125
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Locating Extreme Outliers: Z Score
Maka, Z Score untuk 160 adalah?
160 162 164 150 152 154 156 158
Mean = 162.7
166 168 170 172 174
Z Score162.7 = 0 Z Score154.6 = -1 Z Score170.8 = 1
SD = 8.125
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Locating Extreme Outliers: Z Scores
Perhatikan kembali data berikut:
160 157 162 170 168 174 156 173 157 150
Berapakah Z Scores dari 160, 174, 168 dan 150?
Z160 = -0.33, Z174 = 1.39, Z168 = 0.65, and
Z150 = -0.56
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Locating Extreme Outliers: Z Score
SD
XXZ X
• A data value is considered an extreme outlier if its Z-score is less than -3.0 or greater than +3.0.
• The larger the absolute value of the Z-score, the farther the data value is from the mean.
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SHAPE
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Shape
Perhatikan kembali data berikut:
160 157 162 170 168 174 156 173 157 150
160 162 164 150 152 154 156 158
Mean = 162.7
166 168 170 172 174
Median = 161 Right-Skewed
![Page 82: Week 2 Numerical Descriptive Measures...Week 2 Numerical Descriptive Measures Agenda Time Activity First Session 90 minutes Central Tendency Second Session 60 minutes Variation and](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe2c534069a2d763a4c6ffd/html5/thumbnails/82.jpg)
Shape
Bagaimana jika datanya seperti berikut:
163 168 162 170 168 174 156 173 157 150
160 162 164 150 152 154 156 158
Mean = 164.1
166 168 170 172 174
Median = 165.5 Left-Skewed
![Page 83: Week 2 Numerical Descriptive Measures...Week 2 Numerical Descriptive Measures Agenda Time Activity First Session 90 minutes Central Tendency Second Session 60 minutes Variation and](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe2c534069a2d763a4c6ffd/html5/thumbnails/83.jpg)
Shape
Describes how data are distributed
Mean = Median Mean < Median Median < Mean
Right-Skewed Left-Skewed Symmetric
![Page 84: Week 2 Numerical Descriptive Measures...Week 2 Numerical Descriptive Measures Agenda Time Activity First Session 90 minutes Central Tendency Second Session 60 minutes Variation and](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe2c534069a2d763a4c6ffd/html5/thumbnails/84.jpg)
EXPLORING NUMERICAL DATA
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Exploring Numerical Data
Quartiles
Interquartile Range
Five-Number Summary
Boxplot
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QUARTILES
![Page 87: Week 2 Numerical Descriptive Measures...Week 2 Numerical Descriptive Measures Agenda Time Activity First Session 90 minutes Central Tendency Second Session 60 minutes Variation and](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe2c534069a2d763a4c6ffd/html5/thumbnails/87.jpg)
Quartiles 1
st Q
uar
tile
Q1
2n
d Q
uar
tile
Q2
Median
3rd
Qu
arti
le
Q3
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Quartiles
Perhatikan data tinggi badan berikut:
160 157 162 170 168 174 156
Berapakah Q1, Q2 dan Q3?
Q1 = 157
Q2 = 162 (Median)
Q3 = 170
![Page 89: Week 2 Numerical Descriptive Measures...Week 2 Numerical Descriptive Measures Agenda Time Activity First Session 90 minutes Central Tendency Second Session 60 minutes Variation and](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe2c534069a2d763a4c6ffd/html5/thumbnails/89.jpg)
Quartiles
Perhatikan juga data berikut:
160 157 162 170 168 174 156 173 150
Berapa Q1, Q2 dan Q3?
Q1 = 156.5
Q2 = 162 (Median)
Q3 = 171.5
![Page 90: Week 2 Numerical Descriptive Measures...Week 2 Numerical Descriptive Measures Agenda Time Activity First Session 90 minutes Central Tendency Second Session 60 minutes Variation and](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe2c534069a2d763a4c6ffd/html5/thumbnails/90.jpg)
Quartiles
Dan perhatikan pula data berikut:
160 157 162 170 168 174 156 173 157 150
Berapakah Q1, Q2 dan Q3?
Q1 = 157
Q2 = 161 (Median)
Q3 = 170
![Page 91: Week 2 Numerical Descriptive Measures...Week 2 Numerical Descriptive Measures Agenda Time Activity First Session 90 minutes Central Tendency Second Session 60 minutes Variation and](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe2c534069a2d763a4c6ffd/html5/thumbnails/91.jpg)
Quartiles
160 162 164 150 152 154 156 158
Median = 161
166 168 170 172 174
Q1 = 157 Q3 = 170
25% 25% 25% 25%
of all data
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INTERQUARTILE RANGE
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Interquartile Range
160 162 164 150 152 154 156 158 166 168 170 172 174
Q1 = 157 Q3 = 170
50%
In the middle of all data
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Interquartile Range
160 162 164 150 152 154 156 158 166 168 170 172 174
Q1 = 157 Q3 = 170
Berapakah rentang Interquatile?
Interquartile Range = 170 – 157 = 13
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Interquartile Range
13 QQRangeileInterquart
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FIVE-NUMBER SUMMARY
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Five-Number Summary
max31min XQMedianQX
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Five-Number Summary
Perhatikan data tinggi badan berikut:
160 157 162 170 168 174 156 173 157 150
Apakah Five-Number Summary?
150 157 161 170 174
![Page 99: Week 2 Numerical Descriptive Measures...Week 2 Numerical Descriptive Measures Agenda Time Activity First Session 90 minutes Central Tendency Second Session 60 minutes Variation and](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe2c534069a2d763a4c6ffd/html5/thumbnails/99.jpg)
BOXPLOT
![Page 100: Week 2 Numerical Descriptive Measures...Week 2 Numerical Descriptive Measures Agenda Time Activity First Session 90 minutes Central Tendency Second Session 60 minutes Variation and](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe2c534069a2d763a4c6ffd/html5/thumbnails/100.jpg)
Boxplot
Xmin Xmax Q1 Q3 Median
![Page 101: Week 2 Numerical Descriptive Measures...Week 2 Numerical Descriptive Measures Agenda Time Activity First Session 90 minutes Central Tendency Second Session 60 minutes Variation and](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe2c534069a2d763a4c6ffd/html5/thumbnails/101.jpg)
Boxplot
Perhatikan data berikut:
160 157 162 170 168 174 156 173 157 150
Buatlah Boxplot-nya?
![Page 102: Week 2 Numerical Descriptive Measures...Week 2 Numerical Descriptive Measures Agenda Time Activity First Session 90 minutes Central Tendency Second Session 60 minutes Variation and](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe2c534069a2d763a4c6ffd/html5/thumbnails/102.jpg)
Boxplot for the Height of Business Statistic’s Student 2014
150 174 157 170 161
Height (cm)
![Page 103: Week 2 Numerical Descriptive Measures...Week 2 Numerical Descriptive Measures Agenda Time Activity First Session 90 minutes Central Tendency Second Session 60 minutes Variation and](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe2c534069a2d763a4c6ffd/html5/thumbnails/103.jpg)
Distribution Shape and The Boxplot
Right-Skewed Left-Skewed Symmetric
Q1 Q2 Q3 Q1 Q2 Q3 Q1 Q2 Q3
![Page 104: Week 2 Numerical Descriptive Measures...Week 2 Numerical Descriptive Measures Agenda Time Activity First Session 90 minutes Central Tendency Second Session 60 minutes Variation and](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe2c534069a2d763a4c6ffd/html5/thumbnails/104.jpg)
MEASURE OF SKEWNESS
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Karl Pearson's Measure of Skewness
160 162 164 150 152 154 156 158
Mean = 162.7
166 168 170 172 174
Median = 161
63.0125.8
)1617.162(3
kS
![Page 106: Week 2 Numerical Descriptive Measures...Week 2 Numerical Descriptive Measures Agenda Time Activity First Session 90 minutes Central Tendency Second Session 60 minutes Variation and](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe2c534069a2d763a4c6ffd/html5/thumbnails/106.jpg)
Karl Pearson's Measure of Skewness
S
MedianXSk
)(3
![Page 107: Week 2 Numerical Descriptive Measures...Week 2 Numerical Descriptive Measures Agenda Time Activity First Session 90 minutes Central Tendency Second Session 60 minutes Variation and](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe2c534069a2d763a4c6ffd/html5/thumbnails/107.jpg)
Bowley's Formula for Measuring Skewness
150 174 157 170 161
Height (cm)
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Bowley's Formula for Measuring Skewness
)(
)()(
13
1223
QQQQSk
![Page 109: Week 2 Numerical Descriptive Measures...Week 2 Numerical Descriptive Measures Agenda Time Activity First Session 90 minutes Central Tendency Second Session 60 minutes Variation and](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe2c534069a2d763a4c6ffd/html5/thumbnails/109.jpg)
EXERCISE
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3.10
Data berikut adalah data pengeluaran yang dilakukan oleh sampel sembilan orang konsumen untuk makan siang di sebuah restoran cepat saji (dalam $): 4,20 5,03 5,86 6,45 7,38 7,54 8,46 8,47 9,87 a. Hitung variansi, simpangan baku (standard deviation),
rentang, dan koefisien variasi. b. Apakah datanya menceng? Jika ya bagaimana? c. Berdasarkan hasil perhitungan diatas, apa kesimpulan
yang bisa anda ambil mengenai jumlah pengeluaran konsumen untuk makan siang tersebut?
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HOMEWORK
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3.62
Salah satu produk perusahaan asuransi adalah asuransi jiwa. Proses approval meliputi review formulir aplikasi hingga diterbitkan dan dikirimnya polis ke pelanggan. Kemampuan perusahaan untuk mengirim polis asuransi secepat mungkin merupakan hal yang penting bagi pelayanan.Dalam satu bulan kebelakang dipilih sampel acak 14 polis yang disetujui. Berikut adalah waktu proses approval ke 14 polis tersebut.
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3.62
73 19 16 64 28 28 31 90 60 56 31 56 22 18
a. Hitung rata-rata, median, kuartil pertama dan kuartil ketiga.
b. Hitung rentang, rentang antarkuartil, variansi, deviasi standar/simpangan baku.
c. Apakah datanya menceng? Jika iya, bagaimana?
d. Apa yang akan anda katakan kepada konsumen yang ingin membeli produk asuransi ini jika mereka bertanya tentang waktu yang dibutuhkan untuk proses approval?
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3.-
Berikut data biaya listrik pada bulan juli 2010 dari sampel acak 20 apartemen dengan satu kamar tidur di kota besar:
Biaya Listrik Frekuensi 80 – kurang dari 100 3
100 – kurang dari 120 3 120 – kurang dari 140 2 140 – kurang dari 160 4 160 – kurang dari 180 4 180 – kurang dari 200 2 200 – kurang dari 220 2
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3.-
a. Hitung rata-rata, median, modus.
b. Hitung simpangan baku.
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3.22
Tabel berikut merupakan data kalori dan total lemak (dalam gram per sajian) dari sampel 12 veggie burger
Kalori Total lemak 110 3.5 110 4.5 90 3.0 90 2.5
120 6.0 130 6.0 120 3.0 100 3.5 140 5.0 70 0.5
100 1.5 120 1.5
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3.22
a. Hitung rata-rata, median, modus, kuartil pertama dan kuartil ketiga.
b. Hitung rentang, rentang antarkuartil, variansi, deviasi standar/simpangan baku, deviasi rata-rata.
c. Apakah datanya menceng? Jika iya, bagaimana?
d. Apa kesimpulan yang anda dapatkan mengenai kalori dan total lemak tersebut?
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THANK YOU