Menampilkan dan Mengartikan Data
McGraw-Hill/Irwin
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
Dot Plots Mengelompokkan data sesederhana mungkin identitas data secara individual tetap ada Data ditampilkan dalam bentuk titik sepanjang garis horisontal sesuai nilainya Identik ditumpuk
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Dot Plots - Contoh Jumlah mobil yang dijual dalam 24 bulan terakhir
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Distribusi Frekuensi
Distribusi Frekuensi diguanakan untuk mengorganisasikan data ke dalam bentuk yang memiliki arti Keuntungan Distribusi Frekuensi: gambaran visual tentang bentuk penyebaran data Kerugian Distribusi Frekuensi: (1) Hilangnya identitas asli setiap nilai (2) Sulit melihat penyebaran nilai tiap kelas
Cara lain untuk menggambarkan data kuantitatif adalah stem-and-leaf display 4-4
Stem-and-Leaf
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Tiap nilai dibagi dua. Digit utama menjadi STEM dan digit sisanya menjadi LEAF. Stem dituliskan secara vertikal, Leaf dituliskan secara horisontal
Keuntungan: identitas setiap nilai tidak hilang
Stem-and-leaf Plot Example
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Stem-and-leaf Plot Example
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Quartiles, Deciles and Percentiles
Cara alternatif (selain standar deviasi) untuk menggambarkan penyebaran data adalah dengan menentukan LOKASI NILAI yang membagi data menjadi beberapa bagian yang setara
QUARTILES = KUARTIL (DIBAGI 4) DECILES = DESIL (DIBAGI 10) PERCENTILES = PERSENTIL ( DIBAGI 100)
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Penghitungan Persentil
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Lp = persentil yang dicari (misalnya Persentil 33 L33) n = jumlah data Median = L50
Syarat: Median data diurutkan Rumus Persentil bisa digunakan untuk mencari Desil dan Kuartil
Percentiles - Example Listed below are the commissions earned last month by a sample of 15 brokers at Salomon Smith Barney’s Oakland, California, office. $2,038 $2,097 $2,287 $2,406
$1,758 $2,047 $1,940 $1,471
$1,721 $1,637 $2,205 $1,787 $2,311 $2,054 $1,460
Locate the median, the first quartile, and the third quartile for the commissions earned. 4-10
Percentiles – Example (cont.) Step 1: Organize the data from lowest to largest value $1,460 $1,758 $2,047 $2,287
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$1,471 $1,787 $2,054 $2,311
$1,637 $1,940 $2,097 $2,406
$1,721 $2,038 $2,205
Percentiles – Example (cont.) Step 2: Compute the first and third quartiles. Locate L25 and L75 using:
25 75 4 L75 (15 1) 12 100 100 Therefore, the first and third quartiles are located at the 4th and 12th L25 (15 1)
positions,respectively L25 $1,721 L75 $2,205 4-12
Boxplot - Example
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Boxplot Example Step1: Create an appropriate scale along the horizontal axis. Step 2: Draw a box that starts at Q1 (15 minutes) and ends at Q3 (22 minutes). Inside the box we place a vertical line to represent the median (18 minutes). Step 3: Extend horizontal lines from the box out to the minimum value (13 minutes) and the maximum value (30 minutes).
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Skewness
In Chapter 3, measures of central location (the mean, median, and mode) for a set of observations and measures of data dispersion (e.g. range and the standard deviation) were introduced Another characteristic of a set of data is the shape. There are four shapes commonly observed: – –
– –
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symmetric, positively skewed, negatively skewed, bimodal.
Commonly Observed Shapes
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Skewness - Formulas for Computing Koefisien skewness berkisar antara -3 sampai 3. – Nilai berkisar -3 skewness negatif – Nilai 1.63 skewness cukup positif – Nilai 0,X (terjadi bila mean = median) berarti distribusi simetris dan skewness tidak ada
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Skewness – An Example
Following are the earnings per share for a sample of 15 software companies for the year 2007. The earnings per share are arranged from smallest to largest.
Compute the mean, median, and standard deviation. Find the coefficient of skewness using Pearson’s estimate. What is your conclusion regarding the shape of the distribution?
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Skewness – An Example Using Pearson’s Coefficient Step 1: Compute the Mean X
X n
$74.26 $4.95 15
Step 2 : Compute the Standard Deviation
X X s n 1
2
($0.09 $4.95) 2 ... ($16.40 $4.95) 2 ) $5.22 15 1
Step 3 : Find the Median The middle value in the set of data, arranged from smallestto largestis 3.18 Step 3 : Compute the Skewness sk
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3( X Median ) 3($4.95 $3.18) 1.017 s $5.22
Skewness – A Minitab Example
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Describing Relationship between Two Variables
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When we study the relationship between two variables we refer to the data as bivariate.
One graphical technique we use to show the relationship between variables is called a scatter diagram.
To draw a scatter diagram we need two variables. We scale one variable along the horizontal axis (X-axis) of a graph and the other variable along the vertical axis (Y-axis).
Describing Relationship between Two Variables – Scatter Diagram Examples
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Describing Relationship between Two Variables – Scatter Diagram Excel Example In Chapter 2 we presented data from AutoUSA. In this case the information concerned the prices of 80 vehicles sold last month at the Whitner Autoplex lot in Raytown, Missouri. The data shown include the selling price of the vehicle as well as the age of the purchaser. Is there a relationship between the selling price of a vehicle and the age of the purchaser? Would it be reasonable to conclude that the more expensive vehicles are purchased by older buyers? 4-23
Describing Relationship between Two Variables – Scatter Diagram Excel Example
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Contingency Tables
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A scatter diagram requires that both of the variables be at least interval scale. What if we wish to study the relationship between two variables when one or both are nominal or ordinal scale? In this case we tally the results in a contingency table.
Contingency Tables A contingency table is a cross-tabulation that simultaneously summarizes two variables of interest. Examples: 1. Students at a university are classified by gender and class rank. 2. A product is classified as acceptable or unacceptable and by the shift (day, afternoon, or night) on which it is manufactured. 3. A voter in a school bond referendum is classified as to party affiliation (Democrat, Republican, other) and the number of children that voter has attending school in the district (0, 1, 2, etc.).
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Contingency Tables – An Example A manufacturer of preassembled windows produced 50 windows yesterday. This morning the quality assurance inspector reviewed each window for all quality aspects. Each was classified as acceptable or unacceptable and by the shift on which it was produced. Thus we reported two variables on a single item. The two variables are shift and quality. The results are reported in the following table.
Using the contingency table able, the quality of the three shifts can be compared. For example: 1. On the day shift, 3 out of 20 windows or 15 percent are defective. 2. On the afternoon shift, 2 of 15 or 13 percent are defective and 3. On the night shift 1 out of 15 or 7 percent are defective. 4. Overall 12 percent of the windows are defective 4-27
URAIAN
TINGGI
SEDANG
RENDAH
F
%
F
%
F
%
1
KONFLIK
58
87,9
18
12,1
0
0
2
DURASI
64
97
2
3
0
0
3
KESUKAAN
63
95,5
3
4,5
0
0
4
PEMAIN UTAMA
66
100
0
0
0
0
5
BINTANG TAMU
65
98,5
1
1,5
0
0
6
KONSISTENSI
55
83,4
11
16,6
0
0
7
KECEPATAN CERITA
65
98,5
1
1,5
0
0
8
DAYA TARIK
47
71,2
19
28,8
0
0
9
GAMBAR YANG KUAT
63
94,5
3
5,5
0
0
10
TIMING
46
69,7
20
31,3
0
0
11
TREN
66
100
0
0
0
0
12
KOGNITIF
65
98,5
1
1,5
0
0
13
AFEKTIF
58
87,9
8
12,1
0
0
14
KEBERHASILAN
65
98,5
1
1,5
0
0
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KARAKTERISTIK RESPONDEN VARIABEL
DATA
JENIS KELAMIN
USIA
PEKERJAAN
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KATEGORI
JUMLAH
PERSEN
PRIA
31
47
WANITA
35
53
12 - 19
3
4,5
20-29
18
27,3
30-39
20
30,3
40-49
15
22,7
50-59
9
13,6
>60
1
1,5
PNS
8
12,1
KARYAWAN
18
27,3
IRT
21
31,8
PELAJAR
6
9,1
WIRASWASTA
4
6,1
PEDAGANG
2
3
BURUH
3
4,5
PENSIUNAN
4
6,1
