menampilkan dan mengartikan data -...
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McGraw-Hill/Irwin Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
Menampilkan dan MengartikanData
4-2
Dot Plots
Mengelompokkan data sesederhana
mungkin identitas data secara
individual tetap ada
Data ditampilkan dalam bentuk titik
sepanjang garis horisontal sesuai
nilainya
Identik ditumpuk
4-4
Distribusi Frekuensi
Distribusi Frekuensi diguanakan untukmengorganisasikan data ke dalam bentukyang memiliki arti
Keuntungan Distribusi Frekuensi: gambaranvisual 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
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Stem-and-Leaf
Tiap nilai dibagi dua. Digit utama menjadiSTEM dan digit sisanya menjadi LEAF. Stem dituliskan secara vertikal, Leaf dituliskansecara horisontal
Keuntungan: identitas setiap nilai tidak hilang
4-8
Cara alternatif (selain standar deviasi) untukmenggambarkan penyebaran data adalahdengan menentukan LOKASI NILAI yang membagi data menjadi beberapa bagian yang setara
QUARTILES = KUARTIL (DIBAGI 4)
DECILES = DESIL (DIBAGI 10)
PERCENTILES = PERSENTIL ( DIBAGI 100)
Quartiles, Deciles and Percentiles
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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
Penghitungan Persentil
4-10
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 $1,758 $1,721 $1,637
$2,097 $2,047 $2,205 $1,787
$2,287 $1,940 $2,311 $2,054
$2,406 $1,471 $1,460
Locate the median, the first quartile, and the third quartile for the commissions earned.
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Percentiles – Example (cont.)
Step 1: Organize the data from lowest to
largest value
$1,460 $1,471 $1,637 $1,721
$1,758 $1,787 $1,940 $2,038
$2,047 $2,054 $2,097 $2,205
$2,287 $2,311 $2,406
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Percentiles – Example (cont.)
Step 2: Compute the first and third quartiles.
Locate L25 and L75 using:
205,2$
721,1$
12100
75)115(4
100
25)115(
75
25
7525
L
L
LL
lyrespective positions,
12th and 4th the at located are quartiles third and first the Therefore,
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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:
– symmetric,
– positively skewed,
– negatively skewed,
– bimodal.
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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
4-18
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?
4-19
Skewness – An Example Using Pearson’s Coefficient
017.122.5$
)18.3$95.4($3)(3
22.5$115
))95.4$40.16($...)95.4$09.0($
1
95.4$15
26.74$
222
s
MedianXsk
n
XXs
n
XX
Skewness the Compute :3 Step
3.18 is largest to smallest from arranged data, of set the in value middle The
Median the Find :3 Step
Deviation Standard the Compute :2 Step
Mean the Compute 1: Step
4-21
Describing Relationship between Two Variables
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).
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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?
Describing Relationship between Two Variables – Scatter Diagram Excel Example
4-25
Contingency Tables
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.
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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. Thismorning the quality assurance inspector reviewed each window for all qualityaspects. Each was classified as acceptable or unacceptable and by the shifton 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 thefollowing 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
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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
4-29
DATA
KARAKTERISTIK RESPONDEN
VARIABEL KATEGORI JUMLAH PERSEN
JENIS KELAMIN PRIA 31 47
WANITA 35 53
USIA 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
PEKERJAAN 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