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

4-3

Dot Plots - Contoh

Jumlah mobil yang dijual

dalam 24 bulan terakhir

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

4-5

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

4-6

Stem-and-leaf Plot Example

4-7

Stem-and-leaf Plot Example

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

4-9

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.

4-11

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

4-12

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,

4-13

Boxplot - Example

4-14

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).

4-15

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.

4-16

Commonly Observed Shapes

4-17

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

4-20

Skewness – A Minitab Example

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).

4-22

Describing Relationship between Two Variables – Scatter Diagram Examples

4-23

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

4-24

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.

4-26

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.).

4-27

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

4-28

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