Matakuliah
Tahun
Versi
: I0284 - Statistika
: 2008
: Revisi
Pertemuan 01
Pendahuluan
1

Learning Outcomes
Pada akhir pertemuan ini, diharapkan mahasiswa akan mampu :
• Mahasiswa akan dapat menjelaskan tentang statistika, data, populasi, sampel, variabel, penyajian data, dan skala pengukuran.
2

Outline Materi
• Definisi statistika
• Jenis-jenis Data
• Pengumpulan dan Penyajian Data
• Teknik Sampling
• Distribusi Frekuensi
• Skala pengukuran
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What is Statistics?
• Analysis of data (in short)
• Design experiments and data collection
• Summary information from collected data
• Draw conclusions from data and make decision based on finding
4

Design of Survey Research
• Choose an Appropriate Mode of
Response
– Reliable primary modes
• Personal interview
• Telephone interview
• Mail survey
– Less reliable self-selection modes (not appropriate for making inferences about the population)
• Television survey
• Internet survey
• Printed survey in newspapers and magazines
• Product or service questionnaires
5

Reasons for Drawing a Sample
• Less Time Consuming Than a Census
• Less Costly to Administer Than a Census
• Less Cumbersome and More Practical to
Administer Than a Census of the
Targeted Population
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Types of Sampling Methods
Non-Probability
Samples
(Convenience)
Judgement
Quota
Chunk
Samples
Probability Samples
Simple
Random
Systematic
Stratified
Cluster
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Probability Sampling
• Subjects of the Sample are Chosen Based on Known Probabilities
Probability Samples
Simple
Random
Systematic Stratified Cluster
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Variables and Data
• A variable is a characteristic that changes or varies over time and/or for different individuals or objects under consideration.
• Examples:
– Body temperature is variable over time or (and) from person to person.
– Hair color, white blood cell count, time to failure of a computer component.
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Definitions
• An experimental unit is the individual or object on which a variable is measured.
• A measurement results when a variable is actually measured on an experimental unit.
• A set of measurements, called data, can be either a sample or a population.
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Example
•
•
•
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How many variables have you measured?
• Univariate data: One variable is measured on a single experimental unit.
• Bivariate data: Two variables are measured on a single experimental unit.
• Multivariate data: More than two variables are measured on a single experimental unit.
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Types of Variables
Qualitative Quantitative
Discrete
Continuous
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Types of Variables
•
measure a quality or characteristic on each experimental unit.
•
•Hair color (black, brown, blonde…)
•Make of car (Dodge, Honda, Ford…)
•Gender (male, female)
•State of birth (California, Arizona,….)
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Types of Variables
•
measure a numerical quantity on each experimental unit.

if it can assume only a finite or countable number of values.

if it can assume the infinitely many values corresponding to the points on a line interval.
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Examples
• For each orange tree in a grove, the number of oranges is measured.
– Quantitative discrete
• For a particular day, the number of cars entering a college campus is measured.
– Quantitative discrete
• Time until a light bulb burns out
– Quantitative continuous
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Graphing Qualitative Variables
• Use a data distribution to describe:
– What values of the variable have been measured
– How often each value has occurred
• “ How often ” can be measured 3 ways:
– Frequency in each category
– Relative frequency = Frequency/ n
(proportion in each category)
– Percent = 100 x Relative frequency
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Example
• A bag of M&M ® s contains 25 candies:
• Raw Data: m m m m m m m m m m m m m m m m m m m m m m m m m
• Statistical Table:
Color Tally
Red
Blue
Green
Orange
Brown
Yellow m m m m m m m m m m
2 m m m
3 m m mm m m mm 8
4 m m m m
5
3
Frequency Relative
Frequency
5/25 = .20
3/25 = .12
2/25 = .08
3/25 = .12
8/25 = .32
4/25 = .16
Percent
20%
12%
8%
12%
32%
16%
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Pie Chart:
How the measurements are distributed among the categories
Graphs
Bar Chart:
How often a particular category was observed
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Graphing Quantitative Variables
• A single quantitative variable measured for different population segments or for different categories of classification can be graphed using a pie or bar chart .
A Big Mac hamburger costs $3.64 in
Switzerland, $2.44 in the U.S. and $1.10 in
South Africa.
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Applet
Dotplots
• The simplest graph for quantitative data
• Plots the measurements as points on a horizontal axis, stacking the points that duplicate existing points.
• Example: The set 4, 5, 5, 7, 6
4 5 6 7
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Stem and Leaf Plots
• A simple graph for quantitative data
• Uses the actual numerical values of each data point.
–Divide each measurement into two parts: the stem and the leaf.
–List the stems in a column, with a vertical line to their right.
–For each measurement, record the leaf portion in the same row as its matching stem.
–
Order the leaves from lowest to highest in each stem.
–Provide a key to your coding.
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Example
6
7
4
5
8
9
The prices ($) of 18 brands of walking shoes:
90 70 70 70 75 70 65 68 60
74 70 95 75 70 68 65 40 65
0
0
5 8 0 8 5 5
0 0 0 5 0 4 0 5 0
0 5
Reorder
6
7
4
5
8
9
0 5 5 5 8 8
0 0 0 0 0 0 4 5 5
0 5
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Interpreting Graphs:
Location and Spread
• Where is the data centered on the horizontal axis, and how does it spread out from the center?
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Tabulating and Graphing
Numerical Data
Numerical Data
41, 24, 32, 26, 27, 27, 30, 24, 38, 21
Ordered Array
21, 24, 24, 26, 27, 27, 30, 32, 38, 41
Stem and Leaf
Display
2 144677
3 028
4 1
Frequency Distributions
Cumulative Distributions
1 0 0
1 2 0
8 0
6 0
4 0
2 0
0
O g ive
1 0 2 0 3 0 4 0 5 0 6 0
Tables
Histograms
7
6
5
4
3
2
1
0
1 0 2 0 3 0 4 0 5 0 6 0
Ogive
Polygons
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Tabulating Numerical Data:
Frequency Distributions
• Sort raw data in ascending order:
12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46,
53, 58
• Find range:
58 - 12 = 46
• Select number of classes:
5 (usually between 5 and 15)
• Compute class interval (width):
10 (46/5 then round up)
• Determine class boundaries (limits):
10, 20, 30,
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40, 50, 60

Frequency Distributions,
Relative Frequency
Distributions and Percentage
Distributions
Data in ordered array:
12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58
Class Frequency
Relative
Frequency
Percentage
10 but under 20 3 .15 15
20 but under 30
30 but under 40
6 .30 30
5 .25 25
40 but under 50 4 .20 20
50 but under 60 2 .10 10
Total 20 1 100
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Graphing Numerical Data:
The Histogram
Data in ordered array:
12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58
Histogram
Class Boundaries
5
4
3
2
1
0
7
6
0
5
6
5
4
3
2
0
15 25 36 45 55 More
Class Midpoints
No Gaps
Between
Bars
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Graphing Numerical Data:
The Frequency Polygon
Data in ordered array:
12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58
F r e q u e n c y
7
6
5
2
1
4
3
0
5 1 5 2 5 3 6 4 5 5 5 M o r e
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Class Midpoints

Tabulating Numerical Data:
Cumulative Frequency
Data in ordered array:
12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58
Class
Cumulative Cumulative
Frequency % Frequency
10 but under 20 3 15
20 but under 30
30 but under 40
9 45
14 70
40 but under 50 18 90
50 but under 60 20 100
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Graphing Numerical Data:
Data in ordered array:
12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58
Ogive
100
80
60
40
20
0
10 20 30 40 50
Class Boundaries ( Not Midpoints )
60
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Skala Pengukuran :
– Nominal
– Ordinal
– Interval
– Rasio

Karakteristik SkalaPengukuran
Skala
Penguku ran
Pembedaan
Kategori
Nominal
Ya
Ordinal
Ya
Interval
Rasio
Ya
Ya
-
Urutan/
Peringkat
Ya
Ya
Ya
-
-
Jarak Di antara
Kategori
Ya
Ya
Nilai
Absolut
-
-
-
Ya

Key Concepts
I. How Data Are Generated
1. Experimental units, variables, measurements
2. Samples and populations
3. Univariate, bivariate, and multivariate data
II. Types of Variables
1. Qualitative or categorical
2. Quantitative a. Discrete b. Continuous
III. Graphs for Univariate Data Distributions
1. Qualitative or categorical data a. Pie charts b. Bar charts
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Key Concepts
2. Quantitative data a. Pie and bar charts b. Line charts c. Dotplots d. Stem and leaf plots e. Relative frequency histograms
3. Describing data distributions a. Shapes — symmetric, skewed left, skewed right, unimodal, bimodal b. Proportion of measurements in certain intervals c. Outliers
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• Selamat Belajar Semoga Sukses.
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