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Pertemuan 01Pendahuluan

Matakuliah : I0284 - Statistika

Tahun : 2008

Versi : Revisi

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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.

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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

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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

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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

Quota

Samples

Non-Probability Samples

(Convenience)

Judgement Chunk

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 variablevariable is a characteristic that changes or varies over time and/or for different individuals or objects under consideration.

• Examples: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 unitexperimental unit is the individual or object on which a variable is measured.

• A measurementmeasurement results when a variable is actually measured on an experimental unit.

• A set of measurements, called data,data, can be either a samplesample or a population.population.

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Example

• Variable – Hair color

• Experimental unit –Person

• Typical Measurements –Brown, black, blonde, etc.

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How many variables have you measured?

• Univariate data:Univariate data: One variable is measured on a single experimental unit.

• Bivariate data:Bivariate data: Two variables are measured on a single experimental unit.

• Multivariate data: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

•Qualitative variablesQualitative variables measure a quality or characteristic on each experimental unit. (Categorical Data)

•Examples:Examples:•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

•Quantitative variablesQuantitative variables measure a numerical quantity on each experimental unit.

Discrete Discrete if it can assume only a finite or countable number of values.

Continuous Continuous 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 distributiondata distribution to describe:– What valuesWhat values of the variable have been measured– How oftenHow 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:Raw Data:

• Statistical Table:Statistical Table:

Color Tally Frequency Relative Frequency

Percent

Red 5 5/25 = .20 20%

Blue 3 3/25 = .12 12%

Green 2 2/25 = .08 8%

Orange 3 3/25 = .12 12%

Brown 8 8/25 = .32 32%

Yellow 4 4/25 = .16 16%

m

m

m

mm

mm

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m m

m

m

mm m

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m m

mmmm

mmm

m

m

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m

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mmmm

mm

m

m m

m mm m m mm

m m m

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Graphs

Bar Chart:

How often a particular category was observed

Pie Chart:

How the measurements are distributed among the categories

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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 pie or bar chartbar chart.

A Big Mac hamburger costs $3.64 in Switzerland, $2.44 in the U.S. and $1.10 in South Africa.

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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Dotplots

• The simplest graph for quantitative data• Plots the measurements as points on a

horizontal axis, stacking the points that duplicate existing points.

• Example:Example: The set 4, 5, 5, 7, 6

4 5 6 7

AppletApplet

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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.

–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

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

4 0

5

6 5 8 0 8 5 5

7 0 0 0 5 0 4 0 5 0

8

9 0 5

4 0

5

6 0 5 5 5 8 8

7 0 0 0 0 0 0 4 5 5

8

9 0 5

Reorder

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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?

• 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

0

1

2

3

4

5

6

7

10 20 30 40 50 60

Numerical Data

Ordered Array

Stem and LeafDisplay

Histograms Ogive

Tables

2 144677

3 028

4 1

41, 24, 32, 26, 27, 27, 30, 24, 38, 21

21, 24, 24, 26, 27, 27, 30, 32, 38, 41

Frequency DistributionsCumulative Distributions

Polygons

O g ive

0

20

40

60

80

100

120

10 20 30 40 50 60

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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, 40, 50, 60

• Compute class midpoints: 15, 25, 35, 45, 55

• Count observations & assign to classes

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Frequency Distributions, Relative Frequency

Distributions and Percentage Distributions

Class Frequency

10 but under 20 3 .15 15

20 but under 30 6 .30 30

30 but under 40 5 .25 25

40 but under 50 4 .20 20

50 but under 60 2 .10 10

Total 20 1 100

RelativeFrequency

Percentage

Data in ordered array:12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58

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Graphing Numerical Data: The Histogram

Histogram

0

3

65

4

2

001234567

5 15 25 36 45 55 More

Fre

qu

en

cy

Data in ordered array:12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58

No Gaps Between

Bars

Class MidpointsClass Boundaries

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Graphing Numerical Data: The Frequency Polygon

Frequency

0

1

2

3

4

5

6

7

5 15 25 36 45 55 More

Class Midpoints

Data in ordered array:12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58

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Tabulating Numerical Data: Cumulative Frequency

Cumulative CumulativeClass Frequency % Frequency

10 but under 20 3 15

20 but under 30 9 45

30 but under 40 14 70

40 but under 50 18 90

50 but under 60 20 100

Data in ordered array:12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58

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Graphing Numerical Data:

The Ogive (Cumulative % Polygon)

Ogive

0

20

40

60

80

100

10 20 30 40 50 60

Class Boundaries (Not Midpoints)

Data in ordered array:12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58

Skala Pengukuran :– Nominal– Ordinal– Interval– Rasio

Karakteristik SkalaPengukuran

Skala Skala PengukPengukuranuran

Pembedaan Pembedaan KategoriKategori

Urutan/ Urutan/ Peringkat Peringkat

Jarak Di Jarak Di antara antara KategoriKategori

Nilai Nilai AbsolutAbsolut

NominalNominal YaYa -- -- --

OrdinalOrdinal YaYa YaYa -- --

IntervalInterval YaYa YaYa YaYa --

RasioRasio YaYa YaYa YaYa YaYa

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Key ConceptsI. How Data Are GeneratedI. How Data Are Generated

1. Experimental units, variables, measurements2. Samples and populations3. Univariate, bivariate, and multivariate data

II. Types of VariablesII. Types of Variables1. Qualitative or categorical2. Quantitative

a. Discreteb. Continuous

III. Graphs for Univariate Data DistributionsIII. Graphs for Univariate Data Distributions1. Qualitative or categorical data

a. Pie chartsb. 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.