Pertemuan 01

Pendahuluan

Aji Setiawan

Matakuliah : Statistika

Tahun : 2015

Versi : Revisi

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Penilaian

Kehadiran ; 10%

Tugas ; 20%

UTS : 30%

UAS : 40%

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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

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Quota

Samples

Non-Probability Samples

(Convenience)

Judgement Chunk

Probability Samples

Simple

Random

Systematic

Stratified

Cluster

Probability Sampling

Subjects of the Sample are Chosen Based

on Known Probabilities

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Probability Samples

Simple

RandomSystematic Stratified Cluster

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

Variable

◦ Hair color

Experimental unit

◦ Person

Typical Measurements

◦Brown, black, blonde, etc.

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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

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Qualitative Quantitative

Discrete Continuous

Types of Variables

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•Qualitative variables measure a quality

or characteristic on each experimental

unit. (Categorical Data)

•Examples:•Hair color (black, brown, blonde…)

•Make of car (Dodge, Honda, Ford…)

•Gender (male, female)

•State of birth (California, Arizona,….)

Types of Variables

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•Quantitative variables measure a

numerical quantity on each experimental

unit.

Discrete if it can assume only a

finite or countable number of values.

Continuous if it can assume the

infinitely many values corresponding

to the points on a line interval.

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:

Statistical Table:

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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

m

m m

m

m

mm m

m

m m

mmmm

mmm

m

m

m

m

m

m

mmmm

mm

m

m m

m mm m m mm

m m m

Graphs

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Bar Chart:

How often a particular

category was observed

Pie Chart:

How the measurements are

distributed among the

categories

Graphing Quantitative Variables

A single quantitative variable measured for different population segments or for different categories of classification can be graphed using apie or bar chart.

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A Big Mac hamburger

costs $3.64 in

Switzerland, $2.44 in

the U.S. and $1.10 in

South Africa.

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

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4 5 6 7

Applet

Stem and Leaf Plots A simple graph for quantitative data

Uses the actual numerical values of each data point.

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–Divide each measurement into two parts: the stemand 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.

Example

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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

Tabulating and Graphing Numerical

Data

25

0

1

2

3

4

5

6

7

1 0 2 0 3 0 4 0 5 0 6 0

Numerical Data

Ordered Array

Stem and Leaf

Display

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 Distributions

Cumulative Distributions

Polygons

Ogive

0

2 0

4 0

6 0

8 0

1 0 0

1 2 0

1 0 2 0 3 0 4 0 5 0 6 0

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

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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

Relative

FrequencyPercentage

Data in ordered array:

12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58

Graphing Numerical Data:

The Histogram

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Histogram

0

3

6

5

4

2

0

0

1

2

3

4

5

6

7

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

Graphing Numerical Data:

The Frequency Polygon

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F r e q u e n c y

0

1

2

3

4

5

6

7

5 1 5 2 5 3 6 4 5 5 5 M o r e

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

Tabulating Numerical Data:

Cumulative Frequency

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Cumulative Cumulative

Class 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

Graphing Numerical Data:

The Ogive (Cumulative % Polygon)

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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

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

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Tugas

◦ Jelaskan pengertian dari pengukuran :

Nominal

Ordinal

Interval

Rasio

3434