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Pertemuan 01

PENDAHULUAN: Data dan Statistika

Matakuliah : I0262-Statiatik Probabilitas

Tahun : 2007

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Outline Materi:

• Peranan dan Jangkauan Statistika

• Diagram Dahan dan Daun

• Sebaran Frekuensi

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Business Basic Statistics

Introduction and Data Collection

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PERANAN DAN Jangkauan Statistika

• Why a Manager Needs to Know About Statistics

• The Growth and Development of Modern Statistics

• Some Important Definitions

• Descriptive Versus Inferential Statistics

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Peranan dan Jangkauan Statistika

• Why Data are Needed

• Types of Data and Their Sources

• Design of Survey Research

• Types of Sampling Methods

• Types of Survey Errors

(continued)

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Why a Manager Needs to Know About Statistics

• To Know How to Properly Present Information

• To Know How to Draw Conclusions about Populations Based on Sample Information

• To Know How to Improve Processes

• To Know How to Obtain Reliable Forecasts

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The Growth and Development of Modern Statistics

Needs of government to collect data on its citizenry

The development of the mathematics of probability theory

The advent of the computer

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Some Important Definitions

• A Population (Universe) is the Whole Collection of Things Under Consideration

• A Sample is a Portion of the Population Selected for Analysis

• A Parameter is a Summary Measure Computed to Describe a Characteristic of the Population

• A Statistic is a Summary Measure Computed to Describe a Characteristic of the Sample

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Population and Sample

Population Sample

Use parameters to summarize features

Use statistics to summarize features

Inference on the population from the sample

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Statistical Methods

• Descriptive Statistics– Collecting and describing data

• Inferential Statistics– Drawing conclusions and/or making decisions

concerning a population based only on sample data

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Descriptive Statistics

• Collect Data– E.g., Survey

• Present Data– E.g., Tables and graphs

• Characterize Data– E.g., Sample Mean = iX

n

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Inferential Statistics

• Estimation– E.g., Estimate the

population mean weight using the sample mean weight

• Hypothesis Testing– E.g., Test the claim that

the population mean weight is 120 pounds

Drawing conclusions and/or making decisions concerning a population based on sample results.

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Why We Need Data

• To Provide Input to Survey

• To Provide Input to Study

• To Measure Performance of Ongoing Service or Production Process

• To Evaluate Conformance to Standards

• To Assist in Formulating Alternative Courses of Action

• To Satisfy Curiosity

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Data Sources

Observation

Experimentation

Survey

Print or Electronic

Data Sources

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Types of Data

Categorical(Q ualitative)

Discrete Continuous

Num erical(Q uantitative)

D ata

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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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Organizing Numerical Data

2 144677

3 028

4 1

Numerical Data

Ordered Array

Stem and LeafDisplay

Frequency DistributionsCumulative Distributions

Histograms

Polygons

Ogive

Tables

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

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

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• Data in RawRaw Form (as Collected): 24, 26, 24, 21, 27, 27, 30, 41, 32, 38

• Data in Ordered ArrayOrdered Array from Smallest to Smallest to LargestLargest:

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

• Stem-and-Leaf Display:

Stem and Leaf Display

(continued)

2 1 4 4 6 7 7

3 0 2 8

4 1

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Tabulating and Graphing Numerical Data

O g ive

0

20

40

60

80

100

120

10 20 30 40 50 60

0

1

2

3

4

5

6

7

10 20 30 40 50 60

2 144677

3 028

4 1

Numerical Data

Ordered Array

Stem and LeafDisplay

Histograms Ogive

Tables

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

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

Frequency DistributionsCumulative Distributions

Polygons

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Tabulating Numerical Data: Frequency Distributions

• Sort Raw Data in Ascending Order12, 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 35 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 35 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

Lower Cumulative CumulativeLimit Frequency % Frequency

10 0 0

20 3 15

30 9 45

40 14 70

50 18 90

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

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Graphing Bivariate Numerical Data (Scatter Plot)

Mutual Funds Scatter Plot

0

10

20

30

40

0 10 20 30 40

Net Asset Values

Tota

l Yea

r to

Dat

e R

etur

n (%

)

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Tabulating and Graphing Univariate Categorical Data

Categorical Data

Tabulating Data

The Summary Table

Graphing Data

Pie Charts

Pareto DiagramBar Charts

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Graphing Univariate Categorical Data

0 1 0 2 0 3 0 4 0 5 0

S to c k s

B o n d s

S a vin g s

C D

Categorical Data

Tabulating Data

The Summary Table

Graphing Data

Pie Charts

Pareto DiagramBar Charts

0

5

1 0

1 5

2 0

2 5

3 0

3 5

4 0

4 5

S to c k s B o n d s S a vin g s C D

0

2 0

4 0

6 0

8 0

1 0 0

1 2 0

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Bar Chart(for an Investor’s Portfolio)

Investor's Portfolio

0 10 20 30 40 50

Stocks

Bonds

CD

Savings

Amount in K$

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Pie Chart (for an Investor’s Portfolio)

Percentages are rounded to the nearest percent

Amount Invested in K$

Savings

15%

CD 14%

Bonds

29%

Stocks

42%

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Pareto Diagram

Axis for line graph shows

cumulative % invested

Axis for bar

chart shows

% invested in each

category

0%

5%

10%

15%

20%

25%

30%

35%

40%

45%

Stocks Bonds Savings CD

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%