Download Data in Ordered Array

Matakuliah
Tahun
: A0392-Statiatik Ekonomi
: 2006
Pertemuan 01
PENDAHULUAN:
Data dan Statistika
1
Outline Materi:
• Peranan dan Jangkauan Statistika
• Diagram Dahan dan Daun
• Sebaran Frekuensi
2
Business Basic Statistics
Introduction and Data
Collection
3
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
4
Peranan dan Jangkauan Statistika
• Why Data are Needed
(continued)
• Types of Data and Their Sources
• Design of Survey Research
• Types of Sampling Methods
• Types of Survey Errors
5
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
6
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
7
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
8
Population and Sample
Population
Sample
Use statistics to
summarize features
Use parameters to
summarize features
Inference on the population from the sample
9
Statistical Methods
• Descriptive Statistics
– Collecting and describing data
• Inferential Statistics
– Drawing conclusions and/or making decisions
concerning a population based only on
sample data
10
Descriptive Statistics
• Collect Data
– E.g., Survey
• Present Data
– E.g., Tables and graphs
• Characterize Data
– E.g., Sample Mean =
X
i
n
11
Inferential Statistics
• Estimation
– E.g., Estimate the
population mean weight
using the sample mean
weight
• Hypothesis Testing
– E.g., Test the claim that
theDrawing
population
mean and/or making decisions
conclusions
concerning
a population
weight
is 120
pounds based on sample results.
12
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
13
Data Sources
Data Sources
Print or Electronic
Observation
Survey
Experimentation
14
Types of Data
Data
Categorical
(Qualitative)
Numerical
(Quantitative)
Discrete
Continuous
15
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
16
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
17
Types of Sampling Methods
Samples
Non-Probability
Samples
(Convenience)
Judgement
Quota
Probability Samples
Simple
Random
Chunk
Stratified
Cluster
Systematic
18
Probability Sampling
• Subjects of the Sample are Chosen Based
on Known Probabilities
Probability Samples
Simple
Random
Systematic
Stratified
Cluster
19
Organizing Numerical Data
Numerical Data
Ordered Array
21, 24, 24, 26, 27, 27, 30, 32, 38, 41
Stem and Leaf
Display
Frequency Distributions
Cumulative Distributions
2 144677
3 028
4 1
41, 24, 32, 26, 27, 27, 30, 24, 38, 21
Histograms
Tables
Ogive
Polygons
20
Stem and Leaf Display
(continued)
• Data in Raw Form (as Collected):
24, 26, 24, 21, 27, 27, 30, 41, 32, 38
• Data in Ordered Array from Smallest to
Largest:
21, 24, 24, 26, 27, 27, 30, 32, 38, 41
• Stem-and-Leaf Display:
2
144677
3
028
4
1
21
Tabulating and Graphing
Numerical Data
Numerical Data
Ordered Array
21, 24, 24, 26, 27, 27, 30, 32, 38, 41
41, 24, 32, 26, 27, 27, 30, 24, 38, 21
Frequency Distributions
Cumulative Distributions
O g ive
120
100
80
60
40
20
0
10
Stem and Leaf
Display
2 144677
3 028
4 1
Histograms
20
30
40
50
Ogive
7
6
5
4
Tables
Polygons
3
2
1
0
10
20
30
40
50
60
22
60
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, 2330,
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
10 but under 20
20 but under 30
30 but under 40
40 but under 50
50 but under 60
Total
Relative
Frequency Frequency Percentage
3
6
5
4
2
20
.15
.30
.25
.20
.10
1
15
30
25
20
10
100
24
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
Frequency
Histogram
7
6
5
4
3
2
1
0
6
5
3
2
0
5
Class Boundaries
No Gaps
Between
Bars
4
0
15
25
35
45
Class Midpoints
55
More
25
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
Frequency
7
6
5
4
3
2
1
0
5
15
25
35
45
Class Midpoints
55
More
26
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
Lower
Limit
10
20
30
40
50
60
Cumulative
Frequency
0
3
9
14
18
20
Cumulative
% Frequency
0
15
45
70
90
100
27
Graphing Numerical Data:
The Ogive (Cumulative % 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
Ogive
100
80
60
40
20
0
10
20
30
40
50
60
Class Boundaries (Not Midpoints)
28
Graphing Bivariate Numerical
Data (Scatter Plot)
Total Year to
Date Return (%)
Mutual Funds Scatter Plot
40
30
20
10
0
0
10
20
30
Net Asset Values
40
29
Tabulating and Graphing
Univariate Categorical Data
Categorical Data
Tabulating Data
The Summary Table
Graphing Data
Pie Charts
Bar Charts
Pareto Diagram
30
Graphing Univariate
Categorical Data
Categorical Data
Graphing Data
Tabulating Data
The Summary Table
Pie Charts
CD
Pareto Diagram
S a vi n g s
Bar Charts
B onds
S to c k s
0
10
20
30
40
50
45
120
40
100
35
30
80
25
60
20
15
40
10
20
5
0
0
S to c k s
B onds
S a vi n g s
CD
31
Bar Chart
(for an Investor’s Portfolio)
Investor's Portfolio
Savings
CD
Bonds
Stocks
0
10
20
30
40
50
Amount in K$
32
Pie Chart
(for an Investor’s Portfolio)
Amount Invested in K$
Savings
15%
Stocks
42%
CD
14%
Bonds
29%
Percentages are
rounded to the
nearest percent
33
Pareto Diagram
Axis for
bar
chart
shows
%
invested
in each
category
45%
100%
40%
90%
80%
35%
70%
30%
60%
25%
50%
20%
40%
15%
30%
10%
20%
5%
10%
0%
0%
Stocks
Bonds
Savings
CD
Axis for line
graph
shows
cumulative
% invested
34