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Business Statistics
Session 1
PGDM
Introduction to Statistics 1 7/03/2015
History
The word statistik comes from Italian word statistia which means "statesman".
First used by Gottfried Achenwall (171972).
Long before the 18th century, people had been recording and using data.
Official government statistics are as old as recorded history.
The old testaments contain several accounts of census taking.
Introduction to Statistics 2 7/03/2015
What is statistics?
A branch of mathematics taking and transforming numbers into useful information for decision makers
Methods for processing & analyzing numbers
Methods for helping reduce the uncertainty inherent in decision making
Introduction to Statistics 3 7/03/2015
Why Study Statistics?
Decision Makers Use Statistics To:
Present and describe business data and information properly
Draw conclusions about large groups of individuals or items, using information collected from subsets of the individuals or
items.
Make reliable forecasts about a business activity
Improve business processes
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Chap 1-5
Types of Statistics
Statistics The branch of mathematics that transforms data into
useful information for decision makers.
Descriptive Statistics
Collecting, summarizing, and describing data
Inferential Statistics
Drawing conclusions and/or making decisions concerning a population based only on sample data
Introduction to Statistics 7/03/2015
Subdivisions Within Statistics
Descriptive statistics Inferential statistics.
Graphs, tables and charts that display data so that they are easier to understand are examples of descriptive statistics.
The process of estimation of any parameter is referred as statistical inference.
The method and techniques of statistical inference can be used in decision theory, making decisions under conditions of uncertainty.
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Chap 1-7
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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Chap 1-8
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 about a large group of individuals based on a subset of the large group.
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Chap 1-9
Basic Vocabulary of Statistics
VARIABLE
A variable is a characteristic of an item or individual.
DATA
Data are the different values associated with a variable.
OPERATIONAL DEFINITIONS
Data values are meaningless unless their variables have operational
definitions, universally accepted meanings that are clear to all associated
with an analysis.
Chap 1-10
Basic Vocabulary of Statistics
POPULATION
A population consists of all the items or individuals about which
you want to draw a conclusion.
SAMPLE
A sample is the portion of a population selected for analysis.
PARAMETER
A parameter is a numerical measure that describes a characteristic
of a population.
STATISTIC
A statistic is a numerical measure that describes a characteristic of
a sample.
Chap 1-11
Population vs. Sample
Population Sample
Measures used to describe the
population are called parameters
Measures computed from
sample data are called statistics
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Chap 1-12
Examples of Populations
Names of all registered voters in the United
States
Incomes of all families living in Delhi
Annual returns of all stocks traded on the
New York Stock Exchange
Grade point averages of all the students in
your Institute
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Random Sampling
Simple random sampling is a procedure in which
each member of the population is chosen strictly by chance, each member of the population is equally likely to be
chosen, and every possible sample of n objects is equally likely to be
chosen
The resulting sample is called a random sample
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The Decision Making Process
Begin Here:
Identify the Problem
Data
Information
Knowledge
Decision
Descriptive Statistics, Probability, Computers
Experience, Theory, Literature, Inferential Statistics, Computers
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Chap 1-15
Why Collect Data?
A marketing research analyst needs to assess the effectiveness of a new television advertisement.
A pharmaceutical manufacturer needs to determine whether a new drug is more effective than those currently in use.
An operations manager wants to monitor a manufacturing process to find out whether the quality of the product being manufactured is conforming to company standards.
An auditor wants to review the financial transactions of a company in order to determine whether the company is in compliance with generally accepted accounting principles.
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Chap 1-16
Sources of Data
Primary Sources: The data collector is the one using the data for analysis
Data from a political survey
Data collected from an experiment
Observed data
Secondary Sources: The person performing data analysis is not the data collector
Analyzing census data
Examining data from print journals or data published on the internet.
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Chap 1-17
Types of Variables
Categorical (qualitative) variables have values that can only be placed into categories, such as
yes and no.
Numerical (quantitative) variables have values that represent quantities.
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Chap 1-18
Types of Data
Data
Categorical
Numerical
Discrete Continuous
Examples:
Marital Status
Political Party
Eye Color
(Defined categories) Examples:
Number of Children
Defects per hour
(Counted items)
Examples:
Weight
Voltage
(Measured characteristics)
Introduction to Statistics 7/03/2015
Measurement Levels
Interval Data
Ordinal Data
Nominal Data
Quantitative Data
Qualitative Data
Categories (no ordering or direction)
Ordered Categories (rankings, order, or scaling)
Differences between measurements but no true zero
Ratio Data Differences between measurements, true zero exists
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Classifying Data Elements in a Purchasing Database
Data for Business Statistics
Figure 1.2
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Categorical (nominal) Data
Data placed in categories according to a specified characteristic
Categories bear no quantitative relationship to one another
Examples:
- customers location (America, Europe, Asia)
- employee classification (manager, supervisor,
associate)
Data for Business Statistics
Introduction to Statistics 21 7/03/2015
Ordinal Data
Data that is ranked or ordered according to some relationship with one another
No fixed units of measurement
Examples:
- college football rankings
- survey responses
(poor, average, good, very good, excellent)
Data for Business Statistics
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Interval Data
Ordinal data but with constant differences between observations
No true zero point
Ratios are not meaningful
Examples:
- temperature readings
Data for Business Statistics
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Ratio Data
Continuous values and have a natural zero point
Ratios are meaningful
Examples:
- monthly sales
- delivery times
Data for Business Statistics
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Graphical Presentation of Data
Data in raw form are usually not easy to use for decision making
Some type of organization is needed
Table
Graph
The type of graph to use depends on the variable being summarized
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Graphical Presentation of Data
Categorical Variables
Numerical Variables
Frequency distribution Bar chart Pie chart Pareto diagram
Line chart Frequency distribution Histogram and ogive Scatter plot
(continued)
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Tables and Graphs for Categorical Variables
Categorical Data
Graphing Data
Pie Chart Pareto Diagram
Bar Chart Frequency
Distribution Table
Tabulating Data
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The Frequency Distribution Table
Example: Hospital Patients by Unit
Hospital Unit Number of Patients
Cardiac Care 1,052
Emergency 2,245
Intensive Care 340
Maternity 552
Surgery 4,630
(Variables are categorical)
Summarize data by category
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Bar and Pie Charts
Bar charts and Pie charts are often used for qualitative (category) data
Height of bar or size of pie slice shows the frequency or percentage for each category
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Bar Chart Example
Hospital Patients by Unit
0
1000
2000
3000
4000
5000
Card
iac
Care
Em
erg
en
cy
Inte
nsiv
e
Care
Mate
rnit
y
Su
rgery
Nu
mb
er
of
pa
tie
nts
pe
r y
ea
r
Hospital Number Unit of Patients
Cardiac Care 1,052
Emergency 2,245
Intensive Care 340
Maternity 552
Surgery 4,630
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Hospital Patients by Unit
Emergency
25%
Maternity
6%
Surgery
53%
Cardiac Care
12%
Intensive Care
4%
Pie Chart Example
(Percentages are rounded to the nearest percent)
Hospital Number % of Unit of Patients Total Cardiac Care 1,052 11.93
Emergency 2,245 25.46
Intensive Care 340 3.86
Maternity 552 6.26
Surgery 4,630 52.50
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Pareto Diagram
Used to portray categorical data
A bar chart, where categories are shown in
descending order of frequency
A cumulative polygon is often shown in the
same graph
Used to separate the vital few from the
trivial many
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Example: 400 defective items are examined for cause of defect:
Source of
Manufacturing Error Number of defects
Bad Weld 34
Poor Alignment 223
Missing Part 25
Paint Flaw 78
Electrical Short 19
Cracked case 21
Total 400
Pareto Diagram Example
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Step 1: Sort by defect cause, in descending order
Step 2: Determine % in each category
Source of
Manufacturing Error Number of defects % of Total Defects
Poor Alignment 223 55.75
Paint Flaw 78 19.50
Bad Weld 34 8.50
Missing Part 25 6.25
Cracked case 21 5.25
Electrical Short 19 4.75
Total 400 100%
Pareto Diagram Example (continued)
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Pareto Diagram Example cu
mu
lative % (lin
e grap
h)
% o
f d
efe
cts
in e
ach
cat
ego
ry (
bar
gr
aph
)
Pareto Diagram: Cause of Manufacturing Defect
0%
10%
20%
30%
40%
50%
60%
Poor Alignment Paint Flaw Bad Weld Missing Part Cracked case Electrical Short
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Step 3: Show results graphically
(continued)
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Numerical Data
Histogram Ogive
Frequency Distributions and
Cumulative Distributions
Graphs to Describe Numerical Variables
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