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STATISTICS INTRODUCTIONSTATISTICS INTRODUCTION
Dr.R.VARADHARAJAN
Associate Professor in Statistics
Department of MBA
Vels University, chennai.
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Origin and DevelopmentOrigin and Development
It is not a new discipline.It has been used right from the existence
of life on earth, through its use was very much limited.
In the good old days Statistics was regarded as the ‘Science of Statecraft’ and was the by – product of the administrative activity of the state.
Dr.R.VARADHARAJAN, MBA DEPT, VELS UNIVERSITY
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Origin and Development Origin and Development Contd…Contd…It has been the traditional function of the
governments to keep records of population, births, deaths, taxes, crop yields and many other types of activities\
Also Statistics originated as a science of kings.
Dr.R.VARADHARAJAN, MBA DEPT, VELS UNIVERSITY
Definition:Definition:
“Statistics may be called the science of counting” – A.L.BOWLEY
According to Croxton and Cowden Statistics may be defined as “The science of collection, organization, presentation, analysis and interpretation of numerical data”.
Dr.R.VARADHARAJAN, MBA DEPT, VELS UNIVERSITY
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Descriptive StatisticsDescriptive Statistics
Descriptive statistics are methods for organizing and summarizing data.
For example, tables or graphs are used to organize data, and descriptive values such as the average score are used to summarize data.
A descriptive value for a population is called a parameter and a descriptive value for a sample is called a statistic.
Dr.R.VARADHARAJAN, MBA DEPT, VELS UNIVERSITY
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Inferential StatisticsInferential Statistics
Inferential statistics are methods for using sample data to make general conclusions (inferences) about populations.
Because a sample is typically only a part of the whole population, sample data provide only limited information about the population. As a result, sample statistics are generally imperfect representatives of the corresponding population parameters.
Dr.R.VARADHARAJAN, MBA DEPT, VELS UNIVERSITY
Collection:Collection:
Utmost care must be exercised in collecting data because they form the fundamental of Statistical analysis. If the are faulty, the conclusions drawn can never reliable.
Dr.R.VARADHARAJAN, MBA DEPT, VELS UNIVERSITY
Organization:Organization:
A large mass figures that are collected from a survey frequently needs organization.
The collected data must be edited very carefully so that the omissions, inconsistencies, irrelevant answers and wrong computations in the returns from a survey may be corrected or adjusted
Dr.R.VARADHARAJAN, MBA DEPT, VELS UNIVERSITY
Organization Contd…Organization Contd…
The next step is to classify them .
(Arrange the data according to some common characteristics)
The last step in the organization is tabulation.
(Arrange the data in rows and columns)
Dr.R.VARADHARAJAN, MBA DEPT, VELS UNIVERSITY
Presentation:Presentation:
After the data have been collected and organized they are ready for presentation. Data presented in an orderly manner facilitate statistical analysis. There are two different models in which the collected data may be presented:
Diagrams, and Graphs.
Dr.R.VARADHARAJAN, MBA DEPT, VELS UNIVERSITY
Analysis:Analysis:
The purpose of analyzing data is to dig out information useful for decision – making.
Ex: Measures of Central tendency, Measures of Variation, Correlation and regressions etc…
Dr.R.VARADHARAJAN, MBA DEPT, VELS UNIVERSITY
Interpretation:Interpretation:
Drawing conclusions from the data collected and analyzed.
The interpretation of data is difficult task and necessitates a high degree of skill and experience.
If the data that have been analyzed are not properly interpreted, the whole object of the investigation may be defeated and fallacious conclusion be drawn.
Dr.R.VARADHARAJAN, MBA DEPT, VELS UNIVERSITY
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Functions of StatisticsFunctions of Statistics
These are the important functions of Statistics
• It presents facts in a definite form.
• It simplifies mass of figures.
• It facilitates comparison.
• It helps in formulating and testing hypothesis.
• It helps in prediction.
Dr.R.VARADHARAJAN, MBA DEPT, VELS UNIVERSITY
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Applications of StatisticsApplications of Statistics
The following are the important Applications of Statistics
• Statistics and the State
• Statistics and business
• Statistics and Economics
• Physical sciences
• Natural sciences
• Statistics and Research
Dr.R.VARADHARAJAN, MBA DEPT, VELS UNIVERSITY
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DataData
The measurements obtained in a research study are called the data.
The goal of statistics is to help researchers organize and interpret the data.
Data may be obtained either from the primary source or the secondary source.
Dr.R.VARADHARAJAN, MBA DEPT, VELS UNIVERSITY
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Data Contd…Data Contd…
A primary source is one that itself collects the data.
A secondary source is one that makes available data which were collected by some other agency.
Dr.R.VARADHARAJAN, MBA DEPT, VELS UNIVERSITY
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Methods of collecting Primary DataMethods of collecting Primary Data
Direct personal interviewsIndirect oral interviewsInformation from correspondentsMailed questionnaire methodSchedule sent through enumerators
Dr.R.VARADHARAJAN, MBA DEPT, VELS UNIVERSITY
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Direct Personal InterviewsDirect Personal Interviews
There is a face to face contact with the persons from whom the information is to be obtained (informants).
First hand information or original in character.
Example: A person wants to collect data about the working conditions of
the workers of the Tata textile mill, chennai, he would go to the mill, contact the workers and obtain the desired information.
Dr.R.VARADHARAJAN, MBA DEPT, VELS UNIVERSITY
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Indirect Oral InterviewsIndirect Oral Interviews
The investigator contacts third parties called witnesses capable of supplying the necessary information.
Example: In an enquiry regarding addiction to drugs, alcohol, etc.,
people may be reluctant to supply information about their own habits. In that situation, this type information is collected from their neighbours, friends etc.,
Clues about thefts Murders
Dr.R.VARADHARAJAN, MBA DEPT, VELS UNIVERSITY
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Information From CorrespondentsInformation From Correspondents
The investigator appoints local agents or correspondents in different places to collect information.
These correspondents collect and transmit the information to the central office where the data are processed.
Example: News paper agencies generally adopt this method. Correspondents in different places supply information
relating to such events as accidents, riots, strikes etc.,
Dr.R.VARADHARAJAN, MBA DEPT, VELS UNIVERSITY
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Mailed Questionnaire MethodMailed Questionnaire Method
A list of questions pertaining to the survey (Questionnaire) is prepared and sent to the various informants by post.
The questionnaire contains questions and provides space for answers.
Request is made to the informants through a covering letter to fill up the questionnaire and send back within a specified time.
Example: This method is appropriate in cases where informants are spread over a wide area, i.e., in case of extensive surveys.
Dr.R.VARADHARAJAN, MBA DEPT, VELS UNIVERSITY
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Mailed Questionnaire Method Mailed Questionnaire Method Contd…Contd…
Covering letter Number of Questions should be small Questions should be arranged logically Questions should be short and simple to understand Personal Questions should be avoided Instructions to the informants Questions should be capable of objective answer Yes or No Questions Questions should look attractive
Dr.R.VARADHARAJAN, MBA DEPT, VELS UNIVERSITY
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Schedule Sent Through EnumeratorsSchedule Sent Through Enumerators
The enumerators contact the informants, get replies to the questions contained in a schedule and fill them in their own handwriting in the questionnaire form.
It can be adopted in those cases where informants are illiterate.
This method is costly among the above discussed method.
Some special skills are required to collect the information from the respondents.
Dr.R.VARADHARAJAN, MBA DEPT, VELS UNIVERSITY
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Sources of secondary data:Sources of secondary data:
Published sources
Unpublished sources
Dr.R.VARADHARAJAN, MBA DEPT, VELS UNIVERSITY
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Published SourcesPublished Sources
Reports and official publicationsSemi-official publications of various local
bodies such as municipal corporations and district boards.
Financial and economic journals.Annual report of joint stock companies and
corporations.
Dr.R.VARADHARAJAN, MBA DEPT, VELS UNIVERSITY
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Unpublished SourcesUnpublished Sources
All statistical material is not always published.
There are various sources of unpublished data such as records maintained by various Government and Private offices, studies made by research institutions, scholars, etc., such sources can be used where necessary.
Dr.R.VARADHARAJAN, MBA DEPT, VELS UNIVERSITY
Classification:Classification:
Classification is the grouping of related facts into classes.
Ex: Sorting letters in a post office. (according to their destination like Mumbai, Calcutta etc…)
Dr.R.VARADHARAJAN, MBA DEPT, VELS UNIVERSITY
Classification Contd…Classification Contd…
Types of Classification:
• Geographical (ie) Area – wise
• Chronological (ie) on the basis of time
• Quantitative (ie) in terms of magnitudes
• Qualitative (ie) according to some attributes
Dr.R.VARADHARAJAN, MBA DEPT, VELS UNIVERSITY
Geographical ClassificationGeographical Classification
The data are classified on the basis of geographical or vocational differences between the various items.
Like countries, states, cities, zones, areas, etc.,
Dr.R.VARADHARAJAN, MBA DEPT, VELS UNIVERSITY
Country – Wise Comparison of Yield of Country – Wise Comparison of Yield of Rice (Metric Tones / Hectares) Rice (Metric Tones / Hectares)
Name of the Country Production of Rice
Egypt 9.87
India 8.78
USA 7.67
Japan 6.54
Korea 5.36
Myanmar 6.89
Aveaage 7.52
Dr.R.VARADHARAJAN, MBA DEPT, VELS UNIVERSITY
Chronological ClassificationChronological Classification
When data are observed over a period of time the type of classification is known as chronological classification
We may present the figures of population as follows:
Dr.R.VARADHARAJAN, MBA DEPT, VELS UNIVERSITY
Population of India From 1951 to 2001Population of India From 1951 to 2001
Year Population (In Crores)
1951 37.11
1961 43.92
1971 54.82
1981 68.33
1991 84.64
2001 102.87
Dr.R.VARADHARAJAN, MBA DEPT, VELS UNIVERSITY
Quantitative ClassificationQuantitative Classification
The data are classified according to some characteristics that can be measured.
Such as height, weight, income, sales, profits, production, etc.,
Dr.R.VARADHARAJAN, MBA DEPT, VELS UNIVERSITY
The students of a college may be classified The students of a college may be classified according to weight as followsaccording to weight as follows
Weight No. of Students
40-50 50
50-60 200
60-70 250
70-80 150
80-90 60
90-100 40
Total 750
Dr.R.VARADHARAJAN, MBA DEPT, VELS UNIVERSITY
Qualitative ClassificationQualitative Classification
The data are classified on the basis of some attribute or quality.
Such as sex, colour of hair, literacy, religion, etc.,
The point to note in this type of classification is that the attribute under study cannot be measured.
Dr.R.VARADHARAJAN, MBA DEPT, VELS UNIVERSITY
The Population may be Classified as The Population may be Classified as followsfollows
Dr.R.VARADHARAJAN, MBA DEPT, VELS UNIVERSITY
Tabulation:Tabulation:
A table is a systematic arrangement of Statistical data in columns and rows. Rows are horizontal arrangements whereas columns are vertical ones.
The purpose of a table is to simplify the presentation and to facilitate comparisons.
Dr.R.VARADHARAJAN, MBA DEPT, VELS UNIVERSITY
Tabulation Contd…Tabulation Contd…
Parts of a table:• Table number• Title of the table• Caption stub• Stub• Body• Head notes • Footnotes
Dr.R.VARADHARAJAN, MBA DEPT, VELS UNIVERSITY
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Types of TablesTypes of Tables
Simple and complex tables.
General purpose and special purpose tables.
Dr.R.VARADHARAJAN, MBA DEPT, VELS UNIVERSITY
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Diagrams and GraphsDiagrams and Graphs
Diagrams and graphs are extremely useful because of the following reasons.• They give birds eye view of the entire
data and, therefore, the information presented is easily understood.
• Pictorial presentation helps in proper understanding of the data as it gives an interesting form to it.
Dr.R.VARADHARAJAN, MBA DEPT, VELS UNIVERSITY
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Types of DiagramsTypes of Diagrams
One – dimensional diagrams
Ex: Bar diagrams.Two – dimensional diagrams
Ex: Rectangles, squares and circles.Three – dimensional diagrams
Ex: Cubes, cylinders and spheres.Pictograms and cartograms
Dr.R.VARADHARAJAN, MBA DEPT, VELS UNIVERSITY
Bar diagramBar diagram
Dr.R.VARADHARAJAN, MBA DEPT, VELS UNIVERSITY
Multiple Bar DiagramMultiple Bar Diagram
0
1
2
3
4
5
6
2005 2006 2007 2008
Rice
Wheat
Maize
Dr.R.VARADHARAJAN, MBA DEPT, VELS UNIVERSITY
Sub Divided Bar DiagramSub Divided Bar Diagram
Dr.R.VARADHARAJAN, MBA DEPT, VELS UNIVERSITY
Percentage Bar DiagramPercentage Bar Diagram
Dr.R.VARADHARAJAN, MBA DEPT, VELS UNIVERSITY
Line ChartLine Chart
Dr.R.VARADHARAJAN, MBA DEPT, VELS UNIVERSITY
Pie DiagramPie Diagram
Dr.R.VARADHARAJAN, MBA DEPT, VELS UNIVERSITY
Scatter DiagramScatter Diagram
Dr.R.VARADHARAJAN, MBA DEPT, VELS UNIVERSITY
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VariablesVariables
A variable is a characteristic or condition that can change or take on different values.
Most research begins with a general question about the relationship between two variables for a specific group of individuals.
Dr.R.VARADHARAJAN, MBA DEPT, VELS UNIVERSITY
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Types of VariablesTypes of Variables
Variables can be classified as discrete or continuous.
Discrete variables (such as class size) consist of indivisible categories, and continuous variables (such as time or weight) are infinitely divisible into whatever units a researcher may choose.
For example, time can be measured to the nearest minute, second, half-second, etc.
Dr.R.VARADHARAJAN, MBA DEPT, VELS UNIVERSITY
Continuous variableContinuous variable
Can take any value in the given range of numbers
Can be measuredEx:
• Hb level• Height• Weight etc
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Dr.R.VARADHARAJAN, MBA DEPT, VELS UNIVERSITY