Statistics Introduction

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.


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”.


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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.


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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.


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.


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


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)


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.


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…


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.


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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.


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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


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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.


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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.


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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


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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.


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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


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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.,


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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.


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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


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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.


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Sources of secondary data:Sources of secondary data:

Published sources

Unpublished sources


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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.


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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.


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…)


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


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.,


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


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:


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


Quantitative ClassificationQuantitative Classification

The data are classified according to some characteristics that can be measured.

Such as height, weight, income, sales, profits, production, etc.,


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


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.


The Population may be Classified as The Population may be Classified as followsfollows


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.


Tabulation Contd…Tabulation Contd…

Parts of a table:• Table number• Title of the table• Caption stub• Stub• Body• Head notes • Footnotes


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Types of TablesTypes of Tables

Simple and complex tables.

General purpose and special purpose tables.


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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.


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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


Bar diagramBar diagram


Multiple Bar DiagramMultiple Bar Diagram

0

1

2

3

4

5

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2005 2006 2007 2008

Rice

Wheat

Maize


Sub Divided Bar DiagramSub Divided Bar Diagram


Percentage Bar DiagramPercentage Bar Diagram


Line ChartLine Chart


Pie DiagramPie Diagram


Scatter DiagramScatter Diagram


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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.


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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.


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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Education

Statistics Introduction