definition & scop unit-1

7/28/2019 Definition & Scop Unit-1

1/13

STATISTICSSTATISTICS

UNIT-1UNIT-1

INTRODUCTION OF STATISTICS AND ITS APPLICATIONINTRODUCTION OF STATISTICS AND ITS APPLICATION

IntroductionIntroduction : Statistics is a subject which is very much useful for decision making: Statistics is a subject which is very much useful for decision making

purpose in almost every field of life .The process of decision making ispurpose in almost every field of life .The process of decision making is

described in following diagram.described in following diagram.

Collection of data presenting data Analysis of dataTake decisionCollection of data presenting data Analysis of dataTake decision

Meaning of statistics:Meani

ng of statistics:

Origin and development of statistics :Origin and development of statistics :

The word statistics seems to have been derived from the Latin wordThe word statistics seems to have been derived from the Latin word

status or the Italion word statistia or the German word statistik . Each of thesestatus or the Italion word statistia or the German word statistik . Each of these

word means political state. In ancient times government used to called theword means political state. In ancient times government used to called the

information regarding the population, property of wealth of the country to have aninformation regarding the population, property of wealth of the country to have an

idea of the manpower of the country and to provide bases for introducing new taxes.idea of the manpower of the country and to provide bases for introducing new taxes.

Definitions of statistics:Definitions of statistics:

Statistics has been defined differently by different authors from time toStatistics has been defined differently by different authors from time to

time . Statistics is mostly defined in two ways.time . Statistics is mostly defined in two ways.

1. Statistics as data (plural sense) : i.e numerical statement of facts.:- More1. Statistics as data (plural sense) : i.e numerical statement of facts.:- More exhaustive definition is given byexhaustive definition is given by Prof. Horce SecristProf. Horce Secrist . He has define statistics as. He has define statistics as

By statistics we mean aggregate of facts affected to a marked extent byBy statistics we mean aggregate of facts affected to a marked extent by

multiplicity of causes , numerically expressed , enumerated or estimatedmultiplicity of causes , numerically expressed , enumerated or estimated

according to reasonable standards of accuracy, collected in systematic manneraccording to reasonable standards of accuracy, collected in systematic manner

for a predetermined purpose and placed in relation to each other.for a predetermined purpose and placed in relation to each other.

Thus in plural sense, statistics refers to facts which are expressed inThus in plural sense, statistics refers to facts which are expressed in

figures or simply data e.g Statistics of production, Statistics of unemployment ,figures or simply data e.g Statistics of production, Statistics of unemployment ,

Statistics of national income , figure related to population , figure related toStatistics of national income , figure related to population , figure related to

production of wheat in India in different year.production of wheat in India in different year.

2. Statistics as statistical method (singular sense) i.e principles and techniques used2. Statistics as statistical method (singular sense) i.e principles and techniques used

in collecting and analysing such data.:- Adequate definition is given byin collecting and analysing such data.:- Adequate definition is given by CroxtonCroxton

and Cowdenand Cowden . According to them statistics defined as . According to them statistics defined as The science which dealsThe science which deals

with the collection, analysis and interpretation of numerical datawith the collection, analysis and interpretation of numerical data

Thus in singular sense statistics refers to processing techniques which areThus in singular sense statistics refers to processing techniques which are

applied on raw data to get information e.g percentages , averages andapplied on raw data to get information e.g percentages , averages and

coefficient denied from numerical facts are included in the term statistics incoefficient denied from numerical facts are included in the term statistics in

singular sense.singular sense.

Functions of statistics:Functions of statistics:

Important functions of statistics are;Important functions of statistics are;

1.1. To present the facts in proper form. : One of the most important function ofTo present the facts in proper form. : One of the most important function of

statistics is to present general statements in a precise and definite form.statistics is to present general statements in a precise and definite form.

2.2. To simplify unwieldy and complex data and to make them easily understandable. :To simplify unwieldy and complex data and to make them easily understandable. :

The raw data is often unwieldy and complex. The purpose of statistical methods isThe raw data is often unwieldy and complex. The purpose of statistical methods is

to simplify large bodies of numerical data to make them more intelligible.to simplify large bodies of numerical data to make them more intelligible.

3.3. To help classification of data : Classification is a process of arrangement ofTo help classification of data : Classification is a process of arrangement of

numerical data according to various characteristics possessed by the data.numerical data according to various characteristics possessed by the data.

Classification facilitates comparison and interpretation .Classification facilitates comparison and interpretation .

11


2/13

4.4. To provide techniques for making comparisons: The chief object of statistics is toTo provide techniques for making comparisons: The chief object of statistics is to

facilitate a comparative study of various phenomena. The significance of certainfacilitate a comparative study of various phenomena. The significance of certain

figures can be appreciated when they are compared with others for the same type.figures can be appreciated when they are compared with others for the same type.

5.5. To enlarge individual experience.To enlarge individual experience.

6.6. To formulate policies in different fields.To formulate policies in different fields.

7.7. To study the relationships between different phenomena: Certain statisticalTo study the relationships between different phenomena: Certain statistical

measures such as coefficient of correlation , coefficient of association , regression ,measures such as coefficient of correlation , coefficient of association , regression ,

etc., establish relationship between different types of data.etc., establish relationship between different types of data.

8.8. To indicate trend behaviour : The statistical techniques for extrapolation, time seriesTo indicate trend behaviour : The statistical techniques for extrapolation, time series

and forecasting are highly useful for estimating future events.and forecasting are highly useful for estimating future events.

9.9. To measure uncertainty: Statistical technique called probability is used to ascertainTo measure uncertainty: Statistical technique called probability is used to ascertain

the chance of the occurrence of an event.the chance of the occurrence of an event.

10.10.To test the hypothesis : Statistical methods are extremely used in formulating andTo test the hypothesis : Statistical methods are extremely used in formulating and

testing hypothesis and to develop new theories.testing hypothesis and to develop new theories.

11.11.To draw valid inferences. : Statistical tests are devised to help in drawing validTo draw valid inferences. : Statistical tests are devised to help in drawing valid

inference in regard to the nature and characteristics of the universe on the basis ofinference in regard to the nature and characteristics of the universe on the basis ofthe sample.the sample.

Specific uses of statistics:

Specific uses of statistics:

In Economics :-In Economics :-

The uses of statistical methods in economics can be examinedThe uses of statistical methods in economics can be examined

under some broad heads:under some broad heads:

1.1. Formulation of Economic Laws : The inductive method of generalization isFormulation of Economic Laws : The inductive method of generalization is

based on the observation of economic behaviour of a large number of units . Forbased on the observation of economic behaviour of a large number of units . Forexample, Engels law of consumption was based on the study of family budgetexample, Engels law of consumption was based on the study of family budget

in a town , The Revealed Preference Analysis of Prof. Samuelson is based onin a town , The Revealed Preference Analysis of Prof. Samuelson is based on

actual observation of the behaviour of buyers in the market.actual observation of the behaviour of buyers in the market.

2.2. Study of Economic Problems : Statistical data and methods are used in theStudy of Economic Problems : Statistical data and methods are used in the

proper understanding of economic problems like volume of trade, output ofproper understanding of economic problems like volume of trade, output of

industries, wages, prices, bank deposits , unemployment , disparities in theindustries, wages, prices, bank deposits , unemployment , disparities in the

distribution of income and wealth. Financial Statistics is extensively used in thedistribution of income and wealth. Financial Statistics is extensively used in the

fields of money and banking, credit , consumer finance and public finance.fields of money and banking, credit , consumer finance and public finance.

3.3. Compilation of National Income Accounts : The data is systematically collectedCompilation of National Income Accounts : The data is systematically collected

and classified into certain functional areas , geographical regions sector of theand classified into certain functional areas , geographical regions sector of the economy so as to reveal the state of economy , the degree and the direction ofeconomy so as to reveal the state of economy , the degree and the direction of

change and relation between them on a continuing basis.change and relation between them on a continuing basis.

4.4. Economic planning : Employment statistics in our country are still incompleteEconomic planning : Employment statistics in our country are still incomplete

and unreliable. The information on the past period is collected and used forand unreliable. The information on the past period is collected and used for

projections into the future. Forecasting techniques are used for this purpose.projections into the future. Forecasting techniques are used for this purpose.

Econometric models based on statistical analysis are used for maximumEconometric models based on statistical analysis are used for maximum

exploitation of available resources.exploitation of available resources.

In business :-In business :-Statistical methods are widely used in business planning.Statistical methods are widely used in business planning.

1.1. Location and size decision : A decision on location from amongst variousLocation and size decision : A decision on location from amongst various

alternative places will depend on the collection and analysis of information onalternative places will depend on the collection and analysis of information on

the availability and cost of land , labour , raw materials etc..the availability and cost of land , labour , raw materials etc..

2.2. Study of demand : Statistical methods are extremely helpful in preparing trendStudy of demand : Statistical methods are extremely helpful in preparing trend

lines leading to reliable forecasting. For market survey and research , thelines leading to reliable forecasting. For market survey and research , the

correlation and regression analysis are there for judging the effectiveness ofcorrelation and regression analysis are there for judging the effectiveness of

various sales promotion measures. The study of time series helps in detectingvarious sales promotion measures. The study of time series helps in detecting

cyclical and seasonal behaviour of demand and making the sales forecasts morecyclical and seasonal behaviour of demand and making the sales forecasts more

meaningful.meaningful.

22


3/13

3.3. production Planning : In order to avoid unnecessary loss the productionproduction Planning : In order to avoid unnecessary loss the production

schedule has to be related with sales forecasts. The raw material procurementschedule has to be related with sales forecasts. The raw material procurement

and stocking has also to be related to the production plan . Statistical methodsand stocking has also to be related to the production plan . Statistical methods

facilitate to calculate the most economic levels of ordering material. Graphicfacilitate to calculate the most economic levels of ordering material. Graphic

devices can be used for displaying sales, production and the supply of materialdevices can be used for displaying sales, production and the supply of material

on a time scale .on a time scale .

4.4. Quality control : The quality of a product can also be judged by statisticalQuality control : The quality of a product can also be judged by statistical

methods . There are two broad types of control : (i) Process control (ii) Productmethods . There are two broad types of control : (i) Process control (ii) Product

control . Under the process control it is ensured that the whole productioncontrol . Under the process control it is ensured that the whole production

process is under control. Under the product control the additional question isprocess is under control. Under the product control the additional question is

ask whether the entire lot from which the sample has been drawn is to beask whether the entire lot from which the sample has been drawn is to be

accepted or rejected.accepted or rejected.

5.5. Marketing decision: These decisions are related to the sales of the products .Marketing decision: These decisions are related to the sales of the products .

The sales of products by markets have to be tabulated chronologically or inThe sales of products by markets have to be tabulated chronologically or in

time order.time order.

6.6. Planning Future Operations : Capital investment in plant and equipmentPlanning Future Operations : Capital investment in plant and equipmentrequired long-term forecast about sales , prices, material costs, etc.required long-term forecast about sales , prices, material costs, etc.

7.7. Inventory Control : It helps in coordinating production on one hand and salesInventory Control : It helps in coordinating production on one hand and sales

on the other.on the other.

8.8. Personal Administration : An important use of statistics is in testing thePersonal Administration : An important use of statistics is in testing the

usefulness of a person to the business in items of his interest , aptitude andusefulness of a person to the business in items of his interest , aptitude and

capacity to work.capacity to work.

9.9. Accounts and Auditing.: The use of statistics in accounting and auditing can beAccounts and Auditing.: The use of statistics in accounting and auditing can be

appreciated better in the context of the nature of accounting records. Accountingappreciated better in the context of the nature of accounting records. Accounting

information are very precise ,it is exact to the last paisa . But for decisioninformation are very precise ,it is exact to the last paisa . But for decision

making purpose such precision is not necessary and hence the statisticalmaking purpose such precision is not necessary and hence the statistical

approximations are sought.approximations are sought.

10.10. Operation Research : The common O.R problems are connected with decisionsOperation Research : The common O.R problems are connected with decisions

on transportation, profit maximization , cost minimization , optimum inventoryon transportation, profit maximization , cost minimization , optimum inventory

level, etc. The theory of probability , expected value, theoretical distributions,level, etc. The theory of probability , expected value, theoretical distributions,

Other techniques of drawing inference , Linear programming , Game theory,Other techniques of drawing inference , Linear programming , Game theory,

Critical path method (CPM), programme Evaluation and Review TechniquesCritical path method (CPM), programme Evaluation and Review Techniques

(PERT) are used in working out the problems.(PERT) are used in working out the problems.

Limitations of statistics:Limitations of statistics:

The following are some important limitations of statistics :The following are some important limitations of statistics :

1.1. Statistics does not study individual events.: It deals with the aggregate of facts andStatistics does not study individual events.: It deals with the aggregate of facts and

does not give any specific recognition to individual item of the series. Individualdoes not give any specific recognition to individual item of the series. Individual

items, taken separately, does not constitute statistical data and are meaningless foritems, taken separately, does not constitute statistical data and are meaningless for

any statistical inquiry.any statistical inquiry.

2.2. Statistics does not study qualitative phenomenon: Qualitative phenomena likeStatistics does not study qualitative phenomenon: Qualitative phenomena like

honesty , poverty , wisdom, etc which cannot be expressed numerically , are nothonesty , poverty , wisdom, etc which cannot be expressed numerically , are not

capable for direct statistical analysis.capable for direct statistical analysis.

3.3. Statistical results are true only on an average. Sometimes the average or trendStatistical results are true only on an average. Sometimes the average or trend

indicated by statistics is applied on individual cases which is not proper.indicated by statistics is applied on individual cases which is not proper.

4.4. Statistical laws are not exact. On the basis of statistical analysis of the problem , oneStatistical laws are not exact. On the basis of statistical analysis of the problem , one

can talk only in terms of probability and not certainty.can talk only in terms of probability and not certainty.

5.5. Statistics does not reveal the entire story. The real background of the data may notStatistics does not reveal the entire story. The real background of the data may not

be reflected in certain quantitative facts.be reflected in certain quantitative facts.

6.6. Statistical relation do not necessarily bring out the cause and effect relationshipStatistical relation do not necessarily bring out the cause and effect relationship

between phenomena.between phenomena.

7.7. Statistics is collected with a given purpose and cannot be indiscriminately appliedStatistics is collected with a given purpose and cannot be indiscriminately applied

to any situation.to any situation.

33


4/13

8.8. Statistics is liable to be misused..: the use of statistical tools by inexperienced andStatistics is liable to be misused..: the use of statistical tools by inexperienced and

untrained persons might lead to very fallacious conclusions.untrained persons might lead to very fallacious conclusions.

Characteristics of statistical dataCharacteristics of statistical data

1. They should be aggregate of facts:- It means that the single fact , even though1. They should be aggregate of facts:- It means that the single fact , even though

numerically stated, can not be called statistics. A group idea is always involved innumerically stated, can not be called statistics. A group idea is always involved in

all statistical study to have comparative idea. e.g if it is states that the monthlyall statistical study to have comparative idea. e.g if it is states that the monthly

expenditure of family A is Rs. 1000/- this is not statistics . A single figure does notexpenditure of family A is Rs. 1000/- this is not statistics . A single figure does not

say anything . If we also say that monthly expenditure of family B is Rs. 1500/- .say anything . If we also say that monthly expenditure of family B is Rs. 1500/- .

Now this figures can be compared with family A. So these will be known asNow this figures can be compared with family A. So these will be known as

statistics. Similarly a single figure of production , sale purchase , import, export,statistics. Similarly a single figure of production , sale purchase , import, export,

birth, death, accident etc., can not be regarded as statistics but aggregate of suchbirth, death, accident etc., can not be regarded as statistics but aggregate of such

figure will be called statistics.figure will be called statistics.

2. They should be numerically expressed :- This means that the facts to be called2. They should be numerically expressed :- This means that the facts to be called

statistics must be expressed in numbers. Qualitative words like good , average poor,statistics must be expressed in numbers. Qualitative words like good , average poor, fair, young, bad, beauty etc., can not be called statistics unless a numerical value isfair, young, bad, beauty etc., can not be called statistics unless a numerical value is

assign to each such words, e.g good ,average and poor students areassign to each such words, e.g good ,average and poor students are

qualitative expressions and so they are not statistics. But if we assign a numericalqualitative expressions and so they are not statistics. But if we assign a numerical

value to each such words as , students who gets marks above 60% are good ,studentvalue to each such words as , students who gets marks above 60% are good ,student

who got marks between 40% and 60% are average and student who got below 40%who got marks between 40% and 60% are average and student who got below 40%

are poor. Then they are called statistics.are poor. Then they are called statistics.

3. They should be collected in systematic manner :- The data must be collected in3. They should be collected in systematic manner :- The data must be collected in

systematic manner according to a well prepared plan. If the data are collected in asystematic manner according to a well prepared plan. If the data are collected in a

wrong manner they cannot be called statistics. In such case there will be waste ofwrong manner they cannot be called statistics. In such case there will be waste of

time , energy and money.time , energy and money.

4. They should be placed in relation to each other.:- It means that they should be4. They should be placed in relation to each other.:- It means that they should be

comparable . If comparison is not possible , figures cannot be called statistics e.gcomparable . If comparison is not possible , figures cannot be called statistics e.g

the population of in India 1971 may be compared with the population of otherthe population of in India 1971 may be compared with the population of other

countries like China, UK of 1971. But it would be meaningless to compare thecountries like China, UK of 1971. But it would be meaningless to compare the

height of person with the height of tree.height of person with the height of tree.

5. They should be collected for a predetermined purpose.:- The purpose of the inquiry5. They should be collected for a predetermined purpose.:- The purpose of the inquiry

should be stated clearly before actually going for data collection.should be stated clearly before actually going for data collection.

6. They should be affected to a marked extent by multiplicity of causes:- Statistics are6. They should be affected to a marked extent by multiplicity of causes:- Statistics are

affected to a marked extent by large number of causes e.g. Statistics of prices areaffected to a marked extent by large number of causes e.g. Statistics of prices are affected by condition of demand , supply , import, export , currency in circulationaffected by condition of demand , supply , import, export , currency in circulation

etc., Similarly statistics of production of crop are affected by a number of factorsetc., Similarly statistics of production of crop are affected by a number of factors

like rainfall, quality of soil , seeds and fertilizers , method of cultivation etc..like rainfall, quality of soil , seeds and fertilizers , method of cultivation etc..

7. They should be enumerated or estimated according to reasonable standard of7. They should be enumerated or estimated according to reasonable standard of

accuracy.:- This means margin of error must be minimum. A reasonable standard ofaccuracy.:- This means margin of error must be minimum. A reasonable standard of

accuracy must be maintain in collection of statistical data. e.g An estimate that oneaccuracy must be maintain in collection of statistical data. e.g An estimate that one

lakh people attended Lal Krishna Advani election meeting does not mean exactlylakh people attended Lal Krishna Advani election meeting does not mean exactly

one lakh , it may be few hundred less or more. But if we are counting 100 studentsone lakh , it may be few hundred less or more. But if we are counting 100 students

in a class , they must be 100.in a class , they must be 100.

Collection of Data :Collection of Data :

As point out earlier , Statistics are a set of numerical data. Also according to definitionAs point out earlier , Statistics are a set of numerical data. Also according to definition

of Statistics in singular sense to initialize any Statistical inquiry , the method of collectionof Statistics in singular sense to initialize any Statistical inquiry , the method of collection

of data forms foundation. Thus the raw material of Statistics always originates from theof data forms foundation. Thus the raw material of Statistics always originates from the

operation of counting or measurement of phenomena under study . The person whooperation of counting or measurement of phenomena under study . The person who

conduct the Statistical analysis is known as Respondents OR Informants . The processconduct the Statistical analysis is known as Respondents OR Informants . The process

44


5/13

of counting or enumeration or measurement together with the systematic recording ofof counting or enumeration or measurement together with the systematic recording of

results is called collection of Statistical Dataresults is called collection of Statistical Data

The collection of data refers to a purposive gathering of information relevant to theThe collection of data refers to a purposive gathering of information relevant to the

subject matter of the study from the units under investigation . the method of collectionsubject matter of the study from the units under investigation . the method of collection

of data depends mainly upon the nature , object and the scope of inquiry on the one handof data depends mainly upon the nature , object and the scope of inquiry on the one hand

and the availability of resources and the time on the other hand. Statistical data areand the availability of resources and the time on the other hand. Statistical data are

classified into primary and secondary depending upon the nature of data and mode ofclassified into primary and secondary depending upon the nature of data and mode of

collection.collection.

Primary Data : The data which are collected for the first time by/for thePrimary Data : The data which are collected for the first time by/for the

investigator for his purpose , is called primary data.investigator for his purpose , is called primary data.

Secondary Data : The data which had already been collected by someone else butSecondary Data : The data which had already been collected by someone else but

used by investigator for his purpose is known as secondary data.used by investigator for his purpose is known as secondary data.

Data from primary source are collected, for the first time , keeping in view theData from primary source are collected, for the first time , keeping in view the

objective of investigation. Secondary data , on the other hand , are available from certainobjective of investigation. Secondary data , on the other hand , are available from certain

publications or reports. The primary data collected with a specified objective ofpublications or reports. The primary data collected with a specified objective of

investigation , are likely to be more reliable as compared to secondary data, wheneverinvestigation , are likely to be more reliable as compared to secondary data, whenevernecessary , must be done very carefully. The cost of collection of primary data , however ,necessary , must be done very carefully. The cost of collection of primary data , however ,

is much higher.is much higher.

Distinction between Primary and Secondary Data.Distinction between Primary and Secondary Data.

Primary dataPrimary data Secondary dataSecondary data

1.1. The data which are collected forThe data which are collected for

the first time by/for thethe first time by/for the

investigator for his purpose, isinvestigator for his purpose, is

called primary data.called primary data.

1.1. The data which had alreadyThe data which had already

collected by someone else but usedcollected by someone else but used

by investigator for his purpose isby investigator for his purpose is

known as secondary data.known as secondary data.

2.2. The data collected by primaryThe data collected by primarysource is known as primary data.source is known as primary data.

2.2. The data collected by secondaryThe data collected by secondarysource is known as secondary data.source is known as secondary data.

3.3. The investigator himself collectsThe investigator himself collects

primary data: therefore they areprimary data: therefore they are

firsthand information.firsthand information.

3.3. Someone /some agency collectsSomeone /some agency collects

secondary data therefore they aresecondary data therefore they are

not firsthand information.not firsthand information.

4.4. An investigator isAn investigator is

directly/indirectly Collector as welldirectly/indirectly Collector as well

as User of primary dataas User of primary data

4.4. An investigator is just User ofAn investigator is just User of

secondary datasecondary data

5.5. Collection of data require moreCollection of data require more

time ,fund and men power ortime ,fund and men power or

labour.labour.

5.5. Collection of secondary dateCollection of secondary date

requires less time , fund and menrequires less time , fund and men

power or labour.power or labour.6.6. Since the primary data collected bySince the primary data collected by

/for investigator they are Quite/for investigator they are Quite

accurate ,reliable , suitable andaccurate ,reliable , suitable and

adequate for the purpose ofadequate for the purpose of

i

nquiry.inquiry.

6.6. One has to examine accuracy ,One has to examine accuracy ,

reliability , suitability andreliability , suitability and

adequency before directly using secadequency before directly using sec

Methods for collecting Primary data:Methods for collecting Primary data:

Primary data may be collected using following methodPrimary data may be collected using following method

1.1. Direct personal investigationDirect personal investigation2.2. Indirect oral investigationIndirect oral investigation

3.3. Information from correspondentsInformation from correspondents

4.4. Mail Questionnaire methodMail Questionnaire method

5.5. Questionnaire send through enumeratorsQuestionnaire send through enumerators

The technique of collecting data by various methods is explained belowThe technique of collecting data by various methods is explained below

1.1. Direct personal investigationDirect personal investigation

Under this method, the investigator collects data by having direct contact and face-Under this method, the investigator collects data by having direct contact and face-

to-face approach with all informants. This method is suitable for an intensive typeto-face approach with all informants. This method is suitable for an intensive type

of investigation whereof investigation where

55


6/13

(i)(i) The scope of investigation is narrowThe scope of investigation is narrow

(ii)(ii) The process of investigation requires Personal attention of the investigatorThe process of investigation requires Personal attention of the investigator

(iii)(iii) The investigation is confidentialThe investigation is confidential

(iv)(iv) More emphasis is to be given to the accuracy of the dataMore emphasis is to be given to the accuracy of the data

Under this method , the data may be collected by adopting any of the following twoUnder this method , the data may be collected by adopting any of the following two

ways.ways.

(a)(a)Interview: In this method the investigator has to contact the informants fromInterview: In this method the investigator has to contact the informants from

whom the information is to be obtained directly and personally . He putswhom the information is to be obtained directly and personally . He puts

questions before them regarding the inquiry and collect the required information.questions before them regarding the inquiry and collect the required information.

The answers supplied by an informant will result in a primary data.The answers supplied by an informant will result in a primary data.

(b)(b) Observation : According to this method the investigator obtains the data byObservation : According to this method the investigator obtains the data by

observing the reaction supplied by an informant as a result of treatment /actionobserving the reaction supplied by an informant as a result of treatment /action

performed by an investigator on person under study. He asks no questions, butperformed by an investigator on person under study. He asks no questions, but

just observes the reactions in which he is interested. Observation method isjust observes the reactions in which he is interested. Observation method is

particularly helpful in studying the behaviour of children , tribal, Dumb and Deafparticularly helpful in studying the behaviour of children , tribal, Dumb and Deaf

persons and even women, because direct oral interview in their cases will notpersons and even women, because direct oral interview in their cases will notreceive proper responses. This is very useful method in certain marketing studiesreceive proper responses. This is very useful method in certain marketing studies

where consumer behaviour is studied. For example , if a woman is asked whetherwhere consumer behaviour is studied. For example , if a woman is asked whether

she prefers traditional pattern of garment or modern once, she might express hershe prefers traditional pattern of garment or modern once, she might express her

liking for the traditional ones, but when both types of garments are placed beforeliking for the traditional ones, but when both types of garments are placed before

her, she may actually go for the modern ones.her, she may actually go for the modern ones.

2. Indirect oral investigation :2. Indirect oral investigation :

This method is generally used in those cases where the information required is ofThis method is generally used in those cases where the information required is of

a complex nature and the informants are not willing to respond, if approacheda complex nature and the informants are not willing to respond, if approached

directly. Here the investigator instead of directly approaching to the informants,directly. Here the investigator instead of directly approaching to the informants,

contacts third parties known as witness capable of supplying the necessarycontacts third parties known as witness capable of supplying the necessary

information. Witnesses are assumed to have knowledge of required informationinformation. Witnesses are assumed to have knowledge of required information

about an actual informant.about an actual informant.

To assess reliability and accuracy of the answer provided by the witness , severalTo assess reliability and accuracy of the answer provided by the witness , several

witnesses have to be approached for single informant. Whereas on the otherwitnesses have to be approached for single informant. Whereas on the other

hand ,some times single witness may give information about more number ofhand ,some times single witness may give information about more number of

informants also.informants also.

Police department for clues about the thieves and murders uses this procedure byPolice department for clues about the thieves and murders uses this procedure by

interrogating friends or relative or third parties capable of supplying theinterrogating friends or relative or third parties capable of supplying the

necessary information.necessary information.3. Information from correspondents :3. Information from correspondents :

Under this method of data collection , investigator does not collect theUnder this method of data collection , investigator does not collect the

information himself from the person concerned directly . Investigator willinformation himself from the person concerned directly . Investigator will

appoint Local agents known as correspondents in different places of the areaappoint Local agents known as correspondents in different places of the area

under investigation to collect the necessary information from their allottedunder investigation to collect the necessary information from their allotted

territory as and when required. They will then transmit the collected informationterritory as and when required. They will then transmit the collected information

to the main investigator /central office /head quarter where the information areto the main investigator /central office /head quarter where the information are

processed and primary data are generated.processed and primary data are generated.

This method is more useful when an investigator requires information at regularThis method is more useful when an investigator requires information at regular

interval of time and degree of accuracy is of secondary importance.interval of time and degree of accuracy is of secondary importance.

News papers and magazine agencies , News broadcasting agencies generallyNews papers and magazine agencies , News broadcasting agencies generally

adopt this method .for example , in the construction of wholesale price indexadopt this method .for example , in the construction of wholesale price index

number, regular information is obtained from correspondents appointed innumber, regular information is obtained from correspondents appointed in

different areas.different areas.

4. Mailed Questionnaire method :4. Mailed Questionnaire method :

According to this method an investigator will formulate list of questions , whichAccording to this method an investigator will formulate list of questions , which

are directly or indirectly related with the purpose of inquiry . This list ofare directly or indirectly related with the purpose of inquiry . This list of

questions either in printed / nicely written form with suitable options andquestions either in printed / nicely written form with suitable options and

sufficient spaces to answer is called Questionnaire. A questionnaire includingsufficient spaces to answer is called Questionnaire. A questionnaire including covering letters and self addressed stamped envelope will then sent to variouscovering letters and self addressed stamped envelope will then sent to various

66


7/13

informants through post/mailing service . In the method investigator collect theinformants through post/mailing service . In the method investigator collect the

information through the filling of questionnaires by the respondents. Coveringinformation through the filling of questionnaires by the respondents. Covering

letter states,letter states,

The purpose of inquiryThe purpose of inquiry

Method ,format and understanding , if required for answering questions,Method ,format and understanding , if required for answering questions,

Request to an informant regarding sending filled questionnaire in all respectRequest to an informant regarding sending filled questionnaire in all respect duly back on or before deadlineduly back on or before deadline

A word of thanks for extending co-operation towards participatingA word of thanks for extending co-operation towards participating

information .information .

A self addressed and stamped envelope is also enclosed for informantsA self addressed and stamped envelope is also enclosed for informants

convenience in returning the filled questionnaire.convenience in returning the filled questionnaire.

After receiving required number of responses , processing the answers,After receiving required number of responses , processing the answers,

investigator will get a primary data.investigator will get a primary data.

5. Questionnaire sent through enumerator5. Questionnaire sent through enumerator

The basic difference between Questionnaire and schedules is , questions in theThe basic difference between Questionnaire and schedules is , questions in the

Questionnaire is answered by informant himself in his/her own handwritingQuestionnaire is answered by informant himself in his/her own handwriting

while schedule is the device of obtaining answers to the questions in a form filledwhile schedule is the device of obtaining answers to the questions in a form filled

by interviewer. According to this method an investigator will formulate list ofby interviewer. According to this method an investigator will formulate list of

questions , which are directly or indirectly related with the purpose of inquiry .questions , which are directly or indirectly related with the purpose of inquiry .

An investigator will then select a team of require number of enumerators .An investigator will then select a team of require number of enumerators .

Enumerators are provided training Aabout purpose of inquiry , method andEnumerators are provided training Aabout purpose of inquiry , method and

format of furnishing answers given by informants , tactful way of checkingformat of furnishing answers given by informants , tactful way of checking

accuracy and reliability of information on the spot by asking different additionalaccuracy and reliability of information on the spot by asking different additional

questions , collecting supplementary information etc. Enumerators are thenquestions , collecting supplementary information etc. Enumerators are then

provided with standardized schedules or questionnaires and specific instructionsprovided with standardized schedules or questionnaires and specific instructionsare given to them regarding the manner in which schedules are to be filled.are given to them regarding the manner in which schedules are to be filled.

The enumerators explain clearly the object of the enquiry, the definitions of basicThe enumerators explain clearly the object of the enquiry, the definitions of basic

concept to the information and record response themselves in the questionnaireconcept to the information and record response themselves in the questionnaire

forms. An enumerator will hand over filled schedules to an investigator once theyforms. An enumerator will hand over filled schedules to an investigator once they

finish up their allotted task. After receiving responses , processing the answers,finish up their allotted task. After receiving responses , processing the answers,

investigator will get a primary data.investigator will get a primary data.

Sources of secondary data:Sources of secondary data:

The chief sources of secondary data may be broadly classified into the followingThe chief sources of secondary data may be broadly classified into the following groups.(i) Published sources (ii) Unpublished sources.groups.(i) Published sources (ii) Unpublished sources.

(i) Published sources: There are number of national organizations and also(i) Published sources: There are number of national organizations and also

international agencies which collect statistical data relating to business, trade,international agencies which collect statistical data relating to business, trade,

labour, consumptions , productions , industries, agriculture, income, currency andlabour, consumptions , productions , industries, agriculture, income, currency and

exchange , health, populations and number of socio-economic phenomena andexchange , health, populations and number of socio-economic phenomena and

published their findings in statistical reports on a regular basis. Below are the briefpublished their findings in statistical reports on a regular basis. Below are the brief

summary of these sources.summary of these sources.

(a)(a)Official publications of Central government :Official publications of Central government :

(1)(1) Office of the Registrar General and Census Commissioner of India, New DelhiOffice of the Registrar General and Census Commissioner of India, New Delhi(2)(2) Directorate-General of Commercial Intelligence and Statistics-Ministry ofDirectorate-General of Commercial Intelligence and Statistics-Ministry of

Commerce.Commerce.

(3)(3) Labour Bureau-Ministry of LabourLabour Bureau-Ministry of Labour

(4)(4) Directorate of Economics and Statistics-ministry of Agriculture and IrrigationDirectorate of Economics and Statistics-ministry of Agriculture and Irrigation

(5)(5) The Indian Army Statistical Organization (I.A.S.O.)-Ministry of DefenseThe Indian Army Statistical Organization (I.A.S.O.)-Ministry of Defense

(6)(6) National Sample Survey Organization (N.S.S.O.), Department of Statistics,National Sample Survey Organization (N.S.S.O.), Department of Statistics,

Ministry of PlanningMinistry of Planning

(7)(7) Central Statistical Organization (C.S.O.) Department of statistics ,Ministry ofCentral Statistical Organization (C.S.O.) Department of statistics ,Ministry of

PlanningPlanning

77


8/13

(8)(8) Census data in various census reports Vital statistics of Indian , IndianCensus data in various census reports Vital statistics of Indian , Indian

Population Bulletin- all published by Registrar- General of India ( R.G.I.)Population Bulletin- all published by Registrar- General of India ( R.G.I.)

(9)(9) In addition to the above organizations a number of department in the state andIn addition to the above organizations a number of department in the state and

Central governments like Income Tax, Department , Directorate general ofCentral governments like Income Tax, Department , Directorate general of

Supplies and Disposals, Railway, Post and Telegraphs, Central Board ofSupplies and Disposals, Railway, Post and Telegraphs, Central Board of

Revenues, Textile Commissioners office , Central Excise commissionersRevenues, Textile Commissioners office , Central Excise commissioners

Office, Iron and Steel Controllers office and so on publish statistical reports onOffice, Iron and Steel Controllers office and so on publish statistical reports on

current problems.current problems.

(b)Publications of Semi-government Statistical Organizations(b)Publications of Semi-government Statistical Organizations

(1)(1) Statistics department of the reserve Bank of India (Mumbai), which bringsStatistics department of the reserve Bank of India (Mumbai), which brings

out an Annual Report of Bank, currency and Finance.out an Annual Report of Bank, currency and Finance.

(2)(2) Economic department of Reserve Bank of India.Economic department of Reserve Bank of India.

(3)(3) The institute of Economic Growth, Delhi.The institute of Economic Growth, Delhi.

(4)(4) Gokhale Institute of Politics and Economics, Poona.Gokhale Institute of Politics and Economics, Poona.

(5)(5) The Institute of Foreign Trade , New Delhi.The Institute of Foreign Trade , New Delhi.

(6)(6) The statistical material published by the institute like Municipal and DistrictThe statistical material published by the institute like Municipal and District Boards, Corporations, Block and Panchayat Samitis on Vital Statistics ,Boards, Corporations, Block and Panchayat Samitis on Vital Statistics ,

health, sanitation and other related subjects provides a fairly reliable andhealth, sanitation and other related subjects provides a fairly reliable and

useful information.useful information.

(b)(b) Publications of Research Institutions.Publications of Research Institutions.

Individual research scholars , the different departments in the variousIndividual research scholars , the different departments in the various

universities of India published their findings inuniversities of India published their findings in

Indian Statistical Institute ( I.S.I ) , Kolkata and Delhi ;Indian Statistical Institute ( I.S.I ) , Kolkata and Delhi ;

Indian Council of Agricultural Research ( I.C.A.R.) , New DelhiIndian Council of Agricultural Research ( I.C.A.R.) , New Delhi

Indian Agricultural Statistics research Institute (I.A.S.R.I), New Delhi;Indian Agricultural Statistics research Institute (I.A.S.R.I), New Delhi;

National Council of Educational Research and Training (N.C.E.R.T),NewNational Council of Educational Research and Training (N.C.E.R.T),New

DelhiDelhi

National Council of Applied Economic research, New Delhi ;National Council of Applied Economic research, New Delhi ;

The institute of Applied Man Power Research , New Delhi ;The institute of Applied Man Power Research , New Delhi ;

The Institute of Labour Research ,Mumbai ;The Institute of Labour Research ,Mumbai ;

Indian Standards Institute, New DelhiIndian Standards Institute, New Delhi

(c) Publications of Commercial and Financial Institutions.(c) Publications of Commercial and Financial Institutions.

Federation of Indian Chamber of Commerce and Industries (FICCI) ;Federation of Indian Chamber of Commerce and Industries (FICCI) ;

Institute of Chartered Accountants of India, Trade Unions , Stock Exchanges,Institute of Chartered Accountants of India, Trade Unions , Stock Exchanges,

Bank Bodies , Co-Operative Societies , etc. publish reports and statisticalBank Bodies , Co-Operative Societies , etc. publish reports and statisticalmaterial on current economic, business and other phenomena.material on current economic, business and other phenomena.

(d) Reports of various Committees and Commissions appointed by the government.(d) Reports of various Committees and Commissions appointed by the government.

(e)(e) Newspapers and Periodicals;Newspapers and Periodicals;

(f)(f) International Publications;International Publications;

United Nations Organizations (U.N.O.)United Nations Organizations (U.N.O.)

World Health Organization (W.H.O) on contagious diseasesWorld Health Organization (W.H.O) on contagious diseases

Annual report of International Labour Organization (I.L.O)Annual report of International Labour Organization (I.L.O)

International Memory fund (I.M.F.)International Memory fund (I.M.F.)

World Bank ; Economic and Social Commission for Asia and pacific (ESCAP)World Bank ; Economic and Social Commission for Asia and pacific (ESCAP)

International Finance Corporation (I.F.C.) ;International Finance Corporation (I.F.C.) ;

International Statistical Education Institute ; are very valued publications ofInternational Statistical Education Institute ; are very valued publications of

secondary data.secondary data.

(ii)(ii) Unpublished source : The statistical data need not be always published. There areUnpublished source : The statistical data need not be always published. There are

various sources of unpublished statistical material such as the records maintainedvarious sources of unpublished statistical material such as the records maintained

by private firms or business enterprise who may not like to release their data toby private firms or business enterprise who may not like to release their data to

any outside agencies ; the various department and office of the Central and Stateany outside agencies ; the various department and office of the Central and State

governments; the research carried out by the individual research scholars in thegovernments; the research carried out by the individual research scholars in the

universities or research institutes.universities or research institutes.

88


9/13

ClassificationClassification

Definition :Definition :

Before Tabulating the data , generally ,systematic arrangement of the raw data intoBefore Tabulating the data , generally ,systematic arrangement of the raw data into

different homogenous classes is necessary. This process of arranging the data intodifferent homogenous classes is necessary. This process of arranging the data into

groups or classes according to similarities is technically called classification.groups or classes according to similarities is technically called classification.Secrist has defined Classification as Secrist has defined Classification as Classification is the process of arranging dataClassification is the process of arranging data

into sequence and groups according to their common characteristics , orinto sequence and groups according to their common characteristics , or

separating them into different but related parts.separating them into different but related parts.

Tuttle has defined classification as Tuttle has defined classification as A classification is a scheme for breaking a categoryA classification is a scheme for breaking a category

into a set of parts, called classes, according to some precisely defined differinginto a set of parts, called classes, according to some precisely defined differing

characteristics possessed by all the elements of the category.characteristics possessed by all the elements of the category.

Functions of classification :Functions of classification :

The functions of classification may be briefly summarized as follows:The functions of classification may be briefly summarized as follows:1.1. It condenses the data.It condenses the data.

2.2. It facilitates comparisons.It facilitates comparisons.

3.3. It help to study relationship.It help to study relationship.

4.4. It facilitate the statistical treatment of the data.It facilitate the statistical treatment of the data.

Rules for Classification:Rules for Classification:

No hard and fast rules can be laid down for classification , but the following generalNo hard and fast rules can be laid down for classification , but the following general

guiding principles may be observed for good classification:guiding principles may be observed for good classification:

1.1. It should be unambiguous : The classes should be rigidly defined so that they shouldIt should be unambiguous : The classes should be rigidly defined so that they should

not lead to any ambiguity.not lead to any ambiguity.2.2. It should be Exhaustive and mutually exclusive.: The classes must be exhaustive inIt should be Exhaustive and mutually exclusive.: The classes must be exhaustive in

the sense that each and every item in the data must be belong to one of the classes.the sense that each and every item in the data must be belong to one of the classes.

The various classes should be mutually disjoint or non-overlapping so that anThe various classes should be mutually disjoint or non-overlapping so that an

observed value belongs to one and only one classes.observed value belongs to one and only one classes.

3.3. It should be stable : In order to have meaningful comparison of the results, an idealIt should be stable : In order to have meaningful comparison of the results, an ideal

classification must be stable i.e , the same pattern of classification should be adoptedclassification must be stable i.e , the same pattern of classification should be adopted

throughout the analysis and also for the further inquiries on the same subject.throughout the analysis and also for the further inquiries on the same subject.

4.4. It should be suitable for purpose: The classification must be in keeping with theIt should be suitable for purpose: The classification must be in keeping with the

objective of the enquiry.objective of the enquiry.5.5. It should be flexible.: A good classification should be flexible in that it should beIt should be flexible.: A good classification should be flexible in that it should be

adjustable to the new and changed situations and conditions. However, flexibilityadjustable to the new and changed situations and conditions. However, flexibility

should not be interpreted as instability of classification.should not be interpreted as instability of classification.

Base of Classification ;Base of Classification ;

The bases or the criteria w.r.t which the data are classified depend on the objectives andThe bases or the criteria w.r.t which the data are classified depend on the objectives and

purpose of the enquiry. The data can be classified on the following four basespurpose of the enquiry. The data can be classified on the following four bases

1.1. geographical i.e area-wise or regionalgeographical i.e area-wise or regional

2.2. Chronological i.e w.r.t occurrence of timeChronological i.e w.r.t occurrence of time

3.3. Qualitative i.e w.r.t some character or attribute.Qualitative i.e w.r.t some character or attribute.

4.4. Quantitative i.e w.r.t numerical values or magnitudesQuantitative i.e w.r.t numerical values or magnitudes

1.1. Geographical classification : As the name suggests , in this classification the basis ofGeographical classification : As the name suggests , in this classification the basis of

classification is the geographical or locational difference between the various itemsclassification is the geographical or locational difference between the various items

in the data like States, Regions, Zones , Areas, etc.Geographical classification arein the data like States, Regions, Zones , Areas, etc.Geographical classification are

usually presented either in an alphabetical order or according to size or values to layusually presented either in an alphabetical order or according to size or values to lay

more emphasis on the important are or region. For example , the yield of agriculturalmore emphasis on the important are or region. For example , the yield of agricultural

output per hectare for different countries in some given period is given in theoutput per hectare for different countries in some given period is given in the

following table.following table.

99


10/13

Table 1Table 1

AGRICULTURAL OUTPUTAGRICULTURAL OUTPUT

OF DIFFERENT COUNTRIESOF DIFFERENT COUNTRIES

(in Kg. Per Hectare)(in Kg. Per Hectare)

CountryCountry Average outputAverage output

IndiaIndia 123.7123.7

USAUSA 581.0581.0

PakistanPakistan 257.5257.5

USSRUSSR 733.5733.5

ChinaChina 269.2269.2

SyriaSyria 615.2615.2

SudanSudan 339.8339.8

UARUAR 747.5747.5 Source: Yojana: vol.XV, N0. 18, !9Source: Yojana: vol.XV, N0. 18, !9thth Sept, page 22,Sept, page 22,

2. Chronological Classification: Chronological classification is one in which the data are2. Chronological Classification: Chronological classification is one in which the data areclassified on the basis of difference in time . The time series data, which areclassified on the basis of difference in time . The time series data, which are

quite frequent in Economic and Business Statistics are generally classifiedquite frequent in Economic and Business Statistics are generally classified

chronologically, usually starting with the first period of occurrence. Forchronologically, usually starting with the first period of occurrence. For

example, the population of certain country for different yearsexample, the population of certain country for different years

Table 2Table 2

POPULATION OF INDIA (in crores)POPULATION OF INDIA (in crores)

YearYear PopulationPopulation

19011901 23.823.8

19111911 25.025.0

19211921 25.225.2

19311931 27.927.9

19411941 31.931.9

19511951 36.136.1

19611961 43.943.9

19711971 54.854.8

19811981 68.368.3

19911991 84.484.4

3. Qualitative Classification: When the data are classified according to some qualitative3. Qualitative Classification: When the data are classified according to some qualitativephenomena which are not capable of quantitative measurement like honestyphenomena which are not capable of quantitative measurement like honesty

,beauty, employment , intelligence , occupation, sex, literacy, etc., the,beauty, employment , intelligence , occupation, sex, literacy, etc., the

classification is term as qualitative or descriptive orclassification is term as qualitative or descriptive orattributesattributes . In quantitative. In quantitative

classification the data are classified according to the presence or absence of theclassification the data are classified according to the presence or absence of the

attributes in the given data.attributes in the given data.

If the data are classified into only two classes w.r.t an attribute like presenceIf the data are classified into only two classes w.r.t an attribute like presence

or absence , the classification is calledor absence , the classification is called simplesimple. For example , classifying a. For example , classifying a

given population of individuals as honest or dishonest ; male or female ;given population of individuals as honest or dishonest ; male or female ;

employed or unemployed and so on.employed or unemployed and so on.

PopulationPopulation

Male FemaleMale Female

If the given population is classified into more than two classes w.r.t a givenIf the given population is classified into more than two classes w.r.t a given

attribute , it is calledattribute , it is called manifold classificationmanifold classification . For example , for the attribute. For example , for the attribute

intelligence the various classes may be, Genius, Very intelligent , averageintelligence the various classes may be, Genius, Very intelligent , average

intelligent , below average and dull .intelligent , below average and dull .


1010


11/13

Genius Highly intelligent Average Intelligent Below averageGenius Highly intelligent Average Intelligent Below average

DullDull

Moreover , if the given population is divided into classes on the basis ofMoreover , if the given population is divided into classes on the basis of

simultaneous study of more than one attributes at a time , then also it is termedsimultaneous study of more than one attributes at a time , then also it is termed

asas manifold classificationmanifold classification. For example classify the population by sex into two. For example classify the population by sex into two

classes, males and females. Then each of these is again classified according toclasses, males and females. Then each of these is again classified according to

smoking , smokers and non-smokers Again each of these four classes aresmoking , smokers and non-smokers Again each of these four classes areclassified w.r.t a third attribute, religion into two classes , Hindu and non-classified w.r.t a third attribute, religion into two classes , Hindu and non-

Hindu.Hindu.


MaleMale

FemaleFemale

Smoker Non-smoker SmokerSmoker Non-smoker Smoker

Non-smokerNon-smoker

Hindu Non-Hindu Hindu Non-Hindu Hindu Non-HinduHindu Non-Hindu Hindu Non-Hindu Hindu Non-Hindu

Hindu Non-HinduHindu Non-Hindu

4. Quantitative classification4. Quantitative classification :: If the data are classified on the basis of characterIf the data are classified on the basis of character

which is capable of quantitative measurement like age, height, weight , prices,which is capable of quantitative measurement like age, height, weight , prices,

production income, expenditure, sales profits, etc., it is term as quantitativeproduction income, expenditure, sales profits, etc., it is term as quantitative

classification. The quantitative character is calledclassification. The quantitative character is called VariableVariable and hence thisand hence thisclassification is also sometimes called classification by variable.classification is also sometimes called classification by variable.For exampleFor example

,the earning of different stores may be classified as,the earning of different stores may be classified as

Table 3Table 3

DAILY EARNINGS (IN 00 RUPEES)DAILY EARNINGS (IN 00 RUPEES)

OF 60 DEPARTMENTAL STORESOF 60 DEPARTMENTAL STORES

Daily earningsDaily earnings Number of storesNumber of stores

Up to 100Up to 100 66

101-200101-200 1414

201-300201-300 88

301-400301-400 1010401-500401-500 88

501-600501-600 66

601-700601-700 44

701-800701-800 44

Variable :Variable :

The quantitative phenomenon under study is called variable . Variables are of twoThe quantitative phenomenon under study is called variable . Variables are of twokindskinds

(i)(i) Continuous variableContinuous variable

(ii)(ii) Discrete variableDiscrete variable

Those variable which can take all possible values integral as well as fractional in aThose variable which can take all possible values integral as well as fractional in a

given specified range are termed as continuous variable. For example , the age ofgiven specified range are termed as continuous variable. For example , the age of

students in a school (in years ,months, days, hours minutes ,second) , height (in cms) ,students in a school (in years ,months, days, hours minutes ,second) , height (in cms) ,

weight (in lbs or kgs. )weight (in lbs or kgs. )

On the other hand those variable which cannot take all the possible values within aOn the other hand those variable which cannot take all the possible values within a

given specified range are termed as discrete variable. Discrete variable assumes onlygiven specified range are termed as discrete variable. Discrete variable assumes only

isolated value within some range . For example , Number of mistake per page, Numberisolated value within some range . For example , Number of mistake per page, Number

1111


12/13

of members in the family, The number of accidents on the road, etc., A study ofof members in the family, The number of accidents on the road, etc., A study of

quantitative classification is term asquantitative classification is term as FREQUENCY DISTRIBUTION.FREQUENCY DISTRIBUTION.

FREQUENCY DISTRIBUTIONFREQUENCY DISTRIBUTION

The organization of the data pertaining to a variable involves the following three stages.The organization of the data pertaining to a variable involves the following three stages.

(1)(1) Discrete or ungrouped frequency distribution : A much better way of theDiscrete or ungrouped frequency distribution : A much better way of the

representation of the data is to express it in the form of discrete or ungroupedrepresentation of the data is to express it in the form of discrete or ungrouped

frequency distribution where count the number of times each value of the variablefrequency distribution where count the number of times each value of the variable

occurs in the data. This is facilitated through the technique of tally bars. If theoccurs in the data. This is facilitated through the technique of tally bars. If the

variables takes the values in a wide (large) range then the data still remain unwieldyvariables takes the values in a wide (large) range then the data still remain unwieldy

and need further processing for statistical analysis.and need further processing for statistical analysis.

(2)(2) Grouped frequency distribution : If the identity of the units about whom a particularGrouped frequency distribution : If the identity of the units about whom a particular

information is collected is not relevant , nor is the order in which the observationinformation is collected is not relevant , nor is the order in which the observation

occur, then the first real step is classifying the data into different classes (or classoccur, then the first real step is classifying the data into different classes (or class intervals) by dividing the entire range of the values of the variable into a suitableintervals) by dividing the entire range of the values of the variable into a suitable

number of groups callednumber of groups called classesclasses and then recording the number of observations inand then recording the number of observations in

each group or class. The various groups into which the values of the variable areeach group or class. The various groups into which the values of the variable are

classified are known asclassified are known as classesclasses ororclass intervalsclass intervals; the length of the class interval is; the length of the class interval is

called thecalled the widthwidth of the classes. The two values specifying the class are called theof the classes. The two values specifying the class are called the

class limitsclass limits ;the larger value is called the;the larger value is called the upper class limitupper class limit and the smaller value isand the smaller value is

called thecalled the lower class limitlower class limit..

(3)(3) Continuous frequency distribution ;While dealing with a continuous variable it is notContinuous frequency distribution ;While dealing with a continuous variable it is not

desirable to present the data into a grouped frequency distribution like 0-9, 10-desirable to present the data into a grouped frequency distribution like 0-9, 10-

19,20-29 etc., because this classification does not take into consideration the19,20-29 etc., because this classification does not take into consideration the

observation between 9 to 10 , 19 to 20, so on . In such situation one should formobservation between 9 to 10 , 19 to 20, so on . In such situation one should form

continuous class intervals like 0-10, 10-20, 20-30 etc., the presentation of the datacontinuous class intervals like 0-10, 10-20, 20-30 etc., the presentation of the data

into continuous classes with corresponding frequencies is known as continuousinto continuous classes with corresponding frequencies is known as continuous

frequency distribution.frequency distribution.

Basic principal for forming frequency distribution:Basic

principal for forming frequency distribution:

(1)(1) Types of classes :Types of classes :-- The classes should be clearly defined and should not lead to any ambiguity.The classes should be clearly defined and should not lead to any ambiguity.

-- They should be exhaustive and mutually exclusive so that each and everyThey should be exhaustive and mutually exclusive so that each and every

value of the variable corresponds to one and only one classvalue of the variable corresponds to one and only one class

(2)(2)Number of classes:Number of classes:

Although no hard and fast rule exists for no.of classes but it is depend upon theAlthough no hard and fast rule exists for no.of classes but it is depend upon the

total frequency ,the nature of data and the accuracy aimed at.total frequency ,the nature of data and the accuracy aimed at.

The number of classes should neither be too small nor be too large .i.e the no. ofThe number of classes should neither be too small nor be too large .i.e the no. of

classes should not be greater than 20 and should not be less than 5.classes should not be greater than 20 and should not be less than 5.

The formula given by Prof. Sturges known as Sturges rule for number of classesThe formula given by Prof. Sturges known as Sturges rule for number of classes

which iswhich is

K = 1 + 3.322 logK = 1 + 3.322 log 1010 NN

Where K = number of classesWhere K = number of classes

N= total frequencyN= total frequency

(3)(3) Size of Class Interval ; size of the class interval should be inversely proportional toSize of Class Interval ; size of the class interval should be inversely proportional to

the number of classes .the number of classes .

Maxi. Obs. Min. obsMaxi. Obs. Min. obs

Class interval =Class interval =

Number of classesNumber of classes

(4)(4)Types of Classes :Types of Classes :

1212


13/13

(a)(a) Inclusive types classes : The classes in which both the upper andInclusive types classes : The classes in which both the upper and

lower limit are included in the class are called inclusive classes for example 0-9,lower limit are included in the class are called inclusive classes for example 0-9,

10-19, 20-29 so on. This types of classes are used for classification of discrete10-19, 20-29 so on. This types of classes are used for classification of discrete

grouped frequency distribution.grouped frequency distribution.

(b)(b) Exclusive type classes : The classes in which lower limit is includedExclusive type classes : The classes in which lower limit is included

and upper limit is excluded from the class are called exclusive classes forand upper limit is excluded from the class are called exclusive classes for

examples 0-10,10-20, 20-30 so on. These classes are used for classification ofexamples 0-10,10-20, 20-30 so on. These classes are used for classification of

continuous group frequency distribution..continuous group frequency distribution..

In grouped frequency distribution there are gaps between upper and lower limitIn grouped frequency distribution there are gaps between upper and lower limit

of succeeding classes then there is need to convert the classes in to exclusiveof succeeding classes then there is need to convert the classes in to exclusive

type . the limits of the new exclusive type classes are calledtype . the limits of the new exclusive type classes are called class boundaries.class boundaries.

Upper class boundary = Upper class limit + (class width)Upper class boundary = Upper class limit + (class width)

Lower class boundary= Lower class limit + (class width)Lower class boundary= Lower class limit + (class width)

Mid value of class = (lower limit +upper limit)Mid value of class = (lower limit +upper limit)

= (lower boundary +upper boundary)= (lower boundary +upper boundary)

Open end classes :The classification is termed as open end classification if the lower Open end classes :The classification is termed as open end classification if the lowerlimit of the first class or the upper limit of the last class are not specified.limit of the first class or the upper limit of the last class are not specified.

1313

definition & scop unit-1

Documents