chapter - 1 notes-intro to statistics

8/6/2019 Chapter - 1 Notes-Intro to Statistics

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Chapter : 1 INTRODUCTION TO STATISTICS

The word statistics seems to have been derived from the Latin word Status or Italianword Statista or the German word Statistik or the French word Statistique each ofwhich means a political state. It is not a new discipline, but is as old as the humansociety. In good old days, the term statistics was applied to a branch of statecraft science of statecraft. As such, the term statistics was applied to mean facts andfigures which were needed by the state in its day to day life. Statistics was regardedas a by-product of administrative activities of the State. Now statistics is usually notstudied for its own sake (as a separate branch), but statistics is employed as a tool insolving or analyzing the problems of the State.

In the present age, statistics is regarded as one of the most important tools for takingdecisions. All the branches of science make use of statistics. Statistics helps informing suitable policies; as such it is being used in all the fields. In science, statisticsis freely used. In research work, it has got its own status as a tool of research. Thus inevery situation there is a demand for statistics. The sampling techniques furtherreduce the cost of statistics. This is because by studying a part of the population, the

characteristics of the whole population can be known. Thus the increasing demandand decreasing cost of statistics give way to growth.

Planning and control are the twin-babies of management. Whenever we think of aplan we have to think of statistics. Planning cannot be devised without statistics. Inthis technically advanced and competitive world, a producer has to make a number ofdecisions such as what to produce, where to produce, how to produce, where to sell,at what price to sell etc. Such decisions depend upon sound forecasting andforecasting cannot be made without statistics. Prof. Marshall observed that statisticsare the straw out of which I, like any other economist, have had to make bricks.Statistics helps in formulating suitable policies and as such its need is increasingly feltin all the fields. A businessman needs information on daily demand of the products,

seasonal changes in demand, prices of competitive products etc. All these problemsare resolved in the light of factual information and hence the need for statistics.

By statistics we mean aggregates of facts affected to a marked extent bymultiplicity of causes, numerically expressed, enumerated or estimatedaccording to reasonable standard of accuracy, collected in a systematicmanner for a predetermined purpose and placed in relation to each other. -Horacesecrist

Numerical data alone constitute statistics. Students can be classified very good, good,average, poor, etc. on the basis of their performance in tests. But they are inqualitative expressions and are not statistics. In particular, the qualitativecharacteristics honesty, beauty, intelligence, etc. which cannot be measured

numerically are not statistics. If they are expressed by giving certain scores (marks)as numerical standards, then they can be called as statistics. Another example isbeauty competition of girls; if ranks are assigned, then the quantitative measure ofbeauty of the girls can be regarded as statistics.

The numerical data pertaining to any field of enquiry can be obtained either byenumeration (by actual counting) or by estimation. If the field of enquiry is not large,enumeration (actual counting) can be conducted. If the field of enquiry is wide andlarge, enumeration is out of question; and in such cases, data can be estimated. Forinstance, in the MBA class there are 60 students; this is a case of enumeration. (Wecount the number of students). At the same time we may say that 1,00,000 peopleattended the Independence Day Celebration; it is a case of estimation(approximation).

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A reasonable standard of accuracy is needed in both enumeration and estimation. Forinstance, if the weights of students are being measured, fractions of kilogram (say1/10th or 1/20th ) can be ignored; when measuring the distance from Chennai toKanyakumari, fraction of a kilometer can be easily ignored. No hard and fast rule canbe laid down for all cases. Hence mathematical accuracy cannot be attained instatistical studies.

Statistics is the science of estimates and probabilities This definition is narrow, as the other methods like enumeration, classification;analysis, etc. have been ignored. Therefore, this definition narrows down the scope ofthe science of statistics.

Statistics may be defined as the collection, presentation, analysis andinterpretation of numerical data.

This definition is clear and concise. The data are collected to study a particularproblem. The collected data in mass may be converted in the form of diagrams,graphs, etc. According to this definition, there are four stages.

a. Collection of data: The first step of an investigation is the collection of data.

Careful collection is needed, because further analysis is based on this. Thereare different methods of collection of data (Census, sampling, primary,secondary etc.) and they must be reliable. If the collected data are faulty,results will also be faulty. Therefore, the investigator must take special care incollection.

b. Presentation of data: The collected data are generally in an unintelligibleform and need to be classified and tabulated before they can be analyzed. Forexample, the investigator is interested to know the average income of 1000families of a village. The mass data collected should be difficult to understandand analyze. Therefore, the collected data are to be presented in tabular ordiagrammatic or graphic form. The data presented in a systematic order willfacilitate further analysis.

c. Analysis of data: After the presentation of data, the next step is to analysethe presented data. Analysis includes condensation, summarization, conclusion,etc. though the means of measures of central tendencies, dispersion, skewness,kurtosis, correlation, re-gression, etc.

d. Interpretation of data: Figures do not speak for themselves. The duty ofthe statistician is not complete with mere collection and analysis of data. But,valid conclusions must be drawn on the basis of analysis. A high degree of skilland experience is necessary for the interpretation. Correct interpretation leadsto valid conclusion.

Without an adequate understanding of the statistical methods, the investigator in the

social sciences may be like the blind man groping in a dark room for a black cat that isnot there. The methods of statistics are useful in an over-widening range of humanactivities in any field of thought in which numerical data may be had.

The real purpose of statistical methods is to make sense out of facts and figures, toprove the unknown and to cast light upon the situation.

Broadly speaking, one may say that the statistical methods can be fruitfully applied toany problem of decision making where numerical data are available or can be madeavailable. Therefore, in business, industry and economics; the statistical techniquesare applicable to problems like maintenance to trends of population, production ofagricultural industries, prices, internal and external trades, gross national product,taxation laws and rates; preparation of budgets, computation of consumer price

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indices from time to time o revise the wage structures, preparation of price policies ofnew products, scheduling of the projects and then exercising control over theoperations till the completion, resource allocations for any job carrying out inquiries toknow the potential markets, stock control, quality control, maintenance andreplacement of equipments etc.

In research and technology, the statistical techniques are used to develop optimum

designs of experiments that can be applied to obtain the relevant information withhighest precision at minimum cost. In social sciences, Statistics help in studying thedistribution of wealth, intelligence etc. It is also used in studying the changes instandards of living, food habits and attitudes of people.

Functions of Statistics:

In various fields discussed above and many others, the science of statistics us used toperform the following functions:

1. Statistics helps in developing sound methods of collecting data so that the datacollected can be used to draw the valid inference regarding the desiredobjectives.

2. It presents the information in numerical form.3. It helps in simplifying the complex data by way of classification / tabulation /

graphical representation.

4. The tabular / graphical representation of data and other complex statistics helpin comparison.

5. Statistics can be used to study the relationship between two or more factors.The use of such relationship can be made in estimating one factor when other/sare known.

6. The data regarding a characteristic for a series of past periods can be used toforecast its value for a future period.

7. The powerful function of forecasting leads us to the need of planning and thusfacilitates in formulating policies and helps in planning to implement thesepolicies.

Limitations of Statistics:

Statistics is a very powerful science to study quantitative data. Qualitative datacannot be studied with the help of Statistics except when we make them to be lookedupon a quantitative by defining suitable varieties.

More often than not, Statistics is used to draw conclusions regarding a group of unitsrather than single unit. In case of individual units, the inference drawn is always withan element of chance or on an average.

Sometimes due to bias involved in the collection of data the inference drawn is abiased one.

The potential danger involved in the use of statistics is its misuse. It is easy to misuseit for supporting or contradicting any proposition or a conjuncture. For instance, astatement like During the last month, six street accidents were recorded in themiddle of the road compared to twenty one accidents recorded on the sides of theroad in busy streets of Mumbai may lead one to the conclusion like It is safer to walkin the middle of the road.

SOURCES OF DATA

An application of statistics involves data and therefore the foremost question thatarises is from where to get the data or what the sources of data are.

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The primary data is the information collected by an enumerator or investigator for thepurpose of the enquiry for the first time. The following are the methods using whichthe primary data can be collected.

a. DIRECT PERSONAL INVESTIGATION: Here the investigator meets theinformants personally and collects the information by asking questions. Thequestions should be simple, short and should be so formed as to get brief and

unambiguous answers. The enumerator must be trained, specially hired for the job. His observation should be keen and he should be well acquainted with thelocal conditions. He should possess sufficient knowledge of tastes and preferencesof the informants. The investigator should be polite and courteous yet he shouldbe firm, determined to get answers tactfully from the respondents.

This type of investigation, though very costly and time-consuming is the bestmethod available as far as accuracy concerned. If the scope of the enquiry is verywide, this method cannot be used. Also, care has to be taken to avoid personalbias entering the answers of the respondents; otherwise it will affect the validity ofthe data collected.

b. INDIRECT ORAL INVESTIGATION: If the persons, directly concerned with

the investigation are not willing to supply the necessary information, then it isobtained by questioning witnesses who are supposed to know the situation, to haveknowledge about the persons concerned or the problem involved.

This method is adopted by Inquiry Committees or Commissions. It is applicable inthose situations where indirect informants can give more reliable and accurateinformation than the persons involved. This method can be successful only whenthe witnesses are honest and are not hostile towards the persons concerned. Theyshould be able to express themselves precisely, accurately, without exaggeratingthe situation. The investigators should be able to judge whether the informationprovided by the witness is correct and without bias.

c. QUESTIONNAIRES AND SCHEDULES: In this method, a list of questions isprepared and it is sent by post to various informants. Usually, a sample ofinformants is selected from the concerned population. Sometimes the schedulesare filled in by the enumerators who question the people and write down thenecessary information. If the questionnaire is sent by mail, then a forwardingletter, explaining the objective of the survey and requesting co-operation, shouldaccompany the form. The advantage in this method is that the respondents canwrite the answers of the questions as per their convenience and would not hesitateto give some confidential information asked in the questionnaire. This method hasa wide coverage, it is quick and inexpensive. But still, the response is not verygood. If possible, there should be some incentive like a small prize, lucky numberdraw, concession at some shops etc. to get better response. Every questionnairemust be accompanied by an addressed and stamped envelope.

If a schedule is to be filled in by an enumerator, he should be trained, qualifiedperson. The enumerator should be a person of unquestioned integrity. He must bepatient and tactful with the respondents. He must explain the purpose of theinvestigation and also the questions in detail. While writing the answers, he has totake care that personal bias does not affect the investigation. The reports of theenumerators should be periodically checked by the supervisors. Now, let us seehow a good questionnaire should be prepared.

REQUISITES OF A GOOD QUESTIONNAIRE OR A SCHEDULE:

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1. The number of questions should be as few as possible but at the same time, thequestions should cover all the essential topics on which information is required.

2. The questions should be short, simple and unambiguous. Clarity is essential informing the questions.

3. The questions should be drafted in such a way that the answers to them are ofobjective type and brief in nature, for example, the answers printed should be

yes or no or multiple-choice answers of the type single, married, widowed,divorced.

4. It is possible that some questions cannot be answered accurately by therespondents. So the degree of accuracy for a statistical unit should be mentionedwith the question itself. For example, for age the answer is expected incompleted years or the monthly income is to be expressed in hundreds of rupeesetc.

5. The questions which are unduly inquisitive or which are likely to offend therespondents should not be included in a questionnaire. Questions regardingpersonal habits behaviour with the family members, income should be tactfullyasked. Leading questions providing a hint to the possible answer should be

avoided.6. The questions should be so worded that personal bias of an investigator is not

reflected.

7. The arrangement of the questions should be carefully planned. Proper space foranswers must be kept and there should be logical flow from one question to theother.

8. The questionnaire should be neatly printed on a high quality paper creatinggood impression on the respondents.

9. If possible, the questionnaire should be tried on a small sample before applyingit to a large group so that some revision or amendment of the questionnaire canbe made, if necessary.

EDITING OF THE PRIMARY DATA

The collected data should be edited and then only it can be processed further. Whileediting the data, the following points must be remembered.

i. The data should be consistent. That is, the answers obtained should notcontradict one another.

ii. The answers should be complete and uniform in all respects. If some, importantquestions are left unanswered then the respondent should be contacted againto complete the questionnaire.

iii. The answers should be checked for accuracy. Inaccuracy due to mathematical

errors is to be corrected.iv. The data must be checked for homogeneity of answers. For example, if one

respondent has mentioned the gross pay and if the other has mentioned netpay after tax deduction, then these cannot be compared.

SECONDARY DATA

The data compiled through various published or unpublished sources is known asSecondary Data. The following are the main sources of the secondary data.

a) Various Central or State Government publications supply reliable data, on manysocial and economic activities. For example, Census reports, Pay Commission

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reports, monthly or annual publications like Bulletin on Index of IndustrialProduction, Retail Price Bulletin, Estimates or national product etc.

b) Various international institutions publish the reports on matters of internationalimportance. Organizations like W.H.O., I.M.F., U.N.O., I.B.R.D., regularly publishofficial reports.

c) Semi-official publications of corporations like municipal corporations, LifeInsurance Corporation of India, etc.

d) Publications of private bodies like Chambers of Commerce, Institute ofChartered Accountants, Institute of Bankers provide secondary data, on variousissues.

e) Periodicals like Economic Weekly, Commerce, Economic Times supply reliableinformation.

f) Various universities, research organizations collect data in different fields whichcan be used as Secondary data.

g) Some reference books also supply information over a long period.

h) There are also sources like records of government departments, trade unionoffices, railways, state transport offices which can be used as secondary data.

The secondary data should be carefully checked before using it in any investigation. The data should be suitable and adequate for the investigation. The informationshould be checked for the reliability and accuracy of data. The integrity of theinvestigators or enumerators should be ascertained. The secondary data should neverbe accepted at its face value without checking.

We have seen different methods of data collection. If the data is collected for all unitsof the population, it is called Census and if it is collected only for a sample then it iscalled a Sample Survey.

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chapter - 1 notes-intro to statistics

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