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UNIT - 1: INTRODUCTION & ANALYSIS OF QUANTITATIVE DATA, , Meaning , ance ¢ i, , eaning, scope, importance and limitation of statistics measures of central tend, , ae ee endency, , Arithmetic mean (Simple & weighted), Median, Quartiles, Deciles, Percentiles. i, Ss, s, Mode;, , Merit »me ‘ . net ;, Merits, demerits and uses of mean, median & mode; Requirements of a good average, , UNIT-IL : MEASURES OF DISPERSION, , ~, Range, semi-inter quartile range, Quartile deviation, Mean dev iation, Standard deviation, , and their coefficients, Coefficient of variation & skewness — Karl Pearson's, Bowley’s and, , Kelly’s coefficient of skewness., , UNIT - tll: INDEX NUMBERS, , Meaning and_uses_of index_numbers; Methods of construction of index numbers, Unweighted Indices — Simple aggregative method, simple, Paasche’s method, Fisher’s ideal index number, , Cost of living index: Aggregative expenditure, , average of price relative method,, , Weighted Indices-Laspeyre’s method,, including time and factor reversal tests;, method and family budget method., , UNIT - IV: CORRELATION AND REGRESSION, , types & importance; Methods of studying correlation Karl, , Correlation—Meaning,, Pearson’ s coefficient of correlation, Rank correlz ation and concurrent deviations, (Ungrouped, data only),{probable error j Jand interpretation of data, Regression analysis: Meaning &, , —, objectives; Regression lines, ‘Regression equation of X on Y and Y on X (Ungrouped data, , only) <6
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INTRODUCTION +, STATISTI¢g, , , , , INTRODUCTION, , _The modern age, and effectively used in ili, become an essential ; eee, and conteclinn i L Statistics provides methodology for unde, : ) © the operation of the Society; and thus promotes social welfare It is als, the arithmetic of human w el fare. e fac s auistice ations nee, at, elfare. The facts based on statistical Operations are considered to by, ae ae dependable. The presentation of figures and facts numerically and in quantitative, m Is a modern trend and way of thinking of the society and the social scientists, ., ‘ When You can measure what you are speaking about and express it in numbers, you, how some thing about it, but when you cannot measure it, when you cannot express it in, numbers, your knowledge is of meagre and unsatisfactory kind”’., , —Lord Kelvin, ORIGIN AND GROWTH, , The word statistics has been derived from the Latin word *‘Status’, or German word *‘‘Statistik’’., , “Statistics”, , 's called an age of statistics. The statistics, these, , all fields of social life and as such, like, Part of a human life., , days, are most Extensively, , id and write, have, , ’ the /talian word “‘Statista”’, All these words mean a ‘political state’ In the early years, * meant a collection of facts about the state or the people in the state for political purposes., Thus, it helped int Collecting data about economic and social conditions of the people living in different, parts of the country, For proper functioning of the state, it is essential to know the conditions under, which the people live and work, earn income and spend the wealth. This science was known as, the science of state because it was used by the state. In this way statistics developed as a ‘*king's, subject’’ or as a ‘science of kings’. \t may be noted that Gottfried Achenwall in 1749 was the, first to use the term statistics to refer a subject matter as a whole. He is, as such, regarded as., the fore-runner of the study of statistics., , But with the passage of time, the scope of statistics widened. For some time, statistics was, regarded as a branch of Economics but now it has become a full-fledged independent subject. In, the present times, Statistics is not only a science of the State but it also includes, all types of quantitative, analysis. Sir R.A. Fisher regards the science of statistics as ‘Mathematics to observational data’., , MEANING OF STATISTICS, , Meaning of statistics is taken either in singular sense or in plural sense. In plural sense, it, means a collection of numerical facts. It is in this sense that the public usually think of Statistics, -concérned with population or production of wheat in different years or number of man-hours, lost in a specific years @ See istics, « ges, averages and coefficients derived, from numerical facts, 2, , , , , , , , , , , , study a large terrain, statistics is a science, , cal data whereas others,
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1.2 INTRODUCTION TO STATISTICS, , , , , , “Statistics are a collection of note-worthy facts concerning state both historieal and, descriptive." —Achenwall, “By statistics we mean quantitative data affected to a marked extent by multiptieity of, causes.** Yule and Kendall, “An aggregate of knowledge brought together for a practical end namely knowledge of, @ concrete state.” ~—Wappany, “Statistics are aggregates of facts affected to marked extent by multiplicity of causes,, numerically expressed, enumerated or estimated according to reasonable standards of accuracy,, collected in a systematic manner for a pre-determined purpose and placed in relation to each, other.”’ Horace Secria, The definition given above is the most exhaustive definition, Its main characteristics are <, , CHARACTERISTICS OF STATISTICS AS USED IN PLURAL SENSE, OR NUMERICAL DATA, , Statistics as used in plural sense, i.e., numerical data, must possess the following, characteristics :—, , (@) Aggregates of Facts. By statistics, we do not refer to single figure but to a series of, figures. A single height of 5’.6” or 6.0” is not statistics but a series relating to the height of a group, of persons is called statistics. It means, all those figures which relate to aggregates of facts are, called statistics, , (ii) Affected by Multiplicity of Causes. Statistics are not affected by one factor only, rather, they are affected by a large number of factors, It is because statistics are commonly used in social, sciences, It is not an easy job to study the effects of any one factor separately by ignoring other, fuctors. In statistics we need to study the effects of all factors on a phenomenon and effects of, different sets of factors separately. In a nutshell, we can say that statistics are affected considerably, by multiple causes ¢.g., prices are affected by conditions of demand, supply, money supply, imports,, exports and various other factors., , (iii) Numerically Expressed. Another characteristic of Horace Secrist’s definition is that in, case of statistics, qualitative expressions like young, old, good, bad etc, are not recognised. To all, statistics, a numerical value must be given. For example, the statements like ‘There are 932 females, per 1,000 males in India, whereas in USSR, there are 1,170 females per 1,000 males.’ Thus statistical, statements must contain figures so that they are called numerical statements of facts. Furthermore,, such numerical expressions are precise, meaningful and convenient forms of communication., , (iv) Enumerated or Estimated according to Reasonable Standards of Accuracy. In case, the numerical statements are precise and accurate, then they can be enumerated. But in case the, number of observations is very large and beyond comprehension, in that case the figures are, It is obvious that the estimated figures cannot be absolutely accurate and precise. The, , , , , , , , , , , , , , , standard of accuracy for all types of enquiries., ten students of statistics in a class. It is 100% a, , refers to round about figure e.g. we say that two la, be a few hundreds more or less,, (v) Collected in a Systematic Manner, For, be collected in a systematic manner. If the figures at, of such data will deteriorate. Thus for reasonable, in a systematic manner, otherwise the results wou, Pe a arene oe, igible i COR AS Ret Sree, ts vin some ceive mi The, , , , a
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INTRODUCTION To STATISTics, , prices, then we ‘ 13, , data on retail must be clear whether we hi il pri, , : Prices, what we have to « © have to collect whoelsale or retail prices. If we want, (vii) Placed in Relation ‘0 see is the number of goods required to serve the objective., , motive to compare. If the Pe bas Each Other. The collection of data is generally done with the, , of their significance. mea: Sures collected are not comparable, in that case they lose a large part, , heterogeneous, In case of ki ins the figures collected should be homogeneous for comparison and not, It does not make terogeneity the figures cannot be placed in relation to each other., , accommodation. Such a Sense if we compare the height of a person and the rent he pays for, , generally compared nee do not fall in the category of statistics. The statistical data are, , phenomenon or subject, “wise or region-wise. For this purpose the data should relate to some, Thus, it is 3, , statistics. It et i without the aforesaid characteristics, the numerical data cannot be called, , ‘ S : S, “all stati ‘s ti, , are not statistics,” stics are numerical statements of facts, but all numerical statements, , DEFINITION IN SINGU E, Me LAR SENS HE SENSE OF, o STATISTICAL METHODS een, Some of the statisticians have defined statistics in singular sense or a5 a statistical methodology, ae purpose of collection, classification, presentativn, comparison, analysis and interpretation of, , ’ The method by which statistical data are analysed is called statistical method, Sometimes, this term is used to cover the subject ‘Statistics’ as a whole. The Mathematical theory which is the, basis of these methods is called the Theory of Statistics or Mathematical Statistics. These statistical, methods are used in Economics, Sociology, Psychology, Medicine, Anthropology, Business,, Agriculture, Industry, Trade ete., , For a layman, Statistics are only mass of figures. To understand what statistics is, we should, define it in a way different authors have defined., , A.L. Bowley has given a series of definitions. Some lay emphasis on one aspect and others, on other aspects. At one place he says ‘“‘statistics may be called the science of counting.’, This means that simple counting of data is statistics. This view is not perfect and correct., Statistics is not concerned with counting only. It deals more with estimates. At another place he, says that ‘‘Statistics may rightly be called the science of averages.’’ But calling statistics as a, science of counting or averages, confines the scope of statistics. All these definitions confine the, scope of statistics. Bowley himself realized their drawbacks and stated that statistics cannot be, confined to any one science., , “Statistics is a body of principles and techniques of collecting, classifying, presenting,, comparing and interpreting the quantitative data.”’ —Turtle expresses, , «it Statistics is the science of estimates and probabilities.”’ —Boddington, <<4g the collection, classification, analysis and presentation of numerical data.”’, , —Croxton and Cowden, , “Statistics refers to
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Pes INTRODUCTION TO STATISTICS, , , , CHARACTERISTICS OF STATISTICS AS STATISTICAL METHODS, OR IN SINGULAR SENSE :, , Statistics is considered to be a science, when studied from the view point of statistical methods, of in singular sense statistical methods include all methods which are used in collection, presentation,, analysis and interpretation of quantitative data., , Thus important features of statistical methods or statistics as a science are as under :~, , 1. Collection of Data. Collection of data is the main and the first Step in @ Statistical, enquiry. The technique of collection of data depends upon the objective of the study. The data are, the bases of the analysis, therefore, these should be collected very carefully. These should be such,, 48 to fulfil the basic objectives of the proposed study, , 2. Organisation of data, After collection, the data are organised in a proper form which, involves editing, classification and tabulation. Editing is necessary to remove inconsistencies,, Classification means arrangement of data according to some common characteristics. Tabulation, includes presentation of data in columns and rows., , 3. Presentation of data. After classification the data are presented in some suitable, manner-either by diagrams or graphs., , 4. Analysis of data. Analysis follows the presentation of data. Simple mathematical, techniques are applied in analysis. These include measures of central tendency, measures of dispersion,, correlation and regression etc. The main purpose of analysis is to draw some meaningful conclusions,, , 5. Interpretation. Interpretation is the last step in the statistical methodology. To derive, meaning from analysed data is called interpretation of data. It involves statistical thinking, skill and, experience. The interpretation provides the final conclusions drawn from the analysed data., , All these points have been discussed in detail under the heading subject-matter of statistics., , SCOPE OF STATISTICS, , Like other social sciences, in the Scope of statistics, the following main aspects are, included :—, , 1. Subject-matter of Statistics 2. Nature of Statistics. 3, Limitations of Statistics,, Subject-matter of Statistics., The subject matter of statistics can broadly be studied under two heads:, (A) Statistical Methods (B) Applied Statistics., Subject-matter of Statistics, L, , , , , , , , , , L 1, Statistical Methods Applied Statistics, 4, £ T, Descriptive Applied Scientific Applied, Statistics Statistics, , , , (A) Statistical Methods., , Under statistical methods, as have been, general principles which are applicable to all, a ei ith see send Jn Ge call, to any aspect of the enquiry. xton and Cowde, of statistics, “Statistics may be defined as the, of numerical data’’., , This definition points out four stages : (, Analysis of data, and (iv) Interpretation of data. 1, , , , , , , , , , , , , , Cwonsaz ee, , sp
