1. Introduction & Origin The word ‘statistics’ have been derived from the Latin word ‘status’, Italian word ‘statista’ German word ‘Statustik’ or French word ‘statistique’ all referring to the political state. Achenwall, (father of statistics), defined statistics as “The political science of the several centuries”. In the early years ‘statistics’ connoted a collection of facts about the State or the people in the State for administrative and political purposes.

2. Definitions The word statistics is used in two different but inter-related ways: i.As a plural noun - statistics refers to statistical data. ii.As a singular noun - it refers to statistical methods. Statistical methods include collection, classification, presentation, analysis and interpretation of data.

3. Prof. Horace Secrist: “By statistics we mean aggregate of facts affected to a marked extent by multiplicity of causes, numerically expressed, enumerated or estimated according to reasonable standards of accuracy, collected in a systematic manner for a predetermined purpose and placed in relation to each other.”

4. Empirical and Quantitative Analysis Empirical - refers to something based on experiment, observation or experience rather than on theory. Analysis - refers to detailed examination of statements or observations mainly to draw some conclusions. Empirical analysis - a method of studying a subject whereby knowledge is acquired as a result of actual experience.

5. Quantitative analysis An attempt to level ‘precision’ or ‘ preciseness’ to the facts, so that they can be easily compared. In quantitative analysis, numerical data is classified, tabulated and analyzed to draw reasonable conclusions.

6. Need/ Importance of Quantitative Analysis 1.Statistical analysis is useful in solving complex problems of modern business and industry. 2.It provides systematic and powerful tools to decision makers to take efficient decisions based on quantitative data. 3.It enables proper allocation of resources. 4.It helps in minimizing waiting and servicing cost.

7. 5.It enables the management to decide when to buy and how to buy. 6.It helps in choosing an optimum strategy, i.e., the action which can give maximum benefit at minimum cost. 7.It renders great help in the optimum allocation of resources. 8.Management can know the reactions of the integrated business system through quantitative analysis.

8. Scope of Statistics Scope of statistics is studied under the following three heads: i.Nature of Statistics ii.Subject-matter of Statistics iii.Limitations of Statistics

9. i.Nature of Statistics Nature of statistics - determine whether statistics is an art or a science. Statistics is regarded as an art of applying the science of scientific methods. In statistics, we not only study different methods of studying a problem but also study how those methods should be applied in different situations. In the words of Tippett, “Statistics is both a science and an art. It is a science in that its methods are basically systematic and have general application; and an art in that their successful application depends, to a considerable degree, on the skill and special experience of the statistician, and on his knowledge of the field of application.”

10. ii.Subject-matter of Statistics Subject-matter of statistics is divided into two major parts: a)Descriptive Statistics describe the characteristics of a body of data. They deal with the collection, tabulation and presentation of data and the calculations of measures which describe the data in various ways. May be univariate or bivariate. 1)Frequency distributions 2)Measures of central tendency 3)Measures of variability, i.e., dispersion The study of correlation and regression are a part of bivariate descriptive statistics.

11. b.Inferential or Inductive Statistics Inferential statistics deals with those methods where conclusions about a large group are drawn by studying a part of it. For example, by checking a few grains of rice a housewife makes an estimate whether the whole lot has been cooked.

12. iii.Limitations of Statistics Newshome writes, “It (statistics) must be regarded as an instrument of research of great value, but having severe limitations, which are not possible to overcome and as such, they need our careful attention.” Tippet observes, “The application of statistical methods to investigation in the technological and indeed in any other field is based on assumptions, is subject to limitations and often leads to uncertain results.”

13. LIMITATIONS OF STATISTICS 1.Statistics studies only the quantitative aspect of a problem and does not study its qualitative aspects 2.Statistics deals with averages 3.Statistics does not study individuals 4.Statistical results are only approximately correct 5.Statistical results are not always beyond doubt 6.Statistics is only a means and not an end 7.Misuse of statistics is possible 8.Statistics should be used only by experts 9.Statistical study is not the only method 10.Homogeneity of data

14. Function of Statistics 1)To simplify complex facts 2)To provide comparative study 3)To study relationship between different facts. 4)To enlarge individual knowledge and experience 5)To formulate policies in different fields 6)To measure the effects 7)To test a hypothesis. 8)To provide numerical measurements 9) To forecast ( to indicate trend behaviour). 10)To classify data 11)To measure uncertainty 12)To draw valid inferences

15. Importance of Statistics Statistics is Important in Economics Statistics is Important in Planning Statistics is Important in Business Statistics is Important in State and Administration

16. Distrust of Statistics i.Statistics are lies of the first order ii.An ounce of truth will produce tonnes of statistics iii.Statistics can prove or disprove anything iv.Statistics can prove nothing v.Figures do not lie vi.If figures say so, it can not be otherwise vii.Statistics is another form of lying viii.There are three kinds of lies-lies, damned lies and statistics

17. Collection of Data Sources of Data InternalExternal [Data generated from the[Data obtained from the activities within the firm, e.g.,sources outside the firm] inventory, payroll of the Staff, accounting records, etc.] PrimarySecondarySource [Primary source is a[Secondary source is a source that itselfsource which makes collects the data.]available data which were originally collected by some other agency.]

18. Primary Data Wessel and Simone, “Data originally collected in the process of investigations are known as primary data.” SECONDARY DATA M.M.Blair, “ Secondary data are those which are already in existence and which have been collected for some other purpose than the answering of the question in hand.” According to Wessel, “Data collected by other persons are called secondary data.”

19. Demerits of Primary Data 1)It is expensive 2)It is time-consuming 3)It may be difficult to approach the exact source 4)Collection of primary data usually involves creating new definitions and measuring instruments such as questionnaires or interview forms and training people to use these specifically designed instruments. Merits of Primary Data 1)It is original in nature 2)It is more reliable, authentic and accurate 3)It can be used with greater confidence because the enquirer knows its origin, coverage and definitions. 4)It is generally free from bias 5)It exactly matches the needs of the project

20. Merits of Secondary Data 1)It is readily available 2)It is much less expensive as compared to primary data 3)It is less time-consuming as compared to primary data Demerits of Secondary Data 1)There is a possibility that proper procedure might not have been followed in their collection 2)These may not be relevant in the present context 3)These may not be free from personal bias and prejudices 4)These may not have the needed accuracy or reliability 5)These may not be adequate 6)Proper care and precautions have to be taken before using the secondary data 7)It may be outdated

21. Distinction between Primary and Secondary Data BasisPrimary DataSecondary Data 1.OriginalityThese data are original. These data are not original. 2.Use of timeIn these data time and money is used considerably. The use of time and money in these data is not very significant. 3.EditingNo editing is required because they are originally collected. Editing is required. 4.PrecautionNo special precaution is required. Precaution is very necessary. 5.BiasDo not contain any bias. May contain bias.

22. Precautions for the use of Secondary Data 1)Since the secondary data is less reliable as compared to primary data, it should never be accepted at its face value 2)Investigator should have the confidence that the data available are appropriate for the purpose in hand 3) Make sure that the data are reliable and adequate 4)The investigator should also ascertain as to which method was used in collecting the data and what has been the degree of degree of accuracy.

23. Sources of collection of Data Direct Personal Interview or investigation) Indirect Personal Interview (or investigation) Information from Correspondents Mailed Questionnaires Questionnaires Filled by Enumerators PRIMARY Government Publications Publications of International Organisations Semi-Official Publications Reports of Committees and Commissions Private Publications Published Sources Unpublished Sources SECONDARY Sources of Collection of Primary and Secondary Data (a)Journals and News Papers (b)Research Institutions (c)Professional Trade Bodies (d)Annual Reports of Joint Stock Companies (e)Articles, Market Reviews and Reports

24. Population ( or Universe) - collection of all possible observations of a specified characteristic of interest. Sample - refers to a part of the population selected for analysis to draw inferences about the population. Sampling - The process of drawing a sample from a population. Examples of Sampling i.Handful of grains are checked to evaluate the quality of wheat, rice, pulses, etc. ii.A few bulbs are tested to find out the life span of electric bulbs out of each lot iii.A drop of blood is tested for diseases like malaria, typhoid, etc. iv.A few nuts or bolts are tested from the complete lot of production for final judgment of the quality

25. Enumeration of Data 1.Census Method/Complete Enumeration Method) 2. Sample Method (Partial Enumeration Method) When adequate secondary data is not available for the problem under study, a decision may be taken to collect primary data through original investigation. The original investigation may be obtained either by Census Method or by Sample Method. Census Method In this method each and every unit of the population is investigated for the characteristic under study. Suitability of Census Method i.Limited coverage is required ii.Population contains widely diversed items iii.Intensive examination is required to achieve high degree of accuracy and reliability

26. Merits of Census Method 1.Information about every item in the population is obtained. 2.Information collected is more accurate and highly reliable. 3.Element of bias is practically eliminated because the investigator has to study each item in the population and has no choice in between the items. 4.Information collected through the census method is quite exhaustive and meaningful because all the items of the population are studied. For example, Population Census in India gives exhaustive information relating to the number of people in different parts of the country, their age, sex, education, status, occupation, etc.

27. 5.By using Census Method, one can study diverse characteristics of the universe 6.When items in a universe are of complex nature and it is necessary to study each item only Census Method can suit such situation. 7.Census Method can be successfully used in investigations relating to Unemployment, Poverty, Corruption, etc. Demerits of Census Method 1.Census Method requires great deal of money and time 2.In certain practical situations, specially where the population is complex and it is difficult to contact every item and where items during testing either get destroyed or consumed, the Census Method is not suitable. For example, if some fruits are to be tested by tasting each fruit, then all the fruits will get consumed during tasting. If we want to check the tensile strength of a steel rod by stretching it till it breaks, then also the Census Method cannot be used.

28. 3.It is a time-consuming process. 4.It needs lot of manpower and proper training to the persons deployed for collection of data. 5.If the population is infinite, this method is not applicable. Sampling Method In this method a group of items called Sample is taken from the population and studied. Inference [or conclusion] about the population is drawn on the basis of the results obtained from the sample. Samples are considered to be the devices useful for learning about large masses by observing a few individuals. This method is much more widely used in practice. This method is particularly suitable when: i.The size of the population is very large or infinite. ii.Very high degree of accuracy is not needed. iii.Samples drawn are not very small. iv.Different units of the population are broadly similar to each other.

29. Objectives of Sampling 1)The information gathered from a sample survey may be used to test hypothesis about the population from which the sample is drawn. 2)Sample surveys are also conducted to test the accuracy of the results obtained by a Census. After the Population Census, such surveys are undertaken. 3)To get necessary information to fulfil some specific purpose, Sample Surveys are conducted. Example - Social, economic and business surveys. 4)Such surveys are undertaken to make inferences about the nature of the parent population. The characteristics of parent population can be found from a sample study, which will save money, time and energy. 5)Sample surveys are undertaken to enquire about the condition of the universe continually. Quality control and surveys in medical science fulfil this objective

30. Advantages of Sample Investigation 1.Reduced cost 2.Greater speed 3.Greater scope 4.Detailed enquiry and greater accuracy 5.Administrative convenience 6.It is the only method in many cases Example – testing of blood Shortcomings of Sample Investigation 1)Illusory conclusions 2)Representative sample 3)Specialized knowledge required 4)Impossibility to frame a sample

31. Methods of Sampling

32. Simple Random Sampling Method Merits 1.This is a very simple method 2.This method is free from personal bias of the investigator 3.Each and every item of the population has equal chances of being selected 4.The universe gets fairly represented by the sample Demerits 1.Proportionate representation of different items in the population may not be possible. 2.There may be occasions when only very few items are to be included in the sample. For example, if an intensive study of cities is to be made, and only 4 or 5 cities are to be covered, then random sampling will not be possible.

33. 3.If the size of the sample is small, and there is great variability in the universe, the sample will not be a true representative of the universe. 4.If the units of the universe are spread over a large area, the investigation will then be a difficult job. If some units are left out, it will not be a true random sample. Restricted Random Sampling Restricted Random Sampling is a special type of random sampling. It is mainly used: i.When the data is not homogeneous. In this case, stratified sampling or cluster sampling is used. ii.When a short-cut method of obtaining a virtually random sample is required. In this case systematic sampling is used.

34. Stratified Sampling In this method units are sampled at random from each of these strata. The sample, which is the set of all the sampling units drawn from each stratum, is called a stratified sample and the technique of drawing the sample is termed as stratified random sampling. Merits 1.This method is most effective in dealing with highly skewed groups such as income data or retail sales. 2.The method ensures better representation of the characteristics of group in the sample. 3.Stratified sampling ensures greater accuracy. 4.Stratified samples are more concentrated geographically. Thus, the time and expenses of interviewing may be considerably reduced.

35. 5.On the basis of diverse characteristics of the population, a comparative analysis of the data becomes possible. 6.The units from the different strata may be selected in such a way that all of them are localized in one geographical area. 7.For a non-homogeneous population a properly stratified sample may yield more reliable results than a simple random sample of the same size. Demerits 1.Judgment of the investigator used in dividing the universe into strata may affect the accuracy of the results and the results may be misleading. 2.This method is suitable only when there is a complete knowledge about the diverse characteristics of the population. Therefore, the method has limited scope.

36. 3.When the size of population is small, it is difficult to classify it into small groups: i.If proper stratification of the population is not done, the sample will have an effect of bias. If different strata of a population overlap each over, it is difficult to draw a representative sample. ii.It is a deliberate attempt to make the sample which should contain representative items. Success in such an attempt is not an easy thing. iii.In disproportionate stratification, weights are to be assigned to different strata, and this may lead to some bias.

37. Systematic Sampling A systematic sample is one in which each sample element has a known and equal probability of selection. Steps to Select a Systematic Sample 1.Find the sampling interval by the formula: Number of units in the Population Sampling interval= Desired sample size 2.Select a random number between 1 and the sampling interval figure. This identifies the first element on the universe list to be included in the sample. 3.Add the sampling interval to the serial number of the random number selected in step 2. Total gives the serial number of the second element in the universe list to be included in the sample. 4.Systematic sampling has the advantage over simple random sampling that needs less time and sometimes results in lower costs.

38. Non-random Sampling (i) Judgment sampling or purposive sampling, (ii) Quota sampling, (iii) Convenience sampling. Judgment/ Purposive or Deliberate Sampling - individual items of a sample by the investigator consciously using his own judgment. Merits 1.If the number of items in the universe is small, some items of important characteristics are likely to be left out in other methods. 2.When small sample is to be drawn. 3.When some known characteristics of the universe are to be intensively and carefully studied. 4.It is appropriate for pilot survey.

39. Demerits 1.The selection of sample items may be affected by individual bias. Hence sample may not be a true representative of the population. 2.As selection of items is not subject to chance or probability, it is difficult to calculate correct sampling errors. 3.Sample estimates have less guarantee of accuracy, therefore, this method of purposive sampling is not in much use. 4.In selecting items inclination becomes more important than judgment. 5.No matter how excellent a judgment sample may be, the results are not measurable against a probability distribution to determine the reliability of the sample. The judgment sample is also severally limited by the fact that the results cannot be compared to the results of other sampling methods.

40. Quota Sampling A kind of judgment sampling and is commonly used in surveys of political, religious and social opinion. The following three steps are followed in this method: 1.Universe or population is classified into various groups on the basis of different characteristics such as income or age or sex or religion. 2.Quotas are fixed for each group, such as how many units are to be taken from low income group, how many units are to be taken from middle income group etc. for the sample. 3.According to the prescribed quotas for various groups, the investigator choose the units as per his discretion.

41. Merits and Demerits of Quota Sampling Merits 1.This method is mostly used in marketing research studies and public opinion studies. 2.This method saves time and cost. Demerits 1.This method is not very popular because it allows some bias and prejudice to enter into the process of selection. 2.The results obtained are not very accurate.

42. Convenience Sampling This method is quite different from the other two methods of non-random sampling viz., Judgment sampling and Quota sampling. In this method, a part of the population, i.e., chunk is selected according to the convenience of the investigator. For example, to study the smoking habits of the college students, the investigator may select one or more than one college situated in this neighborhood.

43. Merits and Demerits of Convenience Sampling Merits This method is suitable when: The universe is not clearly defined. Sampling unit is not clear. Complete source list is not available. Demerits Results obtained are not satisfactory because the results may contain the bias of the investigator. The results do not truly represent the universe.