According to Lord Kalvin, “When you can measure what you are speaking about and express it in numbers, you know something about it, but when you cannot measure it and you cannot express it in numbers, your knowledge is of meager and unsatisfactory kind.” Modern age is the age of statistics. h.G. Wells’ prediction that, “Statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write,” has become true. Today our culture has become a statistical culture. Every citizen finds statistics in newspapers, magazines, advertisements in T.V. and radio etc. The figures relating to the various aspects of his life-social, political and economic – represent and support the observed facts or situations. The reader analyses the figures and arrives at certain conclusions. For example, a prospective investor is interested in the profitability of the business enterprise and in its ability to meet debt obligations. He analysis the income statement and balance sheet of the enterprise for a number of years. Such analysis helps him to decide whether to invest or not. With the advent of globalization and information technology every aspect, whether it relates to natural phenomena, politics, economics, management, etc., should be stated in clear and precise form.
Moreover, many have seen statistics as a device to achieve the degree of precision in the concept and theories of social sciences. In nut shell, if we analyze the way in which statistics is looked at, we broadly find two categories, one refers statistics as a set of figures and the other connotes it as a set of techniques.
(1) Origin and growth of Statistics
Statistics, as a subject, is as old a discipline as the human life is. The origin of statistics is revealed by the word itself which is said to have been derived either from the Latin Word ‘Status’ or the Italian word ‘statista’ or the German word ‘Statistik’ which means political state. Statistics originated from two dissimilar areas; political states and games of chance. These two areas are also called as two peculiar disciplines – oe primarily descriptive and the other essentially analytical. The former is concerned with the collection of data and the latter is associated with the concept of chance and probability. Statistics was used as a by-product of administrative activity. Govt. maintains records of various types of numerical data on population, births, deaths, literates, illiterates, employment, unemployment, Income, Taxes, Imports, exports etc. Statistics was used as a technique to collect periodical data to ascertain the manpower and material strength for military and fiscal purposes. In ancient Egypt, census of population and wealth was conducted for the erection of pyramids. In India statistics was an effective system of collecting data about 2000 years ago in ancient works of Manusmriti, Shukraniti, etc., ‘Kautily’s, Arthshastra’ describes facts and figures of Chandragupta Mauraya’s regime. ‘Din-i-akbari and Tuzuk-i-Babri also describe the system of data collection. The histories of the other countries of the world also clearly reveal the use of statistics in the administrative activities. The Old Testament contains several accounts of census taking. Ancient Babylonia and Rome gathered detailed records of population and resources. Governments began to register the ownership of land in the Middle Ages. William, the conqueror, ordered in 1086 the writing of the Domesday Book, a record of the ownership, extent, and value of the lands of England. This was England’s first statistical abstract.
The theoretical development of statistics has its origin in the mid-seventeenth century when many gamblers and mathematicians of France, Germany and England are credited for its development. Pascal and P. Fermat, the two great French mathematicians made innovative efforts to solve the famous ‘Problem of point’ which was posed by the famous French gambler Chevalier De Mere. Their contribution became the foundation stone of the Science of Probability. James Bernoulli (1654-1705) developed the ‘Normal Curve’. The use of ‘Statistics’ was popularized by Sir John Sinclair in his work Statistical Account of Scotland (1791-1799). Modern Theory of Statistics was gradually developed during the 18th, 19th and 20th centuries mathematicians. Laplace (1749-1827) gave the principles of ‘Least squares’ and established the ‘Normal Law of Errors’. The famous statisticians Sir Francis Galton (1822-1911), Karl Pearson (1857-1936) and W.S. Gosset contributed to the study of Regression Analysis, Correlation Analysis as well as Chi-square test of Goodness of Fit, and t-test respectively. R.A. Fisher, who is called “Father of Statistics”, has developed statistics for use in genetics, biometry, agriculture, psychology and education. He also contributed to the Estimation Theory, Sampling Distribution, Analysis of Variance (ANOVA) and design of experiments. Thus Prof. Ronald A. Fisher is the real exponent in the development of the ‘Theory of Statistics”.
The tremendous growth in the use of statistics is primarily due to two reasons; increased demand of statistics and decreasing cost of statistics.
(2) Need or Importance of Statistics in Statistical Analysis
Statistical techniques are of universal applicability. These techniques are used in almost all fields of knowledge e.g. social science, medical science, physical science, natural science and so on. So far as the field of economics is concerned, this technique has become so important that even the understanding of Elementary Economics requires knowledge of statistics. In this regard Marshall opined, “Statistics are the straw out of which I like every other economist have to make bricks.” Similarly C.E. Engeberg remarked, “No economist would attempt to arrive at a conclusion concerning production or distribution of wealth without an exhaustive study of statistics”.
However, the significance of statistical analysis is on the basis of the following grounds:
- It provides a tool for scientific analysis.
- It provides solution for various business problems.
- It enables proper allocation of resources.
- It helps in minimizing waiting and servicing cost.
- It enables the management to decide when to buy and how to buy.
- It helps in choosing an optimum strategy.
- It renders great help in the optimum allocation of resources.
- It facilitates the process of decision making.
- Management can know the reactions of the integrated business system through quantitative analysis.
Meaning of Statistics
According to Tate, “You can compute statistics by statistics from statistics.” Therefore the word statistics has three aspects; (a) Statistics (b) Statistical science (c) Statistical measurement.
According to Oxford Dictionary, “Statistics has two meanings, as in plural sense and singular sense. In plural sense, it means a systematic collection of numerical facts and in singular sense, it is the science of collecting, classifying and using statistics.”
Definition of Statistics
It is not an easy job to define statistics. The reason being that no two statisticians agree on the limits and scope of statistics. According to dictionary meaning of Statistics – it refers to the singular sense where as numerical data refers to the plural sense. It is by this reason to the singular sense where as numerical data refers to the plural sense. It is by this reason that some authors have defined the word in the plural form i.e., numerical data whereas others have defined it in the singular form i.e. statistical method. Thus the term ‘statistics’ is used in two senses.
Statistics In the Plural Sense or Statistical Data
In plural sense, it means a collection of numerical facts. It is in this sense that the public usually think of statistics, say figures concerned with population or production of wheat in India in different years or number of man-hours lost in industry in a specific year. Secondary Statistics e.g., percentages, averages and coefficients derived from numerical facts, are also included in the term statistics in this sense.
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 it and then to conclude its definition.
A.L. Bowley has given as series of definitions. Some lay emphasis on one aspect and others on other aspect. At one place Bowley says “Statistics, may be called the science of counting”. 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. Bowley himself realized this drawback and stated that statistics cannot be confined to any one sense.
Webster defined Statistics as “The classified facts respecting the condition of the people in a state- especially those facts which can be stated in numbers or in tables of numbers or in any tabular or classified arrangement”.
This definition has limited the scope of statistics. It relates statistics only to those facts which are concerned with the condition of the people in a state. This concept does not suit the modern world. Furthermore, this definition is not exhaustive because it does not take into account all aspects of human activity. The definition given by Secrist is regarded as the most exhaustive.
According to Horace Secrist: ‘By statistics we mean aggregate of facts affected to a marked extent by multiplicity of cause, numerically expressed, enumerated or estimated according to reasonable standard of accuracy, collected in a systematic manner for a predetermined purpose and placed in relation to each other.
Characteristics or Features of Statistics in the Plural sense or Numerical Data
The basic feature of statistics as a quantitative or numerical data run as follows:
Aggregate of Facts
Statistics does not refer to a single figure but it refers to a series of figures. A single weigh of 50 kg is not statistics but a series relating to the weight of a group of persons is called statistics. It means, all those figures which relate to the totality of facts are called statistics. Such figures should also be comparable.
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 on a phenomenon and effects of different sets of factors separately. In nutshell, we can say that statistics are affected considerably by multiply causes e.g. prices are affected by conditions of demand, supply, money supply, imports, exports and various other factors.
Another characteristic of statistics is that qualitative expressions like young, old, good, bad etc. are not statistics. To all statistics a numerical value must be attached. For example, the statements like “There are 932 females per 1,000 statements must contain figures so that they are called numerical statements of facts. Furthermore, such numerical expressions are precise, meaningful and convenient form of communication.
Enumerated or Estimated according to Reasonable Standards of Accuracy
In case the numerical statement are precise and accurate, then these can be enumerated. But in case the number of observations is very large, in that case the figures are estimated. It is obvious that the estimated figures cannot be absolutely accurate and precise. The accuracy, of course, depends on the purpose for which statistics are collected. There cannot be uniform standard of accuracy for all types of enquiries. Thus enumeration refers to exact count as there are ten students of statistics. It is 100% accurate statement. On the other hand, estimation refers to round about figure e.g. we say that two lakhs people participated in the Rally. There can be a few hundreds more or less. Thus statistical results are true only on average.
Collected in a Systematic Manner
For accuracy or reliability of data, the figures should be collected in a systematic manner. If the figures are collected in a haphazard manner, the reliability of such data will decrease. Thus for reasonable standard of accuracy, the data should be collected in a systematic manner, otherwise the results would be erroneous.
Collected for a Pre-determined Purpose
The usefulness of the data collected would be negligible if the data are not collected with some pre-determined purpose. The figures are collected with some objective in mind. The efforts made without any set objective would render the collected figures useless. Thus the purpose of collecting data must be decided well in advance. Besides, the objective should be concrete and specific. For example, if we want to collect data on prices, then we must be clear whether we have to collect whole-sale or retail prices. If we want data on retail prices, then we have to see the number of goods required to serve the objective.
Placed in Relation to each other
The collection of data is generally done with the motive to compare. If the figures collected are not comparable in that case, they lose a large part of their significance. It means the figures collected should be homogeneous for comparison and not heterogeneous. In case of heterogeneity, the figures cannot be placed in relation to each other.
Singular Definitions or Statistical Methods
In a singular sense, statistics implies statistics methods. Thus, it is a body or technique of methods relating to the collection, classification, presentation, analysis and interpretation of information. In a sense, statistics can be defined as:
According to Boddington: “Statistics is the science of estimates and probabilities.”
According to Bowley, “Statistics may rightly be called the science of averages.”
According to W.I. King, “Science of statistics is the method of judging collective natural or social phenomena from the results obtained by the analysis of an enumeration or collection of estimates.”
According to P.H. Karmel, “The subject statistics is concerned with the collection, presentation, description and analysis of data which are measurable in numerical terms.”
According to Seligman, “Statistics is the science which deals with the method of collecting presenting, comparing and interpreting numerical data-collected to throw some light on any sphere of inquiry.”
Characteristics or Stages in Statistical Investigations
It is the first step in a statistical inquiry. The collection part is the backbone of the inquiry. If the collection of data is not in proper form, in that case the conclusions drawn can never be reliable. The source of data may be primary i.e., collected directly, or the data may be secondary i.e., available from existing published sources. The first hand collection of data is one of the most difficult and important tasks faced by the investigator.
The data collected from published sources are generally in organized form. But the figures which are collected from a survey, need organisation. The most important point in organizing a group of data is editing. This is done to correct omission, inconsistencies and wrong calculations in the survey. The classification is done to arrange the data according to some common characteristics possessed by the items. The last step in organisation is tabulation. The object of tabulation is to arrange the data in columns and rows for complete clarity as far as presentation of data is concerned. Thus organisation can be classified into three stages, (i) Editing (ii) Classification (iii) Tabulation.
After collection and organisation, the data should be presented. If the data are presented in an orderly manner, the statistical analysis gets facilitated. As far as the presentation of data is concerned. The classified data are to be presented in such a way that it becomes easily understandable.
Once the data are collected, organized and presented, the next step is that of analysis. The main objective of analysis is to prepare data in such a fashion so as to arrive at certain definite conclusions. The methods most commonly used are measures of Central Tendency and are called measures of the first order. Measures of Dispersion are called measures of the second order. Skewness, Correlation, Regression, Interpolation etc. are called measures of the third order. The analysis of facts based on observation is termed as (a) Scientific analysis, (b) Numerical analysis, (c) empirical analysis.
The last stage of statistical investigation is to derive the results and give comments on the inquiry in question. Interpretation means to draw conclusions from the data collected and analyzed. The interpretation of data is not an easy job and requires a high degree of skill and experience. If the analyzed data are not properly interpreted, the whole object of the inquiry may be erroneous. It is only correct interpretation which may lead to reliable conclusions.
Thus it is clear that statistics is a science of taking decisions on the basis of numerical data properly collected, organized, presented, analyzed and interpreted.
Functions / Applications of Statistics
The various applications or functions performed by statistics in modern times are discussed as under:
Simplification of Complex Facts
The foremost purpose of statistics is to simplify huge collection of numerical data. It is beyond the reach of human mind to remember and recollect the huge facts and figures. Statistical method makes it possible to understand the whole in the short span of time and in a better way.
Comparison of data is yet another function of statistics. After simplifying the data, it can be correlated or compared by certain mathematical quantities like averages, ratios, co-efficient etc. In this regard Boddington opined that the object of statistics is to enable comparison to be made between past and present results with a view to ascertain the reasons for changes which have taken place and the effect of such changes in the future.
Relationship between Facts
Statistical methods are used to investigate the cause and effect relationship between two or more facts. The relationship between demand and supply, money-supply and price level can be best understood with the help of statistical methods.
Formulation and Testing of Hypothesis
The most theoretical function of statistics is to test the various types of hypothesis an discover a new theory. For instance, by using appropriate statistical tools we can test the hypothesis whether a particular coin is fair or not, whether Indian consumers are brand loyal etc.
Measurement of Effects
Statistical methods act as a guide to measure the effect of a policy. For example, the effect of a change in bank rate or a change in incomes tax etc. can best be judged by the statistical methods.
Statistical methods are of great use to predict the future course of action of the phenomenon. It is only on the basis of statistical techniques that the planners in India prepare future estimates for production, consumption, investment etc.
Enlarges Individual Knowledge
Statistical methods sharpen the faculty of rational thinking and reasoning of an individual. It is a master-key that solves the problems of mankind in every sphere of life. Thus, Whipple has rightly opined that statistics enables one to enlarge his horizon.
Realization of Magnitude
Statistics facilitates the realization of the magnitude of a problem. For instance, one may say that inflation in India has been increasing very rapidly. From this statement, one is unable to understand the gravity of the problem. But, if one says that inflation is increasing by 5.5% per annum, everyone will properly realize the gravity of the problem.
To Indicate Trend Behavior
Statistics helps to indicate trend behavior of certain fields of enquiry. The statistical techniques like Analysis of Time Series, Extrapolation etc. are highly used to know the trend behavior of the enquiry in question.
Classification of Data
Classification refers to a process of splitting up the data into certain parts which helps in the matters of comparison and interpretation of the various features of the data. This is done by the various improved techniques of statistics.
To measure Uncertainty
In most of the social fields, comprising of business, commerce, economics, it becomes necessary to take decisions in the face of uncertainty and study the chance of occurrence of certain events and their effect on the policies adopted.
Scope of Statistics
The scope of statistics is studied under the following heads:
- Nature of statistics or Statistics as Science or an Art
- Subject matter of Statistics
- Relation of Statistics with other Sciences
- Limitations of Statistics.
Nature of Statistics or Statistics as science or an Art
Under nature, we study whether statistics is a science or an art. According to Tippett, “Statistics is both a science and an art”. As a science, it studies the statistics in a systematic manner. As an art, it uses statistics to solve the problems or real life.
It is a controversial subject that whether statistics is a science or an art. Science refers to a systematized body of knowledge. In general, it deals with the cause and effect relationship. It helps in drawing generalization in the form of principles or laws. The use of statistics in every science is universal. But statistics cannot be known as science. Statistics refer to certain methods which help in arriving at some laws. Design of scientific experiments and the evaluation of their results makes use of principles and practices growing out of the science of statistics.
According to Dr. Bowley, “Statistics is the science of measurement of the social organism regarded as a whole in all its manifestations.” This definition is defective. According to this definition, the scope of the science will be restricted to man and his activities.
Again according to Dr. Bowley, “Statistics is the science of counting.” This is also not correct. Statistics is not only concerned with counting but also with tabulating, summarizing, drawing graphs etc. Again the word counting gives an idea of exactness. But this is not so in statistics.
boddington defines Statistics as a “Science of estimates and probabilities.” This definition is too vague and is concerned with certain methods by which conclusion can be derived in this science but the scope of statistics is not merely confined to these things.
According to Dr. Bowley, “Statistics may rightly be called the science of averages.” This is also not correct since it takes into account only one step in the process of statistical operations.
But a noteworthy point is that statistics is not an exact science like Physics, Chemistry etc. It is because statistical phenomena are generally affected by multiplicity of causes which cannot be measured accurately. It means statistics is a science in a limited sense. It is a specialized branch of knowledge. Wallis and Roberts in their book- “Statistics -A New Approach” have stated that “Statistics is not a body of substantive knowledge but a body of methods for obtaining knowledge.”
It is a known fact that if science is a systematic knowledge then art is an action. From this point in view, statistics is also an art. In statistics, we apply various methods to obtain facts, derive conclusions and finally suggest, policy measures.
We can conclude with Tippet’s Words, “It 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 his knowledge of the field of application, e.g., economics.”
Limitations of Statistics
Although, statistics is a very useful science yet it suffers from certain limitation. According to Newsholme, “It must be regarded as an instrument of research of great value but having several limitations which are not possible to overcome and as such they need a careful attention.”
Statistics does not deal with individuals
Statistics deals only with the aggregates rather than individual items. An individual item like height of a student in a class is 5′ 6′-is not called statistics. In statistical methods, we deal with aggregates and not with a single figure. When we say that average height of a class is 5′ 8′, this individual figure refers to the aggregate of individuals. Statistics cannot be of much help for making a study of the changes which may have taken place in individual cases. Thus it is clear that statistics is concerned with aggregates and not with individual items.
Qualitative Aspect Ignored
The statistical method cannot study the nature of phenomena which cannot be expressed in quantitative form. The phenomena which cannot be expressed quantitatively, cannot be a part of the study of statistics. These characteristics include health, intelligence etc. There is no doubt that the data which cannot be quantitatively expressed, needs conversion of qualitative data into quantitative data. Thus experiments are being conducted to measure the reactions of human mind statistically. Presently there is hardly any field where statistics does not apply. One of the branch of statistics, the “Theory of Attributes” deals with qualitative data.
Statistics deals with Average
Statistical findings are true only on an average. According to W.I. King, “Statistics largely deals with averages and these averages may be made up of individual items radically different from each other.” For instance, if we may say that the average production of wheat in the last ten years is 250 quintals, it does not mean that the production of every year is equal. Production of a particular year may be less or more than the other years. Thus, statistical information is true only on an average.
Statistics can be Misused
Statistics can be misused by ignorant or wrongly motivated persons. The data used by untrained people can lead to misleading results. The statistics can be handled correctly only by those who have sufficient knowledge in statistics. It is correctly W.I. King points out, “One of the short-comings of statistics is that they do not bear on their face the label of their quality.”
Method of Studying Problem
There are many methods to solve the problem. Statistics is one of them. According to Croxten and Cowden, “It must not be assumed that the statistical method is the only method to use in research, neither should this method be considered the best attack for every problem.”
Results true only on an Average
We know that statistics is not as accurate science as other science. Similarly the statistical methods are not very precise and correct. In the same fashion, the laws of statistics are not universal like the laws of physics, Chemistry or Astronomy. The statistical laws are true only on average. Statistics are concerned with those phenomena which are affected by multiplicity of causes. In this way, statistics is less exact science as compared to other natural sciences.
Statistics is only a means
Statistics is only one of the methods of studying a problem. There are other methods of studying a problem like culture, religion, philosophy etc. Statistics is only a means and not an end. It analysis the facts and throws light on the real situation.
What is Statistical Survey
An survey or inquiry means search for knowledge. Statistical survey or statistical inquiry means search for knowledge with the help of statistical methods. Statistical survey is a technical job which requires specialized knowledge and skill. According to Giffin, “Statistical enquiries have always required considerable skill on the part of the statistician, rooted in a broad knowledge of the subject-matter area and combined wit considerable ingenuity in overcoming practical difficulties.”
Planning the Statistical Survey
A proper planning is essential before a statistical survey is conducted. Planning must precede execution. Careful planning of statistical survey is essential to get the best results at the minimum cost and time. It is very essential to consider the following points while planning a statistical survey.
- Nature of information to be collected should be decided.
- Objective of the survey should be fully known.
- Scope of the survey should be determined.
- Source of data collection or types of data to be used i.e., primary data or secondary data should be decided.
- Type of enquiry i.e., census method or sampling method, should be decided before hand.
- Unit of data collection should be defined.
- Reasonable standard of accuracy should be fixed.
- Choice of frame should be made.
- Other considerations should include whether the inquiry is (i) official or semi-official, or private (ii) initial or repitive (iii) confidential or open (iv) direct or indirect (v) regular or adhoc.
Statistical unit is the basis of collection of statistics in a statistical inquiry. These are the units in terms of which data are collected, such as, for production of sugar ‘tonnes’ for weight of persons ‘kilograms’ etc.
Unit is the basis of all these measures in which we, collect, analyses, edit and interpret the data used for the survey. These units are not the same for all the surveys but differ according to the nature and scope of enquiry. Monetary terms are measured in Rs. $ etc. Weight can be measured in gms; kgs; Tonnes etc. According to Prof. W.I. King “It is not only desirable but strictly essential that the units be accurately and unmistakably defined. Definition of units is necessary to avoid any mis-understanding and to bring homogeneity in the data. The need for defining is all the more felt because of the qualitative nature of the units and lack of standard connotations”.
Requirement of Statistical Units
- Statistical units should be simple, specific and unambiguous.
- It should be stable
- It should be comparable.
- It should be appropriate to the objective of enquiry.
- It should be precise and ascertainable.
- Statistics, 4th Edition by David Freedman, Roger Purves, and Robert Pisani
- The Complete Idiot’s Guide to Statistics, 2nd Edition by Jr., Ph.D., Robert A. Donnelly
- Principles of Statistics by M.G. Bulmer
- Statistics for Dummies by Deborah Rumsey
- Cartoon Guide to Statistics by Larry Gonick and Woollcott Smith
- Statistics Workbook For Dummies (For Dummies (Lifestyles Paperback)) by Deborah Rumsey
- Statistics (Cliffs Quick Review) by David H. Voelker, Peter Z. Orton, and Scott Adams
- Statistics: Informed Decisions Using Data (2nd Edition) by Michael Sullivan III
- Statistics, 11th Edition (Book & CD) by James T. McClave, Terry Sincich, and William Mendenhall
- Practical Statistics Simply Explained (Dover books explaining science) by Russell Langley