STATISTICS

MEANING

The term Statistics is used in two senses (1) in a narrow sense and (2) in a wise sense. In the narrow sense, the word statistics denoted some numerical data. That is, it can refer to facts which can be put into numerical form, as in the phrases unemployment statistics, statistics of industrial accidents in India. This is the meaning the man in the street gives to the word statistics. It is to be noted that the word statistics used in the sense of numerical data is a plural noun.

In the wide sense, the word statistics refers to the statistical principles and methods which have been developed for handling numerical data. Statistical methods or statistics have a very wide range. They range from the most elementary descriptive devices like comparison, which may be understood by anyone, to the highly complicated mathematical procedures which are comprehended by only the most expert theoreticians. This is the meaning in which we use the term statistics in our lessons. It is to be noted that the word statistics used in the sense of statistical principles and methods is a singular noun. Again, when we use the term statistics in the sense of statistical method it is a part of applied mathematics.

Subject-matter of statistics:

Statistics is concerned with the collection, presentation, analysis and interpretation of data which are measurable in numerical terms. It is to be noted that the facts which are dealt with in statistics, must be capable of numerical expression Croxton, Cowden and Klein have given in the following illustration in their book applied general statistics, to emphasise this point. With the information that dwellings are built of brick, stone, wood and other materials we cannot employ statistical methods. Instead, if we are given information regarding the number or proportion of dwellings constructed of each type of material, we have numerical data suitable for statistical analysis.

We saw above that statistics is concerned with the collection, presentation, analysis and interpretation of numerical data. Let us briefly examine each of these four procedures.

1. Collection: In any statistical investigation, collection of useful data is the first step. Data must be collected in a systematic manner. Data may be obtained from existing published or unpublished sources or by first hand collection.
2. Presentation — Once collected, data must be assembled into a useful form. This process is the statistical presentation of data. Usually the data are arranged in tables or represented by graphic device.
3. Analysis — By analysis of data we mean the study of the behaviour of the data. The basic characteristics of the data are studied with the help of statistical tools such as average, correlation, association.
4. Interpretation — The final step in any statistical investigation is the interpretation of the data. Interpretation consists in deriving conclusions from the analysis of the data. One who interprets the data must do it bearing in mind the limitations of the original material.

Main divisions of Statistics:

Any modern science is divided into a) pure science and b) applied science. For instance, the science of Economics is divided into a) Pure Economics and b) applied Economics. In the same way statistics as a science has been divided into two main classes a) statistical methods and b) applied statistics.

Statistical methods are concerned with the formulation of the general rules and principles applicable to the collection, classification, analysis and interpretation of data.

Applied statistics deals with the application of those rules and principles to concrete subject matter like wages, prices, trade, population. Applied statistics may consist of biometry, which deals with the measurement of living organism, psychometry, which deals with mental phenomena, vital statistics, administrative, social and economic statistics.

Applied statistics is divided into two classes 1) descriptive applied statistics and 2) scientific applied statistics.

Descriptive applied statistics deals with data which are known and which relate either to the present or to the past. For example business statistics and descriptive applied statistics as they deal with the analysis, measurement and presentation of business facts, relating to past or present. On the basis of these facts, decisions about various business problems are usually taken.

Scientific applied statistics deals with the formulation of scientific laws on the basis of quantitative data collected for descriptive purposes by the use of appropriate statistical methods. For instance, if we are able to make business forecasting by the use of some business statistics we are making use of scientific applied statistics.

Statistics as a science and as an art:

Science is a body of systematized knowledge. It studies cause and effect relationship. It is the business of science to collect facts to arrange and interpret them and to draw inferences from them. Judged by this standard, statistics is a science. For, it collects facts, arranges them and draws inferences from them.

However, Croxton, Cowden and Klein, applied general statistics have expressed the view that statistics is not a science but only a scientific method. To quote them statistics should not be thought of as a subject correlative with physics, chemistry, economics and sociology. Statistics is not a science, it is a scientific method.

Whereas science is concerned with reasoning and building up of a body of knowledge, art is concerned with giving practical application to the knowledge. For instance, when a painter uses his brush on a convas, he is acting on the basis of certain principles. Every science has got its applied side. For instance pure chemistry is the science part of chemistry and applied chemistry is the art part of chemistry. In the same way, we have got a science of statistics and also an art of statistics. Thus statistics is both light bearing and fruit bearing.

FUNCTIONS AND IMPORTANCE OF STATISTICS

Functions of statistics: As an opera glass of telescope increases the field of physical vision, statistics increases the field of mental vision. That is, statistics is able to widen our knowledge. Broadly speaking statistics performs six main functions as noted below:
1. Condensation
2. Comparison
3. Correlation
4. Correction
5. Measures results
6. Enlarges human experience

1. Condensation: Statistics simplifies unwieldy and complex mass of data. Human mind, because of its limitations, is unable to grasp the significance of a large mass of complex data. But statistical methods make those data easily intelligible and readily understandable. The complex data may be reduced to totals, average and presented either graphically or diagrammatically. These devices help us to understand the significant characteristics of the numerical data and consequently save us from a lot of mental stain. Single figures shown as averages or ratios can be grasped easily than a mass of statistical data comprising thousands of facts. In the same way, graphs and diagrams, because of their greater appeal to the eye and imagination, enable proper understanding of numerical data.
2. Comparison: Certain facts, by themselves, may be meaningless unless they are capable of being compared with similar facts at other periods of time, For instance, we collect statistics of industrial production with the primary objective of comparing them with those of the past to find out whether we have advanced or reduced, or with similar statistics collected in other countries of the world to know where we stand in the international industrial field. Some of the modes of comparison provided by statistics are totals, ratios, graphs and diagrams.
3. Correlation: Another function of statistics is to investigate the relationship between two or more phenomena. In all types of enquiries a study of the relationship between different factors is very important. For instance, the relationships between supply and demand, rainfall and agricultural yield, prices and wages, speculation and interest rate, require a very careful study. Statistics describes concisely the existence, direction, degree and nature of relationship or association between one phenomenon and another. The statistical measures generally used for this purpose are coefficient of association, coefficient of covariance.
4. Correction: In the absence of statistics our ideas are likely to be vague, hazy and indefinite. Figures help us to represent things in their true perspective. Statistics enable us to present facts in a definite and unambiguous form. For instance if we say that wholesale prices have risen very high, our knowledge about the price remains some what vague. But when we give index numbers of wholesale prices, our knowledge of price rise is definitely precise. Thus, statistics puts a stamp of precision on our vague and hazy ideas.
5. Measures results: Measuring the results of a particular policy is possible only with the help of statistical methods. For example, we have to find out whether a rise in the bank rate has affected the industries adversely or favourably. Here we have to compare the present situation with the past and find out whether the change has been beneficial or otherwise from the point of view of industries. Here it is impossible to arrive at any sound conclusion without the use of adequate statistical data. Statistics thus helps in measuring the effects of a particular policy and in arriving at a conclusion about it.
6. Enlarges human experience: Statistics makes it easier for man to perceive, describe and measure the effects of his own actions or the actions of others.

Importance of statistics

The methods of statistics are useful in an ever widening range of human activities. That is, they are useful in any field of thought in which numerical data may be had. They are helpful to planners, industrialists, bankers, insurance companies, research, social studies, and formulation of policies. There are few problems relating to business, social policy or state craft for the understanding of which statistic are not required. We have explained below the importance of statistics in various spheres.

1. Important to state: Statistics are very helpful to a state as they help in administration. Modern state makes extensive use of statistical data on various problems. In fact, the Government in most countries is the biggest collector and consumer of statistical data. The state must have accurate information regarding the number of persons living within its boundaries, the total wealth of the country, and extent of evils prevalent. This is impossible without adequate statistics. Moreover, imports and exports, production of goods and services, labour situation in the country, price fluctuations, crimes, all require statistical methods for their compilation. Again, the modern state requires numerical data for formulating economic policies, introducing social reforms and many other matters relating to day to day life. Thus, statistical methods have become quite indispensable to the modern state.
2. Importance in Economics: Statistical data and statistical methods are very helpful in the proper understanding of the economic problems and the formulation of economic policy. A theoretical economist may formulate important economic laws from empirical data or the economist may verify the validity of economic laws with the help of statistical data. Economic history can best be studied with the help of numerical facts. To find out whether a country has made economic progress or not we made use of national income statistics. The study of economic problems is specially suited to statistical treatment. For instance, a proper appreciation of the nature and magnitude of the problem of unemployment necessities knowledge about the following: Is unemployment increasing or decreasing? Is it widespread or confined to certain area? Does it affect the educated and uneducated alike? All these questions can be answered statistically and the data collected will enable us to form a correct estimate of the problem. Again, statistics, a very helpful in all the four branches of economics, consumption, production, value and distribution. Statistics of consumption enable us to find out the way in which people belonging to different income groups in the community spend their incomes. Statistics of production help in adjusting, numeral data are very useful. In distribution we provide answers to questions like How is national income calculated? How does it get distributed? These questions cannot be answered without statistics.
3. Usefulness in business: Statistics is an aid to commerce and industry. It helps the businessmen and industrialists to decide things move precisely and objectively. Statistical information is needed from the time the business is launched. At the time of the floatation of the concern, statistical data are required for the purpose of drawing up the financial plan of the proposed unit. In these days of large scale production and cut throat competition, a manufacturer must know in advance how much is to the produced, how many workers and how much raw material will be needed to produce the estimated quantity and what quality, type, size, colour, or grade of the product is to be manufactured. In short, the manufacturer must have a production plan. And he cannot frame a production plan without quantitative facts. Statistics is thus a tool of production control. Success of a business depends on accurate forecasts of sales. That is a producer or dealer should first estimate the demand for his products, analyse the possible effects of factors like changes in tastes, fashions. This is called business forecasting. Statistical methods are very helpful in business forecasts. For instance, a forecast of sales can be made by studying time series of present and prospective conditions of the concern and related business. Statistics is also useful in conducting market research by the businessmen. A skillful analysis of data on population, purchasing, power, customs of people, competition, transportation costs, should be made before launching a new product. Again, in building up and maintaining an extensive market, it is important to keep accurate records of its present and potential geographical distribution. Again cost accounting is entirely statistical in outlook and it is with the help of this technique that producers are in a position to decide about the prices of various commodities. Statistically quality control is a standard procedure for improving the quality of manufactured goods. The number of defective articles produced by a machine is recorded continuously on a chart and the statistician, looking at the chart, can tell when the production is becoming worse, and thus he maintains the quality of the manufactured articles at a uniformly high level. Statistics is also very helpful in business management. With the growing size of business enterprises centralized management of all the activities of an industrial concern from production to sales has become impossible. Separate business departments are to be created concern from production to sales has become impossible. Separate business departments are to be created on the basis of function they serve such as planning, material control, purchasing, sales promotion, accounting, personnel. For the proper execution of these functions, the management has to depend upon statistical data and accounting records. In fact, at present, many business concerns have got a separate statistical department.
4. Utility to insurance companies: Statistics is extensively used in the field of insurance. The entire working of life insurance schemes rests on the completion of life tables and computation of expectation of life from time to time. Similarly, unemployment insurance and sickness insurance depend on statistical data.
5. Usefulness to public utility concerns: Public utility concerns like railway, electricity supply companies, water works, also use statistics extensively. Statistical analysis of railway working is very useful in the extension programmes. Moreover, railway companies are facilitated in running special and additional trains in some routes on the basis of their estimated traffic. A water work is in need of a list of users of water for various purposes to fix differential rates.
6. Usefulness to bankers: Statistical methods are also useful to bankers and stock exchange brokers. A banker who intends to build up a pyramid of credit should have adequate knowledge of seasonal variations in demand for bank credit. A stock exchange broker or an investor in securities needs knowledge of seasonal variations in securities needs knowledge of interest rate, the fluctuation of investment market and other related data or strike a timely bargain.
7. Statistics and research: Statistics is an indispensable tool of research. Nowadays statistical methods are being used in research in almost every sphere. Even in the fields of medicine and public health, statistical methods are used for testing the efficiency of new medicines and new methods of treatment.