NATURE, SCOPE AND LIMITATIONS OF STATISTICS

Introduction

The term “statistics” is used in two senses: first in plural sense meaning a collection of numerical facts or estimates—the figure themselves. It is in this sense that the public usually think of statistics, e.g., figures relating to population, profits of different units in an industry etc. Secondly, as a singular noun, the term‘statistics’ denotes the various methods adopted for the collection, analysis and interpretation of the facts numerically represented. In the singular sense, the term ‘statistics’ is better described as statistical methods. In our study of the subject, we shall be more concerned with the second meaning of the word ‘statistics’.

Definition

Statistics has been defined differently by different authors and each author has assigned new limits to the field which should be included in its scope. We can do no better than give selected definitions of statistics by some authors and then come to the conclusion about the scope of the subject.

A.L. Bowley defines, “Statistics may be called the science of counting”. At another place he defines, “Statistics may be called the science of averages”. Both these definitions are narrow and throw light only on one aspect of Statistics.
According to King, “The science of statistics is the method of judging collective, natural or social, the phenomenon from the results obtained from the analysis or enumeration or collection of estimates”.

Many a time counting is not possible and estimates are required to be made. Therefore, Boddington defines it as “the science of estimates and probabilities”. But this definition also does not cover the entire scope of statistics. The statistical methods are methods for the collection, analysis, and interpretation of numerical data and form a basis for the analysis and comparison of the observed phenomena.

In the words of Croxton &Cowden, “Statistics may be defined as the collection, presentation, analysis, and interpretation of numerical data”.

Horace Secrist has given an exhaustive definition of the term statistics in the plural sense. According to him:

“By statistics, we mean aggregates of facts affected to a marked extent by a 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”.

This definition makes it quite clear that as numerical statement of facts, ‘statistic’ should possess the following characteristics:

1. Statistics are aggregate of facts
A single age of 20 or 30 years is not statistics, a series of ages are. Similarly, a single figure relating to production, sales, birth, death etc., would not be statistics although aggregates of such figures would be statistics because of their comparability and relationship.

2. Statistics are affected to a marked extent by a multiplicity of causes
A number of causes affect statistics in a particular field of inquiry, e.g., in production statistics are affected by climate, soil, fertility, availability of raw materials and methods of quick transport.

3. Statistics are numerically expressed, enumerated or estimated
The subject of statistics is concerned essentially with facts expressed in numerical form—with their quantitative details but not qualitative descriptions. Therefore, facts indicated by terms such as ‘good’, ‘poor’ are not statistics unless a numerical equivalent is assigned to each expression. Also, this may either be enumerated or estimated, where actual enumeration is either not possible or is very difficult.
4. Statistics are numerated or estimated according to reasonable standard of accuracy
Personal bias and prejudices of the enumeration should not enter into the counting or estimation of figures, otherwise, conclusions from the figures would not be accurate. The figures should be counted or estimated according to reasonable standards of accuracy. Absolute accuracy is neither necessary nor sometimes possible in social sciences. But whatever standard of accuracy is once adopted, should be used throughout the process of collection or estimation.
5. Statistics should be collected in a systematic manner for a predetermined purpose
The statistical methods to be applied for the purpose of inquiry since figures are always collected with some purpose. If there is no predetermined purpose, all the efforts in collecting the figures may prove to be wasteful. The purpose of a series of ages of husbands and wives may be to find whether young husbands have young wives and the old husbands have old wives.
6. Statistics should be capable of being placed in relation to each other
The collected figure should be comparable and well-connected in the same department of inquiry. Ages of husbands are to be compared only with the corresponding ages of wives, and not with, say, heights of trees.

Functions of Statistics

The functions of statistics may be enumerated as follows :
(i) To present facts in a definite form: Without a statistical study our ideas are likely to be vague, indefinite and hazy, but figures help as to represent things in their true perspective. For example, the statement that some students out of 1,400 who had appeared, for a certain examination, were declared successful would not give as much information as the one that 300 students out of 400 who took the examination were declared successful.
(ii) To simplify unwieldy and complex data: It is not easy to treat large numbers and hence they are simplified either by taking a few figures to serve as a representative sample or by taking average to give a bird’s eye view of the large masses. For example, complex data may be simplified by presenting them in the form of a table, graph or diagram, or representing it through an average etc.
(iii) To use it as a technique for making comparisons: The significance of certain figures can be better appreciated when they are compared with others of the same type. The comparison between two different groups is best represented by certain statistical methods, such as average, coefficients, rates, ratios, etc.

(iv) To enlarge individual experience: An individual’s knowledge is limited to what he can observe and see; and that is a very small part of the social organism. His knowledge is extended n various ways by studying certain conclusions and results, the basis of which are numerical investigations. For example, we all have a general impression that the cost of living has increased.
But to know to what extent the increase has occurred, and how far the rise in prices has affected different income groups, it would be necessary to ascertain the rise in prices of articles consumed by them.
(v) To provide guidance in the formulation of policies: The purpose of statistics is to enable correct decisions, whether they are taken by a businessman or Government. In fact, statistics is a great servant of business in management, governance and development. Sampling methods are employed in the industry in tacking the problem of standardization of products. Big business houses maintain a separate department for statistical intelligence, the work of which is to collect, compare and coordinate figures for formulating future policies of the firm regarding production and sales.
(vi) To enable measurement of the magnitude of a phenomenon: But for the development of the statistical science, it would not be possible to estimate the population of a country or to know the quantity of wheat, rice and other agricultural commodities produced in the country during any year.
Importance of Statistics
These days statistical methods are applicable everywhere. There is no field of work in which statistical methods are not applied. According to A L. Bowley, ‘A knowledge of statistics is like a knowledge of foreign languages or of Algebra, it may prove of use at any time under any circumstances”. The importance of the statistical science is increasing in almost all spheres of knowledge, e g., astronomy, biology, meteorology, demography, economics, and mathematics. Economic planning without statistics is bound to be baseless.
Statistics serve in the administration, and facilitate the work of formulation of new policies. Financial institutions and investors utilize statistical data to summaries the past experience. Statistics are also helpful to an auditor when he uses sampling techniques or test checking to audit the accounts of his client.

Limitations of Statistics

The scope of the science of statistic is restricted by certain limitations :
1. The use of statistics is limited to numerical studies: Statistical methods cannot be applied to study the nature of all type of phenomena. Statistics deal with only such phenomena as are capable of being quantitatively measured and numerically expressed. For, example, the health, poverty, and intelligence of a group of individuals cannot be quantitatively measured, and thus are not suitable subjects for statistical study.
2. Statistical methods deal with population or aggregate of individuals rather than with individuals. When we say that the average height of an Indian is 1 meter 80 centimeters, it shows the height, not of an individual but as found by the study of all individuals.
3. Statistical relies on estimates and approximations: Statistical laws are not exact laws like mathematical or chemical laws. They are derived by taking a majority of cases and are not true for every individual. Thus the statistical inferences are uncertain.

4. Statistical results might lead to fallacious conclusions by deliberate manipulation of figures and unscientific handling. This is so because statistical results are represented by figures, which are liable to be manipulated. Also, the data placed in the hands of an expert may lead to fallacious results. The figures may be stated without their context or may be applied to a fact other than the one to which they really relate. An interesting example is a survey made some years ago which reported that 33% of all the girl students at John Hopkins University had married University teachers. Whereas the University had only three girls student at that time and one of them married to a teacher.

Distrust of Statistics

Due to limitations of statistics, an attitude of distrust towards it has been developed. There are some people who place statistics in the category of lying and maintain that, “there are three degrees of comparison in lying-lies, dammed lies and statistics”. But this attitude is not correct. The person who is handling statistics may be a liar or inexperienced. But that would be the fault not of statistics but of the person handling them.
The person using statistics should not take them at their face value. He should check the result from an independent source. Also, only experts should handle the statistics otherwise they may be misused. It may be noted that the distrust of statistics is due more to the insufficiency of knowledge regarding the nature, limitations, and uses of statistics than to any fundamental inadequacy in the science of statistics. Medicines are meant for curing people, but if they are unscientifically handled by quacks, they may prove fatal to the patient. In both the cases, the medicine is the same; but its usefulness or harmfulness depends upon the man who handles it.
We cannot blame medicine for such a result. Similarly, if a child cuts his finger with a sharp knife, it is not a knife that is to be blamed, but the person who kept the knife at a place that the child could reach it. These examples help us in emphasizing that if statistical facts are misused by some people it would be wrong to blame the statistics as such. It is the people who are to be blamed. In fact, statistics are like clay which can be molded in any way.