BUSINESS STATISTICS
Lesson 1
INTRODUCTION
Statistics is not a new discipline but is as old as the human activity itself. In the olden days, it was considered as the ‘science of statecraft’ and was regarded as a by-product of the administrative activity of the State thereby limiting its scope. The governments in those days used to keep records of population, birth, deaths, etc., for administrative purposes. In fact, the word ‘statistics’ seems to have been derived from the Latin word ‘status’ or Italian word ‘statista’ or the German word ‘Statistik’ each of which means a political state. Statistical methods are now widely used in various diversified fields such as agriculture, economics, sociology, business management, etc.
MEANING OF STATISTICS
The word ‘statistics’ has been used in a variety of ways. Sometimes it is used in the plural sense to refer to numerical statements of facts or data. On the other hand it is also used in the singular sense to refer to a subject of study like any other subject such as mathematics, economics, etc. For instance, when we refer to a few ‘statistics’ relating ‘to our country like – there are 932 females per 1,000 males in India, the per capita national product at current prices has increased from Rs. 246 in 1950-51to Rs. 2,596 in 1985-86 here we are using the word statistics in the plural sense (meaning data). To prepare these numerical statements, one must be familiar with those methods and techniques which are used in data collection, organisation, presentation, analysis and interpretations. A study of these methods and techniques is the science of statistics. The use of the word statistics here is in the singular sense. In this sense the word statistics means statistical methods or the science of statistics. Now let us study in detail about these two approaches.
Statistics Defined in Plural Sense
In its plural sense, statistics means data or numerical figures pertaining to any given situation or a phenomenon.
To Bowley statistics “numerical statements of facts in any department of enquiry placed in relation to each other.”
According to Yule and Kendall statistics means “quantitative data affected to a marked extent by multiplicity of causes.”
A more comprehensive definition of statistics was given by Horace Secrist. According to him, statistics means “aggregate of facts affected to a marked extent by multiplicity of causes, numerically expressed, enumerated or estimated according to a reasonable standard of accuracy, collected in a systematic manner for a predetermined purpose and placed in relation to each other.”
Characteristics of Statistics
The above definition points out the characteristics that numerical facts must possess so that they may be called statistics.
a) They must be aggregate of facts: Individual and isolated figures cannot be called statistics. They should form a part of an aggregate of facts relating t o any particular field of enquiry. For example, Ram’s monthly income is Rs. 2,000. This is not a statistical statement. However, when we say that monthly incomes of Ram, Mohan, and Sohan are Rs. 2,000,2,500 and Rs. 3,000 respectively, they will be called statistics.
b) They are affected by multiplicity of factors: There are several factors that affect a phenomenon. For instance, the consumption of a household on any item would be affected by several factors as income, taste, education, etc. Similarly, production of wheat is affected by soil, seeds, rainfall, temperature, etc. The data relating to such phenomenon can be called statistics. But if we write the numbers one to ten along with their squares, then these figures though more than one, cannot be called statistics. These figures are not affected by multiplicity of causes.
c) They must be numerically expressed: To call a statement as statistics, it must be expressed numerically. Therefore, qualitative characteristics such as beauty, colour of eyes, etc., cannot be measured directly and hence, in general, they do not fall under the purview of statistics. We have to quantify these characteristics before they become statistics. For example, in a college we may count the number of girls having black eyes or blue eyes or brown eyes.
d) They are enumerated or estimated according to a reasonable
standard of accuracy: Statistics are either enumerated or estimated, but reasonable standards of accuracy must be maintained. The degree of accuracy will depend on the nature and the object of the study being undertaken. Suppose, as the Principal of a College you are interested in understanding the average level of performance of the students who take admission to B.Com. class. For this purpose, you must collect the marks obtained by the students at the senior secondary level. It may be done in two ways. First you can have a complete enumeration of the marks of all the students and derive their average. Secondly if the complete enumeration is not possible due to some reason, you may select a sample. On the basis of the result of the sample, you may then estimate the average level of performance of all students. Thus, statistics may be obtained by enumeration or estimation. Let us take another example to understand the point reasonable standard of accuracy. If you are estimating .the total production of food crop in India the appropriate units of measurement (or the level of accuracy) may be lakhs of tons. But if you are reporting the total production of gold, the appropriate unit of measurement may be kilograms. Thus, degree of accuracy depends on nature and objective of the study.
e) They must be collected in a systematic manner for a predetermined
purpose: The data should be collected in a systematic manner. Data collected in a haphazard manner will not serve many purposes. The purpose for which data is collected, must be decided in advance. The purpose should be specific and well defined. If the purpose of the enquiry is not specified, either we may collect too much or too little data.
f) They must be placed in relation to each other: The numerical facts should be comparable if they are to be called statistics. For instance, statistics on production and export of an item during a year are related. What they put together are statistics. But if you have three figures: 1) production of rice in India in 1986, 2) the number of children born in USA in 1987, and 3) the number of cars registered in UK in 1988. These figures may be facts alright, but taken together they cannot be called statistics as they have no relation among themselves.
Thus, all statistics are numerical statements of facts but all
numerical statements of facts are not statistics. They will be called
statistics only if the above characteristics are present in them.
Statistics Defined in Singular Sense
Numerical information must be collected, organised, presented, analysed and interpreted if it has to be used for making wise decisions. We require methods that help us in this regard. Thus, statistics, when used in the singular sense, has been defined as a body of methods which provides tools for data collection, analysis and interpretation. Here too, different writers have interpreted statistics differently. Now let us also discuss about some of these definitions. Bowley, for instance, has given a number of definitions. But none of them is comprehensive. They in fact point to the development of science of statistics over time. Some of these definitions are:
i) Statistics may be called the science of counting.
ii) Statistics may rightly be called the science of averages.
iii) Statistics is the science of measurement of social organism, regarded as a whole in all manifestations.
Croxton and Cowden have given a simple and precise definition of statistics. According to them “statistics may be defined as the collection, presentation, analysis and interpretation of numerical data.”
The definition given by Selligrnan is equally simple but comprehensive.
According to him “statistics is the science which deals with the methods of collecting, classifying, presenting, comparing and interpreting numerical data collected to throw some light on any sphere of enquiry.”
The last two definitions are quite precise, comprehensive, and point out the scope of statistical methods. The science of statistics teaches us the methods and techniques which are required for 1) collection of data, 2) classification and tabulation of data, 3) presentation of data, 4) analysis of data, and 5) interpretation of data.
Thus, from the above discussion, we can conclude that the word ‘statistics’ may be used either in a plural sense to refer to data or in singular sense to refer to a body of methods for making wise decisions in the face of uncertainty.
FUNCTIONS OF STATISTICS
The important functions of statistics are:
1) To present facts in a proper form: Statistical methods present general statements in a precise and definite form. For example, you may say that in India average yield of cotton per hectare is 180 Kg. This statement is more precise and convincing than saying that the average yield of cotton in India is very low.
2) To simplify unwieldy and complex data: Statistical methods simplify unwieldy and complex data to make them understand easily. The raw data is often unintelligible. One cannot grasp their characteristics unless the data is classified according to some common characteristics, Suppose, you are given the weekly wages of 1,000 workers in a factory. You will not be in a position to draw any inference from the data unless they are condensed through classification such as the following:
Weekly Wages (Rs.) No. of Workers
Below-600 100
600-700 200
700-800 400
800-900 200
Above 900 100
Total 1000
3) To provide techniques for making a comparison: The primary purpose of statistics is to facilitate a comparative study of different phenomena either over time or space, For instance, the estimation of national income is not done for its own sake. But it is done to compare the income over time to get an idea of whether the standard of living of people is rising or not. Suppose, as compared to 2015, the per-capita income in India has increased by 10% in 2016. On the basis of this information, we shall be in a position to throw some light on the standard of living of an Indian in 2016.
4) To study the relationship between different phenomena: Statistical measures such as correlation and regression are used to study relationships between variables. Such relationships are important for making decisions. For instance, you may find a relationship between the demand of a product and its, prices. In general, if the prices rise, the demand for the product is likely to decline.
5) To forecast future values: Some of the statistical techniques are used or forecasting future values of a variable. O n the basis of sales figures of the last 10 years, a marketing manager can estimate the likely demand for his product during the next year.
6) To measure uncertainty: With the help of probability theory, you can measure the chance of occurrence of uncertain events. Probability concepts are quite useful in decision-making. Suppose, if you are interested in estimating the chance of your passing the B.Com examination, you may get an idea about it by studying the pass percentages of students during the last 10 years.
7) To test a hypothesis: Statistical methods are extremely useful in formulating and testing hypotheses and for the development of new theories. For instance, a company is desirous of knowing the effectiveness of its new drug to control malaria. It could do so by using a statistical technique called Chi-square Test.
8) To draw valid inferences: Statistical methods are also useful in drawing inferences regarding the characteristics of the universe (population) on the basis of sample data.
9) To formulate policies in different fields: Statistical methods are very useful in formulating various policies in social, economic, and business fields. The Government, for instance, utilises vital statistical data for formulating family planning programme. Similarly, the government utilises the information on consumer price indices for granting dearness allowance to its employees.
IMPORTANCE OF STATISTICS
In the ancient times statistics was used as the science of statecraft only. Data on a wide range of activities such as population, births and deaths we recollected by the State for administrative purposes. However, in recent years,the scope of statistics has widened considerably to bring to its fold social and economic phenomena. The developments in the statistical techniques over the years also widened its scope considerably. It is no longer considered to be a by-product of the administrative setup of the State but now it embraces practically all sciences, social, physical, and natural sciences. As a matter of fact, now statistics finds its applications in various diversified fields such as agriculture, business and industry, sociology; economics etc. Thus, these days statistics finds its application in almost all spheres of human activity.
Statistics and State
In earlier times, the role of the State was confined to the maintenance of law and order. For that purpose, it used to collect data relating to manpower,crimes, income and wealth, etc., for formulating suitable military and fiscal policies. But the role of, State has enlarged considerably with the inception of the concept of Welfare State. Thus, today statistical data relating to prices, production, consumption, income and expenditure, etc., are extensively used by the governments world over for formulating their economic and other policies. To raise the standards of living of its population, developing countries such as India are following the policy of planned economic development. For that purpose, the government must base its decisions on correct and sound analysis of statistical data. For instance, in formulating its five-year plans, the government must have an idea about the availability of raw materials, capital goods, financial resources, the distribution of the population according to various characteristics such as age, sex, income, etc., to evolve various policies.
Statistics and Economics
Statistical analysis is immensely useful in the solution of a variety of economic problems such as production, consumption, distribution, etc. For example, an analysis of data on consumption may reveal the pattern of consumption of various commodities by different sections of the society. Data on prices, wages, consumption, savings and investment, etc., are vital in formulating various economic policies. Likewise, data on national income and wealth are useful in formulating policies for reducing disparities of income. The use of statistics in economics has led to the formulation of several economic laws such as Engel’s Law of Consumption, Law of Income Distribution, etc. Statistical tools of index numbers, time series analysis, regression analysis, etc., are vital in economic planning. For instance, the consumer price index is used for grant of dearness allowance (DA) or bonus to workers. Demand forecasting could also be made by using time series analysis. For testing various economic hypotheses, statistical data is now being increasingly used.
Statistics in Business and Management
With the growing size and increasing competition, the activities of modern business enterprises are becoming more complex and demanding. The separation of ownership and management in the case of big enterprises has resulted in the emergence of professional management. The success of managerial decision-making depends upon the timely availability of relevant information much of which comes from statistical data. Statistical data has, therefore, been increasingly used in business and industry in all operations like sales, purchases, production, marketing, finance, etc. Statistical methods are now widely applied in market and production research, purchase,finance, investment policies, personnel, quality control, economic forecasting, auditing and many other fields. One element common to all problems faced by managers is the need to make decisions under uncertainty. And statistical methods provide techniques to deal with such situations. It is, therefore, not surprising when Wallis and Roberts say that “statistics may be regarded as a body of methods for making wise decisions in the face of uncertainty.”
LIMITATIONS OF STATISTICS
In spite of its important functions, statistics has its limitations too. These limitations should be kept in mind while using the various statistical methods.Now, we shall discuss some of the limitations of statistics.
1) Statistics deals only with the quantitative facts: Statistics deals with facts which are expressed in numerical terms. Therefore, those phenomena that cannot be described in numerical terms do not fall under the scope of statistics. Beauty, colour of eyes, intelligence, etc., are qualitative characteristics and hence cannot be studied directly. These characteristics can be studied only indirectly, by expressing them numerically after assigning particular scores. For example, we can study the level of intelligence of a group of persons by using intelligence quotients (I.Qs).
2) Statistics does not deal with individuals: Since statistics deals with aggregate of facts, a single and isolated figure cannot be regarded as statistics. For example, the height of one individual is not of much relevance but the average height of a group of people is relevant from statistical point or view. In this context, you may recall the definition given by Secrist here.
3) Statistical laws are not exact: Unlike the laws of natural sciences,statistical laws are not exact. They are true under certain conditions and always some chance factor is associated with them for being true. Therefore, conclusions based on them are only approximate and not exact. They cannot be applied universally. Laws of pure sciences like physics and Chemistry are universal in their application.
4) Statistical results are true only on an average: Statistical methods reveal only the average behaviour of a phenomenon. The average income of employees of a company will, therefore, not throw much light on the income of a specific individual. They are, therefore, useful [or studying a general appraisal of a phenomenon.
5) Statistics is only one of the methods of studying a problem: A problem can be studied by several methods. Statistical methods arc only one of them. Under all circumstances, statistical tools do not provide the best solution. Quite often it is necessary to consider a problem in the light of social considerations like culture, region, etc. Therefore, statistical conclusions need to be supplemented by other evidences.
6) Statistics can be misused: The various statistical methods have their own limitations. If used without caution they are subject to wrong conclusions. So one of the main limitations of statistics is that, if put into wrong hands, it can be misused. This misuse can be, at times, accidental or intentional. Many government agencies and research tempted to use statistics to misrepresent the facts to prove their own point of view. Suppose you are told that during a year the number of car accidents in a city by women drivers is 10 while those committed by men drivers is 40. On the basis of this information, you may conclude that women are safe drivers. If you conclude like that you are misinterpreting the information. You must know the total number of drivers of both types before you could arrive at a correct conclusion.
DISTRUST OF STATISTICS
Despite its importance and usefulness, the science of statistics is looked upon with suspicion. Quite often it is discredited, by people who do not know its real purpose and limitations. We often hear statements such as:“There are three types of lies: lies, damned lies, and statistics”. “Statistics can prove anything”. “Statistics cannot prove anything”. “Statistics are lies of the first order”. These are expressions of distrust in statistics. By distrust of statistics, we mean a lack of confidence in statistical data, statistical methods and the conclusions drawn. You may ask, why distrust in statistics? Some of the important reasons for distrust in statistics are as follows:
1) Arguments based upon data are more convincing. But data can be manipulated according to the wishes of an individual. To prove a particular point of view, sometimes arguments are supported by inaccurate data.
2) Even if correct figures are used, they may be incomplete and presented in such a manner that the reader is misled. Suppose, it has been found that the number of traffic accidents is lower in foggy weather than on clear weather days. It may be concluded that it is safer to drive in fog. The conclusion drawn is wrong. To arrive at a valid conclusion, we must take into account the difference between the rush of traffic under the conditions.
3) Statistical data does not bear on their face the label of their quality. Sometimes even unintentionally inaccurate or incomplete data is used leading to faulty conclusions.
4) The statistical tools have their own limitations. The investigator must use them with precaution. But sometimes these tools or methods are handled by those who have little or no knowledge about them. As a result, by applying the wrong methods to even correct and complete data, faulty conclusions may be obtained. This is not the fault of statistical methods, but of the persons who use them. It should be kept in mind that statistics neither proves anything nor disproves anything. It is only a tool (i.e. a method of approach) that should be used with caution and by those who are knowledgeable in the subject.
