Statistics Concept, Significance and Data

 Statistics Concept, Significance and Data 

 

Definition of Statistics

There have been many definitions of the term 'Statistics' which can be broadly classified in two senses:

1. Statistics in Plural Sense

2. Statistics in Singular Sense

 

Statistics in Plural Sense

As a plural noun statistics is used for denoting numerical and quantitative information.

Thus, in plural sense, it means the same thing as data. For example, statistics of scores in a cricket match, trade related statistics, labour statistics, census statistics, godown statistics and so on.

All the quantitative observations are not statistics but those quantitative observations which satisfy certain conditions are called 'Statistics'. Also, economist Horace Secrist, defined 'Statistics' as:

"By Statistics we mean aggregates 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 a relation to each other".

According to this definition of statistics, the quantitative expression should satisfy the following conditions:

(i) Statistics are a Collection of Facts: Single or isolated numerical expressions are not statistics as they can't be compared and put in relation. For example, Rohan scored 127 runs in a match, is not statistics but 10 hatsmen scored 32. 57, 10.0 98, 15, 2, 0, 66 and 7 runs respectively are statistics. Hence, a set or a collection of observation forms statistics.

(ii) Statistics are Collected in a Suitable Order: Statistics should be collected with a suitable plan of data collection. Statistics collected without any system or order, will result in failed decisions.

(iii) Statistics are Collected for a Predefined Purpose: The statistics should be collected for a specific purpose. For example, while collecting statistics of trading, we must decide beforehand the regions, commodities and the periods for which they are needed.

(iv) Statistics are Expressed Numerically: Quantitative expression are not statistics unless are expressed in numerical forms. Statements like 'India's population is increasing. prices of petrol will go high, Ram is good at Economics are not statistical statements but statements like There is 63% increase in food items, 'Average poverty ratios in India is 26' are statistical statements

(v) Statistics are Affected to a Marked Extent by Multiplicity of Causes: Statistics or data are affected by a number of forces operating together i.e., they are dependent on a number of phenomena. For example, statistice of production of an agricultural commodity are affected by rainfall, soil quality, manuring process and method of cultivation etc. Similady, it sume for other sectors also.

(vi) Statistics are Placed in Relation to Each Other: Statistics are collected for making comparisons between related phenomena over a specific region or period. For example, the population figures of India UK, USA. China etc. in 2011 census are comparable as they belong to same cemus year. Thus, for a valid comparisom statistics are required to be put in relation to each other

(vii) Statistics are Enumerated or Estimated According to Reasonable Standards of Accuracy: Enumeration means a precise and accurate numerical statement These statements can be obtained by two ways either by actual counting or measurement or by estimate. For example, the number of students in class can be counted with perfect accuracy but in situation, such as in a rally, one has te estimate the number of people. Similarly, exact measurements on heights, weights distances etc are not possible and one has to make estimates with reasonable standards of accuracy.

 Statistics in Singular Sense

Whenever a huge amount of data is collected, there arise a need to organize, present. analyse and interpret them in a systematic order. Statistics, in a singular sense is a branch of science which deals with scientific methods of collection, organization, presentation analysis and interpretation. 

According to Croxton and Cowden, "Statistics may be defined as a science of collection, presentation analysis, and interpretation of numerical data"

Thus, we have the following five stages in a statistical investigation:

(1) Collection of Data: With a specific and well defined purpose is the first step in a statistical investigation. If the collected data are faulty, the conclusions drawn are bound to be fallacious. Hence, data should be collected with a maximum core as they form the foundation of statistical analysis.

(ii) Presentation of Data: Collected and organised data are presented in a systematic order to facilitate statistical analysis. The organised data are presented in the form of tables, graphs and diagrams to allow better understanding and comparison.

(iii) Organisation of Data: is also an important step in statistics as deriving any conclusions from the observations only is difficult. So, its purpose is to provide a methodology for closification and description in a summary form Editing. classification and tabulation are three step in organisation of data

(iv) Analysis of Data: Statistics plays two important roles in analysis of data

(1) Descriptive statistics and (ii) Inferential statistics.

Difference between these two are:

The nature of inference is that we make general statements from the study of a few cases. In such case, generalisation can't be made with certainty. Thus, language of probability is often used in statistics conclusions. 

 Scope of Statistics

Scope of statistics is indeed very fast. It covers all fields of study where in quantitative appear and need analysis. It is essential firm the state of planning to the stage of conclusions. It applies to all sciences and applications, such as agricultural engineering, medical, physical, economics, business, commerce, industry etc.

1. Statistics and State

As per poms of collection of data statistics was developed as a state craft for maintaining ecminnic and military strength and for formidating different policies Gradually, the sphere of data collection to other fields such as sales, health, taxes, import export, production etc. Now, the functions of a state have increiond due to increase in the concept of welfare state. For eg Population.

2. Statistics and Economics

 Statistics as data and methodology have proved immensely useful in solving a variety of economic problems related to wages, prices, analysis of time series, income and demand analysis. The development of various ecmumic theories own greatly to maritical thing. Engel's law of family expenditure. 'Mathusian theory of population. The impact of mathematics and statistics has led to the development of new disciplines like 'economics' and 'economic statistics'.

3. Statistics and Economics Planning 

Statistics is the most important tool in economic planning which is essential for proges utilisation of natural resources Drawing plan, execution and review is based on statutical analysis. Priorities of expendium of a national budget can be determined though the proper understanding of varian ecmumic problems, atz, balance of trade, industrial growth disparities income and wealth, agricultural production etc. Time bound goals are set after listening the prities of growth in differt exc activities Maximum utilisation of available resources can be made by using econometric models based un statistical analysis.

4. Statistics and Business

With growing star and increasing competition, the problems of business enterprises have become complex Statistics is now considered as an indispensable tool in the analysis of activities in the field of business, commerce and industry. In business, the manufactures is always interested to estimates the immediate and future demand of his product. The object can be achieved by properly conducted market survey and research which greatly depend on statistical methods. The trends in sales and production can be determined by statistical methods like time-series analym which are essential fur future planning of the phenomena. Similarly, the correlation and negression analysis can be used to judge the effectiveness of various sales promotion measures.

Statistical concepts and methods are also used in controlling the quality of products to the satisfaction of consumer and the producer. Thn, method of quality control and reliability analysis are invaluable in indhastrial engineering.

5. Statistics and Psychology and Education

 Statistics has found wide application in prychology and education. It forms the basic of scientific approach to problem in which inductive inference is communly sed Students of psychology and education cannot remam ignorant of such methods of problem solving in their disciplines. Also, statistical methods are used to measure human ability (forg intelligence, aptitude, personality, interest enc) by tests. Theory of leaming is al based statistical principles. Application of statistics in pychology and exhat have id to the development of new discipline called Pychometry.

6. Statistics and Medical, Biological and Agricultural Sciences 

Statistics is also one of the most prominent tool in the field of Medicines, Biology and Agriculture. In Medicine sciences, one is greatly concerned with the results obtained from the ase of medicines and drugs. Similarly, the important role of various factors in the growth and development of a plant is important in Biology. In Agriculture, the role of factors riz, manure, rainfall, watering process, seed quality, affecting the production, need to be analyzed for good results statistical techniques like analysis of variance' and "Design of experiments are useful for isolating the role of such factors.

 Limitation of Statistics

Though, statistics has many application in various important areas but it also has some limitations. Hence, for proper use of statistics, it is also necessary to know the limitations/ and misuse of statistics. The following are the limitations of statistics:

1. Statistics can be Misused and Misinterpreted: The greatest limitation of statistics is that it is likely to be misused. Inadequate and faulty procedure of data collection and inappropriate comparisons may arrive at fallacious conclusions For rg, when conclusions are based on incomplete information and are drawn by unskilled investigators, then it is said to be the misuse of statistics

2. Statistics Deals Only with Quantitative Data: If the study yields qualitarive data which cannot be meaningfully converted to quantitative data, then valid conclusions cannot be drawn using statistical analysis.

3. Statistics Deal with Aggregates of Items and not with Individual: Statistics is the study of mass of data and deals with collective information. A single data or individually constituted data is not cunsidered as a statistical analysis. For eg. Akash scored 81 marks out of 100 in Economics, is not a statistical data, whereas Akash's average marks are 92 is statistical data.

4. Statistical Laws are True Only on An Average: Laws of statistics are not universally applicable as the laws of physics, chemistry and mathematics. These may not be true for particular individual. If it is statistically established that annual income of a man is 3 lakhs to 5 lakhs then this statement is true only on an average and not with individual

5. Statistics is Only One of the Methods of Studying a Phenomenon: Statistical methods don't always provide the best possible solution to a given problem. In varying culture and religious situation, it may fail to reveal the underlying facts responsible for the variations in a phenomenon under study. Thus, statistical conclusions are to be supplemented by other variations.

Distrust and Misuse of Statistics

We have observed that tatistical techniques are important tools in analysing problems in different areas of life. But, still there is a considerable distrust in statistics Le, lack of faith and confidence in statistical methods and statements. It is often said that:

1. Statistics is another form of lying.

2. There are three kinds of lying-lies, damned lies and statistics.

3. Statistics can prove or disprove anything.

4. Statistics reveal what is convincing but conceals the truth.

Reasons for Distrust in Statistics

(i) Figures are innocent and convincing due to which unawared people believe them easily.

(ii) Statistical data used for providing arguments may be inaccurate and incomplete and will lead to fallacious conclusions.

(iii) Even if the figures are correct, they may be presented or interpreted in such a manner that the concerned persons get misleaded. For eg. 2 companies X and Y are paving 30,000 and 45,000 per month respectively. Now, by this statement company Y seems more interesting. But, it would be misleading until we know the number of employees and the number of working hours etc. Thus, in such cases, we might draw different conclusions, Hence in the view of this statistics, it should be used with utmost carefulness. Thus, it is commonly said that 'statistics neither proves anything nor disproves anything. It is only a tool, which will be good if used in proper manner otherwise it may lead to bad decisions.

The fault doesn't lie in statistics but this distrust arise because of its misase on the part of untrained practitioners of statistical methods, ignorant users of statistical results and the dishonest people who use statistics to mislead and confuse rather than to clarify and illuminate

"Science of statistics is the most useful servant but only of great value to those who understand its proper use"

For eg. Hockey is a nice game for physical exercise but wrong conduct of the game and wrong rules & regulations may make it a dangerous game. But, game of Hockey can't be blame for a wrong outcome. Similarly, if the statistical facts are mis-interpreted by the people to serve their ends, it will be unjust to blame the science as such. Instead, people are responsible for these faults.

Nature of Statistics (Science or Art)

1. Statistics as Science

Science refers to a systematised body of knowledge. It studies cause and effect relationship and attempts to make generalisation in the form of scientific principles of laws. Like other sciences, statistical methods are also used to answer the question like, how an investigation should be conducted? In what way the valid and reliable conclusions can be drawn? How far are these conclusions dependable? Hence, statistics is a science. The science of statistics is different from physics, chemistry etc. Statistics is called the science of scientific methods. That is why some statisticians do not consider it a pure science but a scientific method. According to Cowden and Croxton, "Statistics is not a science, it is a scientific method". In the words of Tippet. "As science, the statistical method is a part of the general scientific method and is based on the same fundamental ideas and processes"

2. Statistic as an Art

An art is an applied knowledge. It refers to the skill of handling facts so to achieve a given objective. It is concerned with the ways and means of presenting and handling data, making inferences logically and drawing relevant conclusions. Statistics is an art which tells us how to use statistical rules and principles to study the problems and finding their solutions. By the application of statistical method a number of complex problems can be understood easily. Collection of statistical (data), it use and utility are itself an art. How the desired results are obtained by using the rules of statistics, which statistical methods are used to solve special type of problems? How the two facts are compared and by establishing correlation conclusions are drawn? All these aspects actually relate to art and this is the reason why statistics is an art.

3. Statistics is both Science and Art

After studying, the science and art aspect of statistics it is said that statistics is both science as well as Art. Statistics is used not only to gain knowledge but also to understand facts and draw important conclusion from it. This type of conclusions prepare a path of the economic and social progress. According to Tippet, "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 his knowledge of the field of application, g-Economics"

Functions of Statistics

1. It Simplifies Complex Data: Statistical methods like averages, totals, percentages, etc. help in condensing mass of data into a few significant figures so as to make them easily understandable.

2. It Presents the Facts in a Definite Form: Statistics deals with the quantitative statements of facts and thus presents them in a precise and definite form. Quantitative statements of facts are always more convincing than vague statements. For example, the statements like the birth rate in India is decreasing. the prices of commodities are rising'. 'Mr. Yogesh has passed the high school examination, etc. do not convey information in a definite form as they do not involve quantitative statements of facts.

3. It Provides a Technique of Comparison: Comparison of quantitative facts is also an important function of statistics. For example, area-wise and period-wise comparison of data related to production, sales, export, import, population, etc. are helpful for drawing valid conclusions about economic activities.

4. It Studies Relationship: Correlation analysis is used to find the functional relationship between two or more variables. The relationship is very helpful in making estimates and forecasting future trends. For example, the relationship between supply and demand, advertisement and sales, etc. provide us the basic tool for planning these activities.

5. It Helps in Formulating Policies: As discussed earlier, inferential statistical methods are helpful in formulating various economic and business policies. Empirical studies of data concerned with imports, exports, wages, production, etc are helpful in framing suitable policies and plans in the respective areas. Some well established law such as 'Malthusian' theory of population" and "Engel law of family expenditure' are based on statistical analysis of relevant data.

6. It Helps in Forecasting: Statistics is now an indispensable tool in the analysis of activities relating to business, commerce and industry. Such an analysis is useful for determining trends in activities related to these areas, which in turn form the basis of estimation and forecasting about the phenomenon under study.

7. It Helps to Test and Formulate Theories: The function of statistics is also to test and formulate policies in different fields and to measure their effects. For example, statistical methods are used in agricultural and biological science in determining the role of various factors of growth and development of the organism or plant under study. In medical sciences, the effects of drugs are reconded and analysed. In all such studies, effects of different factors can be tested by collecting and comparing the relevant data. Properly conducted consumers and market surveys are indispensable tools in formulating precise and definite production policies.

Statistical Units

1. In Practical Field of Survey the definition of location of statistical unit remains pre-requisite for the collection, interpretation and presentation of the numeric data. A unit stands for the qualitative or quantitative measure in terms of which the data are collected and analysed.

2. Statistical Units can be Divided into the Following Three Categories:

(i) Unit of enumeration is that in terms of which objects are measured and collected. Such units may be simple or composite. A simple unit denotes only one attribute or consideration without any qualifying limit attached to it Suppose at a particular hours and place 4000 passengers travelled ove N-railway and 600 over S-railway. Then the comparison of popularity can not be made without knowing the distance travelled in both the cases. If it i found the N-railway passengers covered a distance 200 kms and those d S-railway 125 kms, then to have a correct comparison of the popularity of two trains, the total number of passengers-kilometers in both the cases ar obtained, which is

        200x4000 800,000 for N-railway 

and 125 x 6000 750,00 for S-railway

indicate that former one is more popular. The other examples of composite unit, naan-hour, killo-watt-hour, rupee-gram etc.

 (ii) Unit of analysis and interpretation is that in terms of which data are analysed, compared and interpreted rates, percentages are used for this purpose.

(iii) Unit of presentation is that in terms of which data are presented. However ultimately the nature of such units will belong to either of the first twe categories only. Because data are presented with respect to time place and condition either after measurement and collection or after its statistical analysis and interpretation.

3. Characteristics of a Good Statistical Unit 

(i) Unit should be clear and unambiguous otherwise different people will different interpretations. For example, the unit of household has to be give defined specifically whether it will stand for a family related by blood, or for those living together collectively or having common kitchen. 

(ii) Unit should be self-explanatory. The persons for whom survey or the investigation has been conducted should be able to understand and interpret

the unit easily.

 (iii) Unit should be rigid and definite without any flexibility in nature. 

(iv) Unit should be relevant. For a unit relevant and suitability to the purpose of enquiry is essential. For example, natural income should be measured in national coins. Similarly, for the study of giving conditions of the people. house hold is a suitable unit. 

Difference between Primary and Secondary Data

(i) The primary data are absolutely new and are collected a fresh whereas the secondary data are those which were previously collected and published by some previous investigators and are being simply used by the present investigators.

(ii) The primary data are collected according to the plan of the investigator and so it requires much money, labour and time in collecting them, whereas the secondary data is always readily available and can be borrowed easily by the present investigator for his purpose.

(iii) The primary data are collected according to the requirement of the problem unde consideration while, the secondary data was collected for another purpose and moulded according to the present requirement.