## Definition of Statistics

The word 'Statistics' is derived from Latin word 'Status', German word 'Statistik', Italian word 'Statista', French word 'Statisttique' each of which means political state. In those days "Statistics" was used only in collecting the information relating to the population of the state military strength, incomes etc. for framing the military and the fiscal policies. So, at that time, "Statistics" was considered only as the science of statecraft. However with passage of time, the science of statistics has been applied very widely. So, in modern times, the scope of statistics has considerably enlarged. It is used not only to the state in administration but it is used in Economics, Science, Business, Research, Bank etc. There is hardly any place of human activity where statistics has not been used.

The word "Statistics" is used in singular as well as plural sense. In the plural sense, it means the quantitative information or numerical facts collected systematically. As for example: Statistics of population, national incomes, unemployment, poverty, exports, imports etc. in the singular sense, it means the various methods and techniques adopted for the collection, presentation, analysis and the interpretation of the figures. But to a layman, it is simply a mass of figures.

### Definition of Statistics in singular Sense

A.L. Bowley has defined "Statistics as the science of counting". Again he defined "Statistics as the science of averages". There are the narrow definitions because they cover only one aspect of Statistics. The first definition is limited only in counting. No doubt, counting is used in the collection of data. But counting alone is not statistics. The second definition includes only the averages which are related to the measures of central tendency. But there are other measures such as dispersion, skewness, correlation etc. which are not less important. So, the second definition is also not complete.

Boddingston has defined "Statistics as the science of estimates and probabilities". This definition is also unsatisfactory because estimates and probabilities are only the part of statistical methods.

Croxton and Cowden have given a very comprehensive definition of statistics. The definition given by them is as follows "Statistics may be defined as the collection, presentation, analysis and interpretation of the numerical data."

This definition covers clearly the following aspects of statistics:
1. Collection of data: For any statistical investigation, the data must be collected first. The result of the analysis and its interpretation depends upon the data collected. So, data must be collected very carefully. If the data collected be faulty, the conclusion drawn will not be reliable.
2. Organization: The day may be obtained from different sources. If the data is obtained from the published source, it will generally be in organized form. If the data is obtained from some sort of surveys then it needs organization. The data are organized by editing, classifying and tabulating them.
3. Presentation: After collecting and organizing the data, the next step is to present them systematically so that they can be presented in various forms such as table form, diagrammatic form and graphical form.
4. Analysis: After the collection, organization and the presentation of data, the next step is to analyze the data. Various statistical tools like average, dispersion, correlation, test of significance etc. can be used to analysis the data. Statistical tool or appropriate technique of analysis depends upon the nature of the data and the purpose of the inquiry.
5. Interpretation: The last step of the statistical inquiry is to interpret the result obtained from the analysis. To interpret means to drawn the valid conclusion from the data which has been analyzed. For the interpretation of data, high degree of skill and experience is necessary because if the interpretation is not made properly, fallacious conclusion may be obtained.

### Definition of Statistics in plural sense

Webster defined Statistics as "Classified facts respecting the conditions of people in a given state". This definition is not comprehensive because it is limited only with those facts and figures which are related to the conditions of people in the state.

Yule and Kendall define that "By statistics, we mean quantitative data affected to a marked extent by a multiplicity of causes". This definition is also not adequate as it includes only the following tow aspects of statistics (i) they are quantitative (ii) they are affected by a set of causes.

The most comprehensive and exhaustive definition of statistics has been given by Horace Secrist. He defines: "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 pre-determined purpose and placed in relation to each other."

This definition includes all aspects of Statistics. This definition has the following features.
1. Aggregates of facts: To constitute statistics, there should be aggregates of facts. Single or isolated figure cannot constitute statistics because such figures are unrelated and incomparable. For example, the estimated population of Nepal in 1987 is 17.6 millions, is not statistics though this is a numerical statement of fact. But the estimated populations of Nepal, India and Pakistan in 1987 are 17.6 million, 800.3 million and 104.5 million respectively, constitute statistics.
2. Affected by multiplicity of causes: The facts and figures should be affected by a set of causes. For example: the production statistics of a certain crop depends upon a number of factors such as quality of seed, weather condition, irrigation facility, fertility of soil, fertilizer used, method of cultivation and so on.
3. Numerically expressed: Statistical methods are applicable to only those information or facts which are reducible to quantitative form. So, the constitute statistics the information or facts collected must be expressed in terms of numbers. The statements like "The oil is to be imported from India", "Nepal is rich in hydro-electricity", "Everest is the highest mountain in Nepal" etc. do not constitute statistics. But the statement that " the production of a certain crop increased by 6.5% in 1986 against 5.3% in 1985 is a statistical statement.
4. Enumerated or estimated according to reasonable standards of accuracy: For statistical investigation, the data can be obtained either by enumeration or by estimation. If the data be collected by enumeration the data will be exact and accurate. Wherever enumeration is not possible, we collect the data by estimation in which case the data may not be accurate. Anyway, 100% accuracy in the statistical work is rare. The degree of accuracy desired depends upon the nature and the object of the enquiry. For example: In measuring the heights of individuals, accuracy will be aimed in terms of fraction of a centimeter whereas in measuring the distance between two cities Kathmandu and New York, the difference between the fraction of a kilometer may be neglected. However certain standards of accuracy must be maintained for drawing valid conclusion.
5. Collected in a systematic manner: Before collecting the data, well plan of data collection should be prepared and the work should be carried out in a systematic manner. If the data be collected haphazardly, the fallacious conclusion may occur.
6. Collected for a pre-determined purpose: Before collecting the data, purpose of the enquiry should be stated. The data collected without any pre-determined purpose may not be useful for enquiry. So, the purpose of the inquiry should be clear and specific.
7. Placed in relation to each other: The numerical data collected constitutes statistics if they are comparable. To make valid comparison the data should relate to the same phenomenon or subject. For example: the data relating to the production of wheat for different years constitutes statistics because they can be compared. But the weight of a student and marked obtained by him in an examination do not constitute statistics, because in this case the data cannot be compared.
Thus, we can conclude that "All statistics are numerical statements of facts but all numerical statements of facts are not statistics."

## Importance of Statistics

In ancient times, statistics was considered only as a science which was used for collecting information about population, military strength, and wealth for framing administrative and fiscal policies. But in modern times, statistical methods are used in every sphere of life. Here we discuss the uses of statistics in planning, economics and business.

### Statistics in Planning

Modern age can be considered as the age of planning. No work without well planning can be successful. So, most of the organizations are resorting to plan for efficient work and for formulating policy decisions. The success of the planning depends upon the correct and sound analysis of statistical data. For example: the water supply corporation will unable to face the problem relating to the supply of water in Kathmandu valley unless the population of Kathmandu, the quantity of water required per day, the quantity of water to be supplied and by which source additional quantity of water can be supplied if necessary, is known. These are the necessary information to be collected by Water Supply Corporation. This problem can be solved through the powerful statistical tools by making use of statistical data.

### Statistics in Economics

There is a close relationship between Statistics and Economics. Statistical data and statistical methods have great importance in the proper understanding of the economic problems and the formulation of economic policy. Economic problems almost always involve facts that can be expressed numerically such as production, consumption, distribution of incomes, wages, expenditures, unemployment etc. The study of economic problems requires the use of statistical methods.

In the field of consumption, statistics helps to know how the people of different classes of society spend their incomes. This will enable us to have the idea about their purchasing capacity and their standard of living.

Study of production statistics tries to make a balance between supply and demand. With the proper statistical data, statistics of production helps in adjusting the supply according to the demand.

Statistics plays a vital role in case of distribution of incomes too. The questions such as how the national income is calculated and how it is to be distributed can bitterly be solved with the help of statistical methods.

In the field of exchange, we study market prices based on demand and supply, cost of production etc. Effect in the price of commodity due to increase or decrease in supply, costs with the monopolist want to take for maximum profit etc. are the questions that can be answered with the help of statistics. Thus, exchange statistics helps in the commercial development of a nation.

Statistics have a greater importance in reducing the disparities in the distribution of incomes and wealth. The problem relating to the rising prices, rising unemployment, poverty etc. can be solved with the help of statistics.

Besides the economic policy, statistics has made a lot of development in economic theory. Economic laws such as Malthus's theory of population, Engel's law of family expenditure etc. were propounded after statistical tests. The importance of statistics in the study of economic problems has resulted a new branch known as "Econometrics."

## Functions of Statistics

Important functions of statistics are given below:
1. Statistics simplifies complexity: Statistic consists of aggregate of numerical facts. Huge facts and figures are difficult to remember. The complex mass of figures can be made simple and understandable with the help of statistical methods. Statistical techniques such as averages, dispersion, graph, diagram etc. make huge mass of figures easily understandable. So, the function of statistics is to reduce the complexity of the huge mass of figures to a simpler form.
2. Statistics presents fact in a definite form: One of the important functions of statistics is to present the general statements in a precise and definite form. The conclusion stated numerically is definite and hence more convincing than the conclusions stated qualitatively. This fact can readily be understood by the following example: "The population of Nepal is 1981 has been increased than in 1971". There will be no clear idea about this statement. Everybody wants to know to what extent the population of Nepal has increased. But the statement that "the population of Nepal has increased from 11555983 in 1971 to 15022839 in 1981" is a definite form.
3. Statistics facilities comparison: The science of statistics does not mean only counting but also comparison. Unless the figures are compared with other figures with the same kind, they are meaningless. Statistical methods such as averages, ratios, percentages, rates, coefficients etc. offer the best way of comparison between two phenomena which will enable to draw valid conclusion. So, statistics helps in the comparison of two phenomena. For example: The statement that "the per capita income of Nepal is \$160" is not so clear unless it is compared with the per capita income of any other country.
4. To help in formulation of policies: Statistics helps in formulating the policies in different fields mainly in economics, business etc. The government policies are also framed on the basis of statistics. In fact, without statistics, suitable policies cannot be framed. For example: The quantity of food grains to be imported in a particular year depends upon the expected internal production and the expected consumption. That is if the expected wheat production in the particular year be 701 thousands metric tons and that of consumption 710 thousand metric tons so we must import 9 thousand metric tons of food grains.
5. Statistics helps in forecasting: While preparing suitable policies and plans, it is necessary to have the knowledge of future tendency. This is mostly in case of industry, commerce and so on. Statistical methods provide helpful means in forecasting the future by studying and analyzing the tendencies based on passed records. For example: Suppose a businessman wants to know the expected sales of T.V. for the next year, the better method for him would be to analyze the sales data of the past years for the estimation of the sales volume for the next year.
6. Statistics helps in formulating and testing hypothesis: Statistical methods are helpful not only in estimating the present forecasting the future but also helpful in formulating and testing the hypothesis for the development of new theories. Hypothesis like 'whether a particular fertilizer is effective for the production of a particular commodity' 'whether a dice is biased or not' can be tested with the help of statistical tools.

## Limitations of Statistics

Besides the importance of statistics in every field of life, it has some limitations. The following are the main limitations of statistics are:
1. Statistics does not deal with individuals: A part of the definition of statistics is that it must be the aggregates of facts. That is, it deals only with the mass phenomena. A single item or the isolated figure cannot be regarded as statistics. This is a serious limitation of statistics. For example: the mark obtained by a student in English is 75 does not constitute statistics but the average of a group of students in English is 75 forms statistics.
2. Statistics does not study qualitative phenomena: The science of statistics studies only the quantitative aspect of the problem. Statistics cannot directly be used for the study of qualitative phenomena such as honesty, intelligence, beauty, poverty etc. however, some statistical techniques can be used to study such qualitative phenomena indirectly by expressing them into numbers. For example: the intelligence of the boys can be studied with the help of marks obtained by them in an examination.
3. Statistical laws are not exact: 100% accuracy is rare in statistical work because statistical laws are true only on the average. They are not exact as, are the laws of Physics and Mathematics. For example: the probability of getting a head in a single toss of a coin is ½. This does not imply that 3 heads will be obtained if a coin is tossed 6 times. Only one head, 2 times head or all the times head or no head may be obtained.
4. Statistics is only a means: Statistical methods provide only a method of studying problem. There are other methods also. These methods should be used to supplement the conclusions derived with the help of statistics.
5. Statistics is liable to be misused: The most important limitation of statistics is that it must be handled by experts. Statistical methods are the most dangerous tools in the hands of inexpert. Since statistics deals with masses of figures, so it can easily be manipulated by inexperienced and skilled persons. Statistical methods if properly be used, may conclude useful results and if misused by inexpert, unskilled persons, it may lead to fallacious conclusion. We have the following example consisting the result concluded by an inexpert and unskilled person.
The average height 4 members of a family is 1.56 meters and the average depth of the river is 1.06 meters. If they are willing to cross the river, they can safely cross the river.

## Statistical tools used in Economics

Economics is basically quantitative. Every problem in economics contains numerical facts. For the study of each problem in economics, the following tools are to be used step by step.
1. Collection of data: For any statistical investigation, the first tool to be used is the collection of data. The data may be primary or secondary. The collection of primary or secondary data depends upon the nature, object, scope of the enquiry, financial resource, time factor and the degree of accuracy. The result of the analysis and its interpretation totally depend upon the data collected. So, the data must be collected carefully.
2. Organization: After completing the process of collecting the data, the second tool to be used is the method of organization. Organization of the data depends upon the source from which the data are obtained. If the data are obtained from the published source, it will generally be in the organized form. But if the data be obtained from some sorts of survey, then it needs to organize. The data is organized by editing, classifying and tabulating them.
3. Presentation: After collection and organizing the data, the next tool to be used is to present them systematically so that they can be presented in various forms such as table form, diagrammatic form and graphical form. With the help of this tool, comparison between two can be made easily.
4. Analysis: After collection, organization and presentation of the data, the important step to be used is the analysis of data. Various statistical tools such as averages, dispersion, correlation, test of significance, index number, time series etc. can be used to analyze the data. Statistical tools or appropriate technique depends upon the nature of the data and the purpose of the inquiry.
Completing all the above mentioned statistical tools, the next important step is to draw the conclusion obtained from the analysis. For the interpretation of data, high degree of skill and experience is necessary if not fallacious conclusion may obtain.