Economics - XI

1

Statistics

Definition of Statistics: The word „Statistics‟ has been defined in two senses i.e. singular sense and plural sense. When the word statistics is used in singular sense, it means various methods and techniques adopted for the collection, presentation, analysis and interpretation of data. On the other hand, when the word statistics is used in plural sense, it refers to data themselves or numerical facts collected systematically. For eg: Statistics of total population, national income, export, import, etc. Definition of statistics in singular sense: According to Croxton & Cowden, “Statistics may be defined as the science of collection, presentation, analysis and interpretation of numerical data.” This definition is simple and comprehensive. It clearly indicates the following four aspects of statistics: Connection of data: This is the first steps of statistical enquiry. Representation of data: After the data has been collected, they are presented in a systematic way. This is the second step for statistical investigation. Analysis of data: After the data has been presented, the next step is to analyze them. Intrepretation of data: The last step of statistical enquiry is the interpretation of data. In this step, the researcher has to draw the conclusion from the data which has been analyzed.

Definition of Statistics in plural sense: According to A.L. Bowley, “Statistics are numerical statement of facts in any department of enquiry, placed in relation to each other.” This definition point out the three aspects of statistics: Statistics are numerical statement of facts. Statistics are concerned with any enquiry. Statistics are placed in relation to each other for the purpose of comparison. Functions of Statistics: The major functions are as follows: Statistics simplifies complexity: Statistics helps to simplify the raw and complex information by means of organization, presentation and analysis of data. Huge facts and figures are difficult to remember. The complex mass of figure can be made simple and understandable with the help of statistical methods. Statistics presents facts in definite form:

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Economics - XI

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One of the important function of statistics is to is to present the general statements in a definite form. The conclusion stated numerically is definite and more conviencing than the conclusion sated qualitatively. Statistics facilitates comparison: This is another function of statistics. Unless the figures are compared with other figures of the same kind, they are meaningless. Statistical techniques like classification, tabulation, average, ratio etc. can be used for comparison between two or more group of data. Statistics helps to formulate policies: Statistical data and tools are necessary for formulating suitable policies. Government policies are formulated on the basis of available data of the country. Statistics helps in forecasting: Various statistical tools and techniques are used to forecast for the future. For Eg: Regression analysis can be used in forecasting market demand. Statistics helps in formulating and testing hypothesis: Statistics is helpful in formulating and testing the hypothesis for the development of new theories.

Importance of statistics: In ancient time, the importance of statistics was limited. But now, its importance has been extended in multiple fields of human life. It is important in various sectors of the economy. The major importance of statistics are as follows: Importance of statistics to state: Statistics is very important to the state. Now – a – days, a state collects statistical data to solve most of the problems. On the basis of such statistical the state makes appropriate plan for development. Importance of Statistics to planning: In order to achieve the determined goals, planning is essential for the government of a country. But without proper statistics, we cannot make any planning. Thus, statistics plays an important role in planning. Importance of Statistics to economics: Many economists have been using statistical tools and techniques to develop the area of economics. Therefore, statistics is very essential to develop & prove the principles & laws of economics. Importance of Statistics to industrialists and business: Statistics is very important for industrialist & businessman. Nowadays, the business sectors are expanding and become very competitive. Therefore, if they

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Economics - XI

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do not take care of the things like demand, price and market of the commodity they cannot fully successful. Importance of Statistics to Mathematics: Statistics is the branch of applied mathematics, which is related with data. Modern theories of statistics have their foundation on mathematical theories. Similarly, mathematics is also dependent on statistics regarding the formulation of various mathematical models. Therefore, statistics is important in mathematics as well.

Limitations of Statistics: There are some limitations of statistics which are as follows: Statistics doesn’t deal with an individual: Statistics is always related with groups. It deals with aggregate of facts. Therefore, it doesn‟t deal with an individual. Statistics doesn’t study qualitative phenomenon: In statistics, we study the numerical statements or facts. But it doesnot study the qualitative characteristics like beauty, honesty, love, etc. Statistics laws are not exact: 100 % accuracy is rare in statistical work because statistical laws are true only on the average. Statistics is only a means: Statistics acts as a facilitator subject to other disciplines. It helps to analyze data and draw conclusions from the findings. Therefore, it is only a means. Statistics is liable to be misuse: The greatest limitation of statistics is that it must be used by experts only. If statistics are used by those persons who are not expert in this field, then the conclusion drawn may be wrong. Statistical data should be of similar nature: To draw the correct conclusion the data should be similar in nature. If there are not of similar types and are of different natures collected by different techniques then the conclusion drawn from the data could be misleading.

Collection and organization of data: Types of data: Primary data:

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Economics - XI

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The data which is originally collected by an investigator or an agent for the first time for the purpose of statistical enquiry is called primary data. This data are original in character. This data are also called first hand data because such data used for the first time by the investigator. For Eg: If an investigator wants to study about the educational status of Dharan and if he or his agent collects the necessary information then, the data is primary. Secondary data: The data which were already collected and used by someone else but are also useful for other investigators are called secondary data. This types of data are not original in character for the user. This data are also called second hand data. For Eg: If an investigator wants to investigate about the educational status of Dharan and if he uses necessary information from Dharan municipality record, it is secondary data for the investigator.

Methods of collecting Primary data: There are various methods of collecting Primary data which are as follows: Direct personal interview: In this method, the investigator collects the data personally from the source concerned. In other words, the investigator goes up to the respondents personally and asks the necessary questions and obtain the required information. Indirect oral interview: In this method, the investigator obtains the necessary information by contacting the other persons who are familiar with the problem under study. Such person is called witness. This method is applied when the informants hesitate to give information directly. Information through correspondents: In this method, the investigator appoints local agents in different parts of the field of enquiry. These agents collects the necessary information from their respective fields and send them to the central office. This method is widely used by newspapers, radio, TV, to obtain the information. Mailed questionnaire method: In this method, first of all, questionnaires are send to individual respondents by post. The respondents are requested to answer all the questions and return the questionnaires by post within a certain period of time. Schedule sent through enumerators: In this method, the questionnaire are sent through the enumerators. The enumerators go to the respondents personally and ask them the questions and obtain the necessary information. This method is appropriate if the field of enquiry is very large.

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Economics - XI

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Source of Secondary data: There are various sources of secondary data which are as follows: Governments official publication like plan documents, economic survey, budget speech, etc. Reports given by various committees and commissions appointed by the government. The publications of commercial and trade organization. Official publication of Nepal Rastra Bank. Official publications of International Agencies like World Bank, IMF, UN, UNDP, WHO, etc. Population census, Agriculture census, conducted by CBS (Central Bureau of Statistics). Publications of universities and research institution. Publication of individual research workers. Reports of private organizations. Research works conducted by students. Reliability of Secondary data: Before using the secondary data, we should check whether the data are reliable or not. While testing the reliability the following things should be taken into consideration. Who collected the data and what were the objectives of collecting data? Was the investigator experience, honest, capable and unbiased or not? Whether the appropriate techniques of collecting data were applied or not. What degree of accuracy was maintained in the degree? In which time period were the data collected?

Precaution in the uses of secondary data: Secondary data are those which are collected by someone else and used by others. Therefore, while using secondary data the following precautions should be taken: The data should be reliable. The data should be suitable. The data should be adequate.

Techniques of data collection: There are two techniques of data collection. They are: Census method: Sample method: Census method: In this method, the informations is obtained from each and every units of population, under study. In other words, if the information is collected from the possible units in the universe it is called census method. The census method is also called complete enumeration method. In Nepal, population census is conducted by applying census in Nepal every 10 years. For example: If we want to study about the smoking

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Economics - XI

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habit of adults of a locality then, in census method, information are obtained from each and every adults of that locality. Merits of census method: The following are the merits of census method: It gives complete information about the population. It gives more accurate, reliable and representative results. The data will be adequate because no item is left in this method. If the study area is small then this method is very useful. Demerits of Census method: The following are the demerits of census method. This method is more expensive and time consuming. This method is not applicable if the population is infinite. This method is not suitable in some special conditions. For Eg: This method cannot be applied if the units under study get destroyed while testing. Sample method: In this method, the information is obtained only from a part of the population assuming that it is the population assuming that it is the representative of the whole. Thus, in this method, a part is studied and on that basis conclusion is drawn for the entire population. For Eg: If we want to study about the smoking habits of 5000 adults of a locality then we collect the information from only 500 adults of them and find out their smoking habit. On the basis of smoking habit of these 500 adults, we draw conclusion for the whole 5000 adults. Merits of Sample method: This method is less expensive. This method is less time consuming. The detail information can be obtained because only a part of the universe is studied. In case of infinite population this method is suitable. This is better method of investigation if the items are totally destroyed while testing. This method is used to check the result obtained from census method. Demerits of Sample method: If the sample selected from the population is not representative one, it may give the wrong conclusion. This method should be handled only by experts. Otherwise, the result will be misleading. The result obtained from this method may not be reliable due to the possibility of personal biases in sampling. Selection of sample size is difficult task. Methods of Sampling: There are various methods of Sampling which are as follows:

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Economics - XI

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Judgement or Deliberate Sampling: In this method, the choice of items in the sample depends upon the judgement of the investigator. For Eg: If there are 80 Students in a class and teacher has to select 20 Students for survey then the selection of 20 Students would depend upon the judgement of Investigator. Random Sampling: In this method, every unit of the universe has equal chance of being selected in the sample because the selection of any unit depends on chance. Lottery method can be used for random sampling. Stratified Random Sampling: In this method, the universe is divided into different groups or strata according to some characteristics. Then sample is selected at random from each group or strata. Systematic Sampling This method can be applied only if the complete list of items in the universe is available. In this method, first the units are arranged in some systematic order and then the sample unit is selected on the basis of sampling interval. The sampling interval is calculated as, K = N n

Where, K = Sampling interval N = Total no. of items n = No. of sample items. For example: If we have to select 8 persons out of 40, then K = = = N n 40 8 5 (Sampling interval)

Multi – Stage Sampling: In this method, sampling is carried out in various stages. First of all, the population is divided into large sample units and a sample is taken at random. Again these are further divided into smaller units and a sample is taken at random. This process is repeated many times.

Diagrammatic and Graphic Representation of data:

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Economics - XI

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Diagrams and Graphs are nothing but the presentation of statistical data in the form of geometrical figure like points, lines, bars, rectangles, circles, etc. Rules of Constructing diagrams: There are certain rules for constructing diagrams which are as follows: Choice of diagram Selection of scale Proportion between width and height Neatness and cleanliness Title of the diagram (Heading) Index Types of Diagrams: Simple bar diagram: A simple bar diagram is used to present one variable only. For Eg: Production, profit, sales, marks, etc. can be solved with the help of simple bar diagram. It consists of set of equi–distance rectangle of equal width. Sub – divided bar diagram: A sub – divided diagram is a diagram which is used to represent the various components of the total. Here we have to keep the index. Multiple bar diagram: It is used to present two or more sets related data. The different values of each set are presented by drawing a lot of physically joined rectangles. Here the different shades or colours are used to distinguish the bars of one type from the other. Pie – diagram: A pie – diagram is a diagram in the form of a circle whose area represents the total value. It is used to show the relation between the components with one another to the other.

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1

Statistics

Definition of Statistics: The word „Statistics‟ has been defined in two senses i.e. singular sense and plural sense. When the word statistics is used in singular sense, it means various methods and techniques adopted for the collection, presentation, analysis and interpretation of data. On the other hand, when the word statistics is used in plural sense, it refers to data themselves or numerical facts collected systematically. For eg: Statistics of total population, national income, export, import, etc. Definition of statistics in singular sense: According to Croxton & Cowden, “Statistics may be defined as the science of collection, presentation, analysis and interpretation of numerical data.” This definition is simple and comprehensive. It clearly indicates the following four aspects of statistics: Connection of data: This is the first steps of statistical enquiry. Representation of data: After the data has been collected, they are presented in a systematic way. This is the second step for statistical investigation. Analysis of data: After the data has been presented, the next step is to analyze them. Intrepretation of data: The last step of statistical enquiry is the interpretation of data. In this step, the researcher has to draw the conclusion from the data which has been analyzed.

Definition of Statistics in plural sense: According to A.L. Bowley, “Statistics are numerical statement of facts in any department of enquiry, placed in relation to each other.” This definition point out the three aspects of statistics: Statistics are numerical statement of facts. Statistics are concerned with any enquiry. Statistics are placed in relation to each other for the purpose of comparison. Functions of Statistics: The major functions are as follows: Statistics simplifies complexity: Statistics helps to simplify the raw and complex information by means of organization, presentation and analysis of data. Huge facts and figures are difficult to remember. The complex mass of figure can be made simple and understandable with the help of statistical methods. Statistics presents facts in definite form:

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Economics - XI

2

One of the important function of statistics is to is to present the general statements in a definite form. The conclusion stated numerically is definite and more conviencing than the conclusion sated qualitatively. Statistics facilitates comparison: This is another function of statistics. Unless the figures are compared with other figures of the same kind, they are meaningless. Statistical techniques like classification, tabulation, average, ratio etc. can be used for comparison between two or more group of data. Statistics helps to formulate policies: Statistical data and tools are necessary for formulating suitable policies. Government policies are formulated on the basis of available data of the country. Statistics helps in forecasting: Various statistical tools and techniques are used to forecast for the future. For Eg: Regression analysis can be used in forecasting market demand. Statistics helps in formulating and testing hypothesis: Statistics is helpful in formulating and testing the hypothesis for the development of new theories.

Importance of statistics: In ancient time, the importance of statistics was limited. But now, its importance has been extended in multiple fields of human life. It is important in various sectors of the economy. The major importance of statistics are as follows: Importance of statistics to state: Statistics is very important to the state. Now – a – days, a state collects statistical data to solve most of the problems. On the basis of such statistical the state makes appropriate plan for development. Importance of Statistics to planning: In order to achieve the determined goals, planning is essential for the government of a country. But without proper statistics, we cannot make any planning. Thus, statistics plays an important role in planning. Importance of Statistics to economics: Many economists have been using statistical tools and techniques to develop the area of economics. Therefore, statistics is very essential to develop & prove the principles & laws of economics. Importance of Statistics to industrialists and business: Statistics is very important for industrialist & businessman. Nowadays, the business sectors are expanding and become very competitive. Therefore, if they

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Economics - XI

3

do not take care of the things like demand, price and market of the commodity they cannot fully successful. Importance of Statistics to Mathematics: Statistics is the branch of applied mathematics, which is related with data. Modern theories of statistics have their foundation on mathematical theories. Similarly, mathematics is also dependent on statistics regarding the formulation of various mathematical models. Therefore, statistics is important in mathematics as well.

Limitations of Statistics: There are some limitations of statistics which are as follows: Statistics doesn’t deal with an individual: Statistics is always related with groups. It deals with aggregate of facts. Therefore, it doesn‟t deal with an individual. Statistics doesn’t study qualitative phenomenon: In statistics, we study the numerical statements or facts. But it doesnot study the qualitative characteristics like beauty, honesty, love, etc. Statistics laws are not exact: 100 % accuracy is rare in statistical work because statistical laws are true only on the average. Statistics is only a means: Statistics acts as a facilitator subject to other disciplines. It helps to analyze data and draw conclusions from the findings. Therefore, it is only a means. Statistics is liable to be misuse: The greatest limitation of statistics is that it must be used by experts only. If statistics are used by those persons who are not expert in this field, then the conclusion drawn may be wrong. Statistical data should be of similar nature: To draw the correct conclusion the data should be similar in nature. If there are not of similar types and are of different natures collected by different techniques then the conclusion drawn from the data could be misleading.

Collection and organization of data: Types of data: Primary data:

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Economics - XI

4

The data which is originally collected by an investigator or an agent for the first time for the purpose of statistical enquiry is called primary data. This data are original in character. This data are also called first hand data because such data used for the first time by the investigator. For Eg: If an investigator wants to study about the educational status of Dharan and if he or his agent collects the necessary information then, the data is primary. Secondary data: The data which were already collected and used by someone else but are also useful for other investigators are called secondary data. This types of data are not original in character for the user. This data are also called second hand data. For Eg: If an investigator wants to investigate about the educational status of Dharan and if he uses necessary information from Dharan municipality record, it is secondary data for the investigator.

Methods of collecting Primary data: There are various methods of collecting Primary data which are as follows: Direct personal interview: In this method, the investigator collects the data personally from the source concerned. In other words, the investigator goes up to the respondents personally and asks the necessary questions and obtain the required information. Indirect oral interview: In this method, the investigator obtains the necessary information by contacting the other persons who are familiar with the problem under study. Such person is called witness. This method is applied when the informants hesitate to give information directly. Information through correspondents: In this method, the investigator appoints local agents in different parts of the field of enquiry. These agents collects the necessary information from their respective fields and send them to the central office. This method is widely used by newspapers, radio, TV, to obtain the information. Mailed questionnaire method: In this method, first of all, questionnaires are send to individual respondents by post. The respondents are requested to answer all the questions and return the questionnaires by post within a certain period of time. Schedule sent through enumerators: In this method, the questionnaire are sent through the enumerators. The enumerators go to the respondents personally and ask them the questions and obtain the necessary information. This method is appropriate if the field of enquiry is very large.

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Economics - XI

5

Source of Secondary data: There are various sources of secondary data which are as follows: Governments official publication like plan documents, economic survey, budget speech, etc. Reports given by various committees and commissions appointed by the government. The publications of commercial and trade organization. Official publication of Nepal Rastra Bank. Official publications of International Agencies like World Bank, IMF, UN, UNDP, WHO, etc. Population census, Agriculture census, conducted by CBS (Central Bureau of Statistics). Publications of universities and research institution. Publication of individual research workers. Reports of private organizations. Research works conducted by students. Reliability of Secondary data: Before using the secondary data, we should check whether the data are reliable or not. While testing the reliability the following things should be taken into consideration. Who collected the data and what were the objectives of collecting data? Was the investigator experience, honest, capable and unbiased or not? Whether the appropriate techniques of collecting data were applied or not. What degree of accuracy was maintained in the degree? In which time period were the data collected?

Precaution in the uses of secondary data: Secondary data are those which are collected by someone else and used by others. Therefore, while using secondary data the following precautions should be taken: The data should be reliable. The data should be suitable. The data should be adequate.

Techniques of data collection: There are two techniques of data collection. They are: Census method: Sample method: Census method: In this method, the informations is obtained from each and every units of population, under study. In other words, if the information is collected from the possible units in the universe it is called census method. The census method is also called complete enumeration method. In Nepal, population census is conducted by applying census in Nepal every 10 years. For example: If we want to study about the smoking

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Economics - XI

6

habit of adults of a locality then, in census method, information are obtained from each and every adults of that locality. Merits of census method: The following are the merits of census method: It gives complete information about the population. It gives more accurate, reliable and representative results. The data will be adequate because no item is left in this method. If the study area is small then this method is very useful. Demerits of Census method: The following are the demerits of census method. This method is more expensive and time consuming. This method is not applicable if the population is infinite. This method is not suitable in some special conditions. For Eg: This method cannot be applied if the units under study get destroyed while testing. Sample method: In this method, the information is obtained only from a part of the population assuming that it is the population assuming that it is the representative of the whole. Thus, in this method, a part is studied and on that basis conclusion is drawn for the entire population. For Eg: If we want to study about the smoking habits of 5000 adults of a locality then we collect the information from only 500 adults of them and find out their smoking habit. On the basis of smoking habit of these 500 adults, we draw conclusion for the whole 5000 adults. Merits of Sample method: This method is less expensive. This method is less time consuming. The detail information can be obtained because only a part of the universe is studied. In case of infinite population this method is suitable. This is better method of investigation if the items are totally destroyed while testing. This method is used to check the result obtained from census method. Demerits of Sample method: If the sample selected from the population is not representative one, it may give the wrong conclusion. This method should be handled only by experts. Otherwise, the result will be misleading. The result obtained from this method may not be reliable due to the possibility of personal biases in sampling. Selection of sample size is difficult task. Methods of Sampling: There are various methods of Sampling which are as follows:

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Economics - XI

7

Judgement or Deliberate Sampling: In this method, the choice of items in the sample depends upon the judgement of the investigator. For Eg: If there are 80 Students in a class and teacher has to select 20 Students for survey then the selection of 20 Students would depend upon the judgement of Investigator. Random Sampling: In this method, every unit of the universe has equal chance of being selected in the sample because the selection of any unit depends on chance. Lottery method can be used for random sampling. Stratified Random Sampling: In this method, the universe is divided into different groups or strata according to some characteristics. Then sample is selected at random from each group or strata. Systematic Sampling This method can be applied only if the complete list of items in the universe is available. In this method, first the units are arranged in some systematic order and then the sample unit is selected on the basis of sampling interval. The sampling interval is calculated as, K = N n

Where, K = Sampling interval N = Total no. of items n = No. of sample items. For example: If we have to select 8 persons out of 40, then K = = = N n 40 8 5 (Sampling interval)

Multi – Stage Sampling: In this method, sampling is carried out in various stages. First of all, the population is divided into large sample units and a sample is taken at random. Again these are further divided into smaller units and a sample is taken at random. This process is repeated many times.

Diagrammatic and Graphic Representation of data:

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Economics - XI

8

Diagrams and Graphs are nothing but the presentation of statistical data in the form of geometrical figure like points, lines, bars, rectangles, circles, etc. Rules of Constructing diagrams: There are certain rules for constructing diagrams which are as follows: Choice of diagram Selection of scale Proportion between width and height Neatness and cleanliness Title of the diagram (Heading) Index Types of Diagrams: Simple bar diagram: A simple bar diagram is used to present one variable only. For Eg: Production, profit, sales, marks, etc. can be solved with the help of simple bar diagram. It consists of set of equi–distance rectangle of equal width. Sub – divided bar diagram: A sub – divided diagram is a diagram which is used to represent the various components of the total. Here we have to keep the index. Multiple bar diagram: It is used to present two or more sets related data. The different values of each set are presented by drawing a lot of physically joined rectangles. Here the different shades or colours are used to distinguish the bars of one type from the other. Pie – diagram: A pie – diagram is a diagram in the form of a circle whose area represents the total value. It is used to show the relation between the components with one another to the other.

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