SUBJECT: ECONOMICS (126), HSEBCLASS: 11

TRINITY INTERNATIONAL COLLEGEDillibazaar, Kathmandu, 2014

PART 'A'

QUANTITATIVE TECHNIQUE IN ECONOMICS

UNIT: 1 BASIC STATISTICS USED IN ECONOMICS (2) Chapter: I Introduction to Statistics (2) Chapter: II Collection of Data (6) Chapter: III Classification and Tabulation of Data (11) Chapter: V Condensation of Data (17)

UNIT: 3 QUANTITATIVE ANALYSIS IN ECONOMICS (18)

Prakash Rai, prdon2006@yahoo.com

UNIT: 1 BASIC STATISTICS USED IN ECONOMICS

Chapter: I Introduction to Statistics

Origin and Meaning of Statistics

The English term ‘Statistics’ has been derived from the Latin word ‘Status’, German word ‘Statistik’, Italian word ‘Statista’, and French word ‘Statistique’, which have the same meaning, i.e., ‘Political State’.

The term ‘Statistics’ can be used in both singular as well as plural sense/noun. In singular sense/noun, statistics means various methods and techniques adopted for the collection, organization, presentation, analysis and interpretation of quantitative data and it is called science of statistics. In plural sense/noun, statistics means quantitative information or numerical facts and figures collected systematically for special purpose and such figures are called statistical data.

Definition of Statistics in Singular Sense/Noun

According to A.L. Bowley, “statistics may be called the science of counting” and “statistics may rightly be called the science of average”.According to Croxton and Cowden, “Statistics may be defined as the collection, presentation, analysis, and interpretation of numerical data”.

Definition of Statistics in Plural Sense/Noun

According to Yule and Kendall, “By statistics we mean quantitative data affected to a marked extent by multiplicity of causes”.

According to Horace Secrist, “statistics may be defined as the aggregate of facts affected to a marked extent by a multiplicity of causes, numerically expressed, enumerated or estimated according to reasonable standards of accuracy, collected in a systematic manner for a predetermined purpose and placed in relation to each other”.

From these definitions, statistics should have following characteristics:

(i)Statistics are aggregate of facts.(ii) Statistics are affected to a marked extent by multiplicity of causes.(iii) Statistics are numerically expressed.(iv) Statistics are enumerated or estimated according to reasonable standards of accuracy.(v) Statistics are collected in a systematic manner.(vi) Statistics are collected for a predetermined purpose.(vii) Statistics are placed in relation to each other.

Functions of Statistics

The main functions of statistics are as follows:

(i) Statistics presents facts in a definite form: Statistics presents the general statement in a precise and definite form. It presents the general statement in

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quantitative/numerical value. The quantitative/numerical value makes any general statement easily understandable. For example: General statement: Population growth rate of Nepal is high.

Definite form presented by statistics:

Heading 1991 A.D. 2001 A.D. 2011 A.D.Annual Population Growth Rate of Nepal 2.10 % 2.24 % 1.35 %

(ii) Statistics simplifies the complexity: Complex mass figures are difficult to remember. Statistics condenses the complex mass figures into a few, simple, and easily understandable figures. For this, various types of statistical methods and tools are used, such as, diagrams, graphs, averages, correlation, regression, index numbers, etc.

(iii) Statistics facilitates comparison: If the data are not compared with other data with same kind, they are meaningless. Collected data are classified, tabulated, and presented in diagrams and graph. Consequently, two or more sets of data can easily be compared. In this way, statistics facilitates comparison.

(iv) Statistics formulates and tests the hypothesis: In research process, hypothesis is formulated and tested. Statistics helps to formulate and test the hypothesis. For this, statistical tools (z-test, t-test, x2-test, etc.) are used. For example: Hypothesis: “Average income of lecturers of a college is equal to Rs. 25,000”. This hypothesis can be tested by statistical method and data.

(v) Statistics helps to forecast the future events: While preparing suitable policies and plans, it is necessary to have the knowledge of future events/tendency. Statistical methods and data are used to forecast the future events/tendency. For example: A businessman can forecast sale of T.V. in next year on the basis of past and present sale data.

(vi) Statistics helps to formulate policy: Various data are required to formulate appropriate policy. Statistical tools and methods are used to collect such data. Policy makers formulate policies after carefully studying and analyzing the data.

Importance /Uses of Statistics in Different Fields

In ancient time, people used statistics to keep the information of domestic animals, properties, income, expenditure, production, etc. State/Government also used statistics to keep information regarding the number of police, soldier, etc. But, nowadays, it is used in various fields, such as, planning, economics, business and management, mathematics, natural science, etc.

A. Statistics in Planning

Statistics plays a vital role in planning. Appropriate planning is essential for the overall development of a country. Statistics provides adequate information and data for the formulation of effective planning. The national accounting statistics depicts clear picture of the economy of a country. Similarly, statistics related to the macro-

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economic variables like production, income, expenditure, saving, investment, etc. are used in order to compute national income.

B. Statistics in Economics

(i) Understanding Economic Problems: Statistics helps to understand the economic problems. Economic problems related to production, distribution, consumption, exchange, etc. can be understood properly through statistical methods and statistical data.

Production: What to produce, how to produce and for whom to produce are the problems related to production. We need a lot of statistical data to answer these questions. Statistical data of production help to make balance between demand and supply and to adjust the supply according to the demand.

Distribution: Distribution refers to the how the national income is to be distributed among the nationals. It is related with the determination of prices of factors of production (Rent, Wage, Interest, and Profit). Statistics helps us to understand how the national income is calculated and how it is to be distributed.

Consumption: Statistical data of consumption help us to find out how the people of different strata of the society spend their incomes. Such information is helpful in knowing the living standard, purchasing power, and the tax paying capacity of people.

Exchange: Exchange refers to the determination of price of goods and services in different markets. In the field of exchange, some questions may arise like what will be the price of a particular item if its supply increases or decreases?, what should be the price in order to get a maximum profit?, etc. These questions can be answered with the help of statistics.

(ii) Formulation of Economic Policies: Statistical method and statistical data help to formulate suitable economic policies and to evaluate their effect. Unequal distribution of national income, rising prices, rising unemployment, poverty, etc. are the major economic problems. These problems can be solved by implementing economic policies formulated by means of statistical method and statistical data.

(iii) Development of Economic Laws: Statistics helps to develop economic laws. Economic laws like Malthusian theory of population, Engel’s law of family expenditure, etc. were propounded after statistical test.

C. Statistics in Business and Management

Nowadays, the business sector is expanding very rapidly and it is competitive. Consequently, business as well as management sector has become complex. We can reduce such complexity by using statistics. So, statistics tries to solve the problems like Production control, How much raw materials and labors require? What are the quality, shape, and color of output?

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D. Statistics in Mathematics

Statistics and Mathematics are intimately related. The statistical techniques are the outcome of wide application of advanced mathematics. Statistics helps us to analyze a large number of related numerical facts systematically. The role of mathematics is increasing in statistical analysis.

E. Statistics in Natural Science

The tools of statistics are useful in the study of natural science like biology, physics, chemistry, etc. Statistics ensures adequate information or numerical facts needed to study the above-mentioned subjects. Statistical tools are widely used in the study of these subjects.

Limitations of Statistics

The limitations of statistics are as follows:

(i) Statistics does not deal with individual: In statistics, we study the aggregate of facts, but not the individuals. For example: “Mark obtained by Mr. Ram is equal to 75” has no meaning in statistics, but “Average marks of students of section A, B, and C are 70, 65, and 80 respectively”, then these figures have meaning in statistics.

(ii) Statistics does not deal with qualitative characteristics: Statistics does not deal with the qualitative characteristics, such as: love, honesty, intelligence, efficiency, etc. It is difficult to express qualitative characteristics in number.

(iii) Statistical results are true only on an average: In statistical work, hundred percent accuracy is rare. The laws of statistics are true only on an average. So, the statistical laws are not universally applicable like the laws of natural science (physics, biology, chemistry, mathematics, etc.).

(iv) Statistics is only one of the methods of studying the problems: Statistical method helps to study the problems, but it does not provide the best solution of the problems. Sometimes, it is desirable to study the country’s problems of culture, religion, and castes. Statistics cannot be so helpful to study such problems unless other evidences supplement them.

(v) Statistics can be misused: A high degree of knowledge, skill, and experience are essential to draw valid conclusion from statistical data otherwise fallacious conclusion may be drawn. Incomplete and insufficient statistical information may also lead to fallacious conclusion. In this way, statistics can be misused.

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Chapter: II Collection of Data

Collection of Data

Collection of Data is the first and basic step in statistical investigation. If the data are inaccurate and inadequate, the whole analysis and conclusion may be wrong. So, care must be taken while collecting the required data.

There are two types of data, namely: (i) primary data and (ii) secondary data. Data, which are collected for the first time, are called primary data. For example: data collected by Central Bureau of Statistics (CBS) are primary data for the CBS. Data, which are already collected, are called secondary data to others. For example: data collected by CBS are secondary data to others.

Q. Distinguish between Primary and Secondary Data. What are the methods of collecting Primary Data?

Ans: Distinction between Primary and Secondary Data

Primary Data Secondary Data(i) Data, which are collected first time, are

called Primary Data. Primary Data are original.

(i) Data, which are already collected, are called Secondary Data to others. Secondary Data are not original. Secondary Data are collected from published or unpublished sources.

(ii) Primary Data are first hand in character. (ii) Secondary Data are second hand in character.

(iii) Primary Data are like raw materials. (iii) Secondary Data are like finished goods.

(iv) Primary Data usually give more detailed information.

(iv) Secondary Data usually give less information.

(v) Collection of Primary Data is more expensive/tedious/time consuming.

(v) Collection of Secondary Data is less expensive/tedious/time consuming.

(vi) Primary Data may be relatively more reliable.

(vi) Secondary Data may be relatively less reliable.

Methods to Collect Primary Data are as follows

(i) Direct Personal Interview: According to this method, the investigator/interviewer collects the desired data by contacting personally with the informants/interviewee. In other words, investigator himself/herself goes to the field and makes direct personal contact with the people from whom the data are to be collected. So, there is a face-to-face contact with the interviewees.

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The investigator asks various questions to informants and collects first hand data from them. The success of this method largely depends upon the unbiasedness of the investigator and informants. This method is suitable for intensive field survey.

(ii) Indirect Oral Interview: According to this method, the investigator collects the required information/data from third person. So, in this method, investigator should contact to those persons, who may directly or indirectly in touch with the desired information. This method is usually used in those cases when the required information is complex and informants do not respond through direct approach. For example: information about addict of drug can be obtained from family members, neighbors, relatives, and friends. Similarly, information about accident, riot, etc. can be obtained from eyewitnesses.

This method is generally used by the enquiry committee and commission appointed by the government. The main advantages of this method are to save time, money, labor, and to cover a wide areas easily.

(iii) Information from Correspondents: According to this method, the investigator appoints local agents or correspondents in different places to collect information. Such correspondents collect and transmit the information to the central office, where the data are processed. Newspaper, Television, and Radio Agencies generally adopt this method.

The most important advantage of this method is that it is cheap and appropriate for extensive investigation on regular basis.

(iv) Mailed Questionnaire: According to this method, a list of questions called questionnaire, is prepared and sent to the various informants by post. The questionnaire contains questions with space for answer. Informants are requested to answer the questions and send back within a specified period of time through a letter. This method may be relatively cheap and quick if informants respond in time. It is useful when informants are scattered over wide geographical areas.

(v) Schedule to be Filled by Enumerators: According to this method, the questionnaire is sent through trained enumerator. The enumerator goes to the informants with schedule and meets them personally. He explains the purpose of his visit and asks them questions contained in the schedule and fills the schedule with his own handwriting. National Population Census is conducted by this method in Nepal. This method is suitable in that case when the informants are illiterate.

Collection of Secondary Data

Secondary Data can be collected mainly through two sources, which are as follows:

(A) Published Source: The various sources of Published Data are:

(i) Official or Governmental Publications - ‘Statistical Pocket Book’, ‘Population Monograph of Nepal’, and so on

published by Central Bureau of Statistics (CBS). - ‘Economic Survey’ published by Ministry of Finance (MOF). - ‘The Five Years Plan’ published by National Planning Commission

(NPC).

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- Report of Commission/Committee appointed by government, such as, Pay Commission, National Education Commission, etc.

(ii) Semi-official or Semi Governmental Publications of various Local Organizations

- Reports published by Nepal Rastra Bank (NRB). - Reports published by NIDC and Nepal Food Corporation. - Reports published by Security Board and Municipalities.

(iii) Un-official or Private Publications - Reports published by Trade and Professional Bodies, such as, Nepal

Chambers of Commerce. - Journal published by Central Department of Economics (CEDECON). - Reports published by Trade Association, Research Scholars, and

Research Institutes.

(iv) International Publications - Publications of World Bank, International Monetary Funds (IMF),

International Labour Organization (ILO), etc.

(B) Unpublished Source: There are various unpublished sources of data, such as, Hospital Record, Theses written by University Students, Manuscripts, etc.

Precautions in the Use of Secondary Data

Before using Secondary Data, investigator should consider following points:

(i) Adequacy of Data: Secondary data must be adequate for present investigation. Adequacy of data can be tested by comparing geographical area covered by original investigation with the area to be covered by the present investigation. For example: the data relating to household income of Kathmandu valley is not adequate to study the household income of whole country.

(ii) Reliability of Data: Secondary data should be reliable. The reliability of data can be judged from the point of view of objective, method of data collection, sampling technique, etc.

(iii) Suitability of Data: Secondary data should be suitable for present investigation. Suitability of secondary data can be examined in terms of nature, objectives, and scope of investigation. If the nature, objective, and scope of available data are similar to the present investigation, the data are said to be suitable, otherwise not. For example: the data collected for the study of household income in urban area are not suitable for the study of household income in rural area.

Census and Sample Methods of Data Collection

Census Method

In the Census Method, data/information are collected from each and every unit of population or universe under study. For example: if the purpose of the investigation is to study household

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income of Kathmandu district, an investigator will collect the data of each and every household’s income of the Kathmandu district.

Merits/Advantages of Census Method

(i) Complete information about the population is obtained through this method.(ii) Data/Informations obtained from this method are more

accurate/adequate/reliable/representative.(iii) This method is most useful and suitable for intensive investigation (deep study

covering small area).

Demerits/Disadvantages of Census Method

(i) This method is more expensive and time/labors consuming.(ii) This method is impossible if the population size is infinite and the nature of units is

destructive.

Sample Method

In sample method, only some units of population are selected as the representative of the whole population. The selected units are called sample and the technique or method of selecting the sample is called sample method or sampling. For example: an investigator may select only 1,000 household’s income out of 40,000 household’s income as a sample.

Merits/Advantages of Sample Method

(i) The cost of this method is less.(ii) This method is less time/labour consuming.(iii) More trained and skilled manpower and modern instruments can be used for greater

accuracy under this method.(iv) This method is suitable if the population size is infinite and the nature of population

units is destructive.

Demerits/Disadvantages of Sample Method

(i) If there is lack of full co-operation between informant and enumerator/investigator, information may be wrong and unreliable.

(ii) If the sample is not representative of the population, conclusion of the investigation may be wrong and unreliable.

(iii) If unskilled, untrained, and inexperienced persons conduct sample survey, conclusion of the investigation will be wrong and unreliable.

Methods of Sampling

The various methods of Sampling are as follows:

(i) Simple Random Sampling: According to this method, sample items are selected in such a way that each unit of the population has an equal chance of being selected. Items of sample are selected in two ways. They are as follows:

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a. Lottery Method: According to this method, each and every item of the population is numbered. These numbers are written in separate slips of paper of the same size, shape, and color. The slips are folded and thoroughly mixed up and the numbers of slips required for the sample are drawn one by one in blindfold manner.

b. Random Number Table Method: According to this method, units of sample are selected on the basis of random number table made by statisticians like Fisher, Tippet, etc.

(ii) Stratified Random Sampling: According to this method, the population is divided into a certain number of groups called strata and then sample items are selected randomly from each stratum or group. The division of population into strata is called stratification.

Mathematically,

N = N1 + N2+…………..+ NN Population n = n1+ n2+…………. .+ nn Sample

Where, N = Population size n = Sample size

(iii) Systematic Sampling: If complete list of population items is available, this method can be applied. Under this method, sample items are selected at a uniform interval.

Symbolically,

N = nk or k = N/n

Where, k = Sample interval N = Population size and n = Sample size

Selected sample items are i, i + k, i + 2k, i + 3k,…………, i + (n-1)k

(iv) Judgment Sampling: In this method, sample items are drawn in the judgment of individual. Investigator uses own knowledge and opinion in this method. It is less costly and less time consuming method.

(v) Quota Sampling: In this method, sample items are selected on the basis of quota. Within quota, the selection of sample items depends upon the personal judgment.

For example: In TV viewing survey,

Total number of TV viewers (N) = 100 Sample size (n) = 25

Quota: Housewives (n1) = 10 Farmers (n2) = 8 Students (n3) = 7 n = n1 + n2 + n3

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(vi) Convenience Sampling: In this method, the selection of sample items is made from an available source like telephone directory, automobile registration record, stock exchange directory, etc. These sources are convenient to users. The use of these sources depends on the purpose of the inquiry.

Chapter: III Classification and Tabulation of Data

Classification of Data

Classification of Data is the process of arranging collected data in different groups or classes on the basis of common characteristics. Collected data are not suitable for immediate analysis because they are in jumbled and raw form. So, collected data are to be classified.

Objective of Classification

(i) To present the data in a comprehensible (easily understandable) form by removing unnecessary things.

(ii) To arrange the scattered data in an organized form.(iii) To facilitate comparison.(iv) To make data fit for tabulation.

Types of Classification

There are following 4 types of classification of data:

(A)Geographical Classification: According to geographical classification, data are classified on the basis of geographical location or division. For example:

Development Regions

Paddy Production ('000 MT)

1. Eastern 1202. Central 1403. Western 964. Mid-western 805. Far-western 75

Total 511

(B) Chronological Classification: According to chronological classification, data are classified on the basis of time interval. For example:

Years No. of Population1995 1,90,30,0001996 1,92,40,0001997 1,97,03,0001998 2,02,33,000

(C)Qualitative Classification: According to qualitative classification, data are classified on the basis of quality, which cannot be measured, such as, intelligence, sex, religion, beauty, honesty, etc. For example:

Students

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Genius Highly Intelligent Average Intelligent Below Average Dull

(D)Quantitative Classification: According to quantitative classification, data are classified on the basis of such characteristics, which can be measured, such as, height, weight, income, production, etc. For example:

i. Individual Series/Observation

Roll No. Obtained Marks (X)1 452 653 434 455 25

N = 5 ∑X=223

ii. Discrete Series or Discrete Frequency Distribution

iii. Continuous Series or Continuous Frequency Distribution

Exclusive Class IntervalObtained Marks (X) No. of Students (f)

0 – 20 320 – 40 540 – 60 460 – 80 280 - 100 1

∑ f= N = 15

Inclusive Class IntervalObtained Marks (X) No. of Students (f)

0 -19 320 -39 540 -59 460 –79 280 - 99 1

∑f = N = 15

Method of Changing Inclusive to Exclusive Class Interval

Obtained Marks (X) No. of Students (f)46 352 558 479 285 1

∑X = 320 ∑f = N = 15

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C.F. = (L1 – L2)/2

Where, C.F. = Correction Factor L1 = Lower Limit of 2nd class L2 = Upper Limit of 1st class

Add C.F. to upper limit, i.e. Upper Limit + C.F. Deduct C.F. from lower limit, i.e. Lower Limit - C.F.

Problem: Change the following Inclusive Class Interval into Exclusive Class Interval.

Obtained Marks (X) No. of Students (f) 0 -19 320 -39 540 -59 460 –79 280 - 99 1

∑f = N = 15

Cumulative Frequency Distribution

Cumulative Frequency is obtained by adding successive frequencies of the variables. Distribution made by such addition of frequencies is called Cumulative Frequency Distribution. There are following two types of Cumulative Frequency Distribution:

(i) Less than Cumulative Frequency Distribution

Obtained Marks (X)

No. of Students (f)

Less than 20 3Less than 40 8Less than 60 12Less than 80 14

Less than 100 15∑f = N = 15

(ii) More than Cumulative Frequency Distribution

Obtained Marks (X)

No. of Students (f)

More than 0 15More than 20 12More than 40 8More than 60 6More than 80 1

∑f = N = 15

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Problem 1: Change the above Cumulative Frequency Distribution into Continuous Series.

Problem 2: Change the following Continuous Series into Less than and More than Cumulative Frequency Distribution.

Income ('000) 2 -3 3 - 4 4 - 5 5 - 6 6 - 7Family No. 3 2 12 8 1

Tabulation of Data

Q. What is Tabulation of Data? Explain the Importance of Tabulation of Data.

Ans: Tabulation of Data is the systematic arrangement of statistical data in rows and columns. Rows are horizontal arrangement whereas columns are vertical arrangement. Statistical data are tabulated after classification. The main purpose of tabulation is to simplify the presentation and to facilitate comparison.

Importance of Tabulation of Data

Tabulation of data helps to present a huge mass of data in a systematic manner within minimum space. The importance of tabulation can be explained under following grounds:

(i) It simplifies complex data: When data are tabulated, unnecessary details and repetitions are removed. Data are presented in table easily within a short period of time.

(ii) It facilitates comparison: Tabulation facilitates comparison. A table is divided into various parts and for each part, there are total and sub-total. Data of different parts can be compared easily.

(iii) It gives identity to the data: When data are arranged in the table with table number and title, they can be clearly identified. Such arranged data help to interpret the problems.

(iv) It gives patterns: Tabulation reveals patterns within the figures, which cannot be seen in raw form of the data. It may also facilitate to sum up the figures if the reader desires to check the totals.

General Rules of Tabulation of Data

There is no hard and fast rule for tabulation of data. Experience and common senses are required to construct good table. Following points should be kept in mind while tabulating data:

(i) Size of table should be suitable with available size of paper. Usually, number of rows should be more than the number of columns.

(ii) Captions and Stubs of table should be arranged in alphabetical order or in geographical order or in chronological order.

(iii) Unit of measurement, such as, Price in Rs., Weight in kg, etc. should be given in the table.

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(iv) Figures should be written in rounded form.(v) If certain figures are to be emphasized, such figures should be in distinctive form

or in box or in circle.(vi) Table should not be overloaded with unnecessary details.(vii) A 'Miscellaneous Column' should be added for those data, which do not fit in the

classification.(viii) Items related to each other should be placed nearabout. Total, Percentage, and

Ratio should be computed if necessary and they should be kept close to the tabulated data.

(ix) Don't use Zero for the information, which is not available. Use N.A. (Not Available) or – (Dash) to indicate it. Use '0' to indicate zero value only.

(x) If any number is repeated, write again that number, but don't use Ditto Mark (") and avoid using etc. and e.g. in the table.

(xi) Source should be given for secondary data.

Parts of Table

The major parts of a table are as follows:

(i) Table Number(ii) Title of Table(iii) Caption (Column Heading)(iv) Stub (Row Heading)(v) Body (Numerical Information)(vi) Head Note (Enclosed in Brackets Like 'In lakh', 'In kg', etc.)(vii) Foot Note (To clarify anything of the Table)(viii) Source

A Sample of Table

Table No. 3Title: Population of Nepal

(In lakh)Regions No. of Population Total

Female* Male*1. Terai ----- ----- -----2. Hilly ----- ----- -----3. Mountain ----- ----- -----Total ----- ----- -----

* Both literate and illiterate Source: Central Bureau of Statistics (CBS)

Types of Table

There are following two types of table:

(i) Simple and Complex Table(ii) General Purpose and Special Purpose Table

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Simple and Complex Table

Simple Table shows only one character. So, it is also called One-way Table. Complex Table shows two or more than two character. Complex Table with two characters is called Two-way Table and Complex Table with more than two characters is called Higher Order or Manifold Table.

Simple or One Way Table: Employees of a factory as per age group

Age No. of EmployeeBelow 30 330 – 40 1040 – 50 12Above 50 5Total 30

Two Way Complex Table: Employees of a factory as per age group and gender

Age No. of Employee TotalFemale Male

Below 30 1 2 330 – 40 4 6 1040 – 50 4 8 12Above 50 2 3 5Total 11 19 30

Higher Order or Manifold Complex Table: Employees of a factory as per age group, gender, and rank

General Purpose and Special Purpose Table

General Purpose Table gives detailed information for general purpose. This type of table is also called Reference Table. It is placed at the last pages of the Books or Reports as an Appendix.

Special Purpose Table gives information for special discussion. This type of table is also called Summary Table. It is placed in the body of the Books or Reports.

AgeNo. of Employee

TotalFemale MaleOfficer Assistant Officer Assistant

Below 30 1 - - 2 330 – 40 2 2 4 2 1040 – 50 1 3 2 6 12Above 50 2 - 3 - 5Total 6 5 9 10 30

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Chapter: V Measure of Central Tendency (Condensation of Data)

Q. What is Measure of Central Tendency? What are the requisites of an Ideal Measure?

Ans: A Measure of Central Tendency is a typical value that represents the entire mass of data. The measures of central tendency are also called averages. Thus, an average is a single value that represents a group of values.

The objectives of studying the measures of central tendency are:

(i) to facilitate comparison.(ii) to help for computing various other statistical measures such as mean deviation,

standard deviation, etc.(iii) to represent the mass of data by a single typical value.(iv) to help in decision making.

Requisites/Essentials of an Ideal/Good Measures of Central Tendency

Following properties are essential for the measure of central tendency to be ideal:

(i) It should be rigidly defined: The average should be defined rigidly so that it has only one interpretation, i.e., the average computed for a given data by different people should be same and definite value.

(ii) It should be easy to understand: Statistical methods are designed to simplify complexity. Therefore, it is desirable that an average should be easy to understand.

(iii) It should be simple to compute: The computation of an average should be simple so that it can be used widely.

(iv) It should be based on all observations: In order to be the average representative of the whole data, it should be computed by including all the items as far as possible.

(v) It should be unaffected by extreme items (i.e., largest and smallest value): If there are one or two very small or large items in the given series, the average cannot be typical of the entire series. So, the average should not be affected by largest or smallest value.

(vi) It should be capable of further algebraic treatment: An average could be used for further statistical treatments. For example: we should be able to compute combined average of two or more series from their individual average.

(vii) It should have sampling stability: If two independent samples are drawn in a particular field, the obtained average from one sample should not significantly vary from the average of the other samples.

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UNIT: 3 QUANTITATIVE ANALYSIS IN ECONOMICS

Need for Quantitative Analysis in Economics

Quantitative Analysis refers to those methods in which a subject is studied on the basis of various facts or data used in quantitative forms. The main purpose of quantitative analysis is to provide preciseness to the facts so that they can be easily compared. Quantitative analysis combines statistical and mathematical analysis. Quantitative analysis is needed due to following reasons:

(i) In early days, words were sufficient to explain or analyze everything in economics. But, nowadays, economic theory and practice have become more and more complex and it is difficult and also tedious to explain or analyze them in words.

(ii) Economic theory can be easily tested/verified through quantitative analysis.

(iii) Quantitative analysis helps to select representative samples and to test them.

Use of Mathematics in the Field of Economics

Economic Theory is generally presented either in verbal form or in mathematical form. Economic theories and problems can be simplified and clarified through mathematical symbols. Geometry was the first mathematical tool used in economics. Geometrical diagrams are commonly used to show the relationship between economic variables. Other mathematical tools like ratio, equations, indices, logarithm, derivation, etc. are also used to show the relationship between economic variables. Economic problems like cost minimization, profit maximization, sales maximization, etc. can be solved with the help of equations, linear programming, maxima-minima, etc.

Use of Statistics in the Field of Economics

Statistics helps economists to formulate Economic Theories and Economic Policies. Economists use statistical information to justify the relationship between economic variables. Statistical data are necessary to analyze business cycle, national income, economic growth, inflation, unemployment, etc. Time series analysis, Index number, Forecasting technique, etc. are some of the very powerful statistical tools, which are used in Economics.

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