3. Emphasis on social dand susevelopment, securities and protection for high and
sustainable human development.
4. Promotion of good governance through economic and administration reform,
competant and accountable public finance, transparent and people friendly public
services and protection and promotion of human right.
5. Enhancement of gender equality, inclusion, environment protection, maximum use
of science and technology and institutional capability.
Quantitative Targets
The quantitative targets of the key indicators for the Fourtenth Plan are shown in the
table given below
S.N Indicators Situation in Current Plan
FY 2015/16 Targets
1 Annual average economic growth rate (%) 0.77 7.10
2 Annual average agriculture sector growth rate 1.33 4.70
(%)
3 Annual average non agriculture sector growth 0.63 8.30
rate (%)
4 Rate of Inflation 9.5 8.30
5 GDP per capita (in Rs. thousands) 80.90 105.70
6 Population below poverty line (in %) 21.6 17.00
7 Human Development Index 0.54 0.57
8 Gender Empowerment Index 0.56 0.58
9 Life Expecancy (age) 71 72
10 Population with access to drinking water (%) 83.60 90.20
11 Secondary level net enrolment rate (%) 37.70 45.00
12 Literacy rate of age group 15-24 88.6 91.0
13 VDC connected with road transportation (Nos.) 2739 3062
14 Electricity generation (Installed capacity MW) 829 1500
15 Population with access to electricity 74.00 87.00
16 Irrigation (hectare) 13.96 15.20
17 Population with access to internet service (%) 46.40 65.00
Review READING BETWEEN THE LINES
Reviewing the 14th plan, NPC has said that fair progress has been achieved in agriculture,
social development, poverty reduction, average economic growth and access to drinking water.
However, the report admits that physical infrastructures couldn’t be significantly improved
as per the plan’s objective. Attributing the improvement in labour relations, smooth supply of
electricity and a political stable system in the country, the report is highly hopeful of the new
plan inching closer to its goals by 2023-24. Improved access to drinking water and Human
Development Index of 0.574 are positive signs of country marching ahead in the direction
of economic prosperity reads the same report. The Finance Minister also mentioned that
the average economic growth rate in the same period has remained 6.64 during the report
presentation ceremony.
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8.4 CURRENT PLAN- FIFTEENTH PLAN (2019/20-2023/24)
Background:
The constitution of Nepal envisages creating a prosperous, independent and socialist-
oriented economy. The Fifteenth Plan has a vision of rapid and balanced economic
development, prosperity, good governance and happiness for the citizens. This will be
the first plan to achieve the target in the federal structure through three levels of efficient
intergovernmental finance management and cooperation with the private, cooperative
and community sectors.
It is necessary to achieve the target of long term development goals by 2087 B.S. as
promised in the Millennium Development Goals. Furthermore, it is of utmost concern to
upgrade Nepal from Least Developed Country to Developing Country by 2079 B.S and to
achieve the target of upgrading Nepal to the level of middle income country by 2087 B.S
This fifteenth plan of Nepal will focus on building a foundation for the realization of
economic prosperity and civic happiness by maintaining harmony in the functioning of
the three levels of government through the mobilization of internal and external resources
and resources and intergovernmental finance.
Challenges:
1. The task of equitable economic prosperity and qualitative improvement in the lives of the
citizens is challenging. The elimination of absolute and multidimensional poverty and the
need to reduce income inequality drastically require huge resources and resources.
2. The task of systematic urbanization, integrated and secure settlement development, rural
infrastructure development, increase in consumption of clean energy and development
of information technology, commercialization of agriculture and forest products, the
expansion of the industry sector and the enhancement of the quality of the service sector.
3. The development of productive employment opportunities through the development
of healthy and educated citizens and skilled human resources, the use of demographic
benefits and the efficient and effective implementation of financial federalism while
maintaining macroeconomic stability are challenging.
4. The implementation of the fundamental rights guaranteed by the constitution will require
plenty of resources and resources to achieve its progress and sustainable development
goals.
5. Creating a comfortable environment for investment focus by identifying the conductive
sectors of the economy’s auxiliary sectors and converting areas, improving the public
service flow through capital transfers at the state and local level, improving public service
flows, employment, income generation and poverty alleviation and development of the
local economy.
Opportunities:
1. There is potential for a huge contribution to the creation of national capital through
investment in the private sector, professionalism and competitiveness enhancement and
mobilization of productive sectors of the community and cooperative sectors.
2. During the planning period, investment in the connector sectors of the economy and
transformational programs/projects will help in building a more equitable society through
the increase in the size of the economy and the equitable distribution of the returns it
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receives. There is a possibility of increasing public investment by expanding the scope of
finance towards internal sources.
3 Inter-government partnerships and public-private partnerships have shown that it can
mobilize the necessary investment for capital formation. Also, the commitment from the
bilateral and bilateral development partners provides the assurance of resources. The
expansion of the service sector by the development of economic, social and physical
infrastructure will help increase the productivity and productivity of the economy.
4. Due to the active government and institutional stability at the union, state and local levels,
the country is moving forward towards economic prosperity including social justice and
the competitive spirit of sustainable development, prosperity and good governance at the
state and local level is in itself an opportunity.
5. The potential for utilizing the available demographic benefits in the development of the
country through human capital creation is high.
Objectives of 15th periodic plan of Nepal:
a. To provide easily accessible, qualitative and modern infrastructure, productive employ-
ment generation, high sustainable inclusive economic growth through poverty alleviation.
b. To provide qualitative health and a healthy environment, social justice, accountable social
service and quality of life.
c. To protect the national benefit of democracy, sovereignty and ensure socio-economic
transformation for a strong economic foundation.
National Goals:
The Fifteenth Plan of Nepal will be the basis for achieving long-term thinking of “Prosperous
Nepal, Happy Nepali“. In accordance with this, the national goal of the scheme is to build
a foundation for upgrading high-income countries by transforming it into a socialist-
oriented public welfare state with a rich economy, social justice, and sophisticated living.
The plan has the goal to increase the economic growth rate to 10.5% and eradicate absolute
poverty (reduce to 0%) by 2100 B.S. .
Strategies of the Plan:
1. Promoting Rapid, Sustainable and Economical Employment: Rapid, sustainable and
employment-based economic growth will be achieved through basic and macro-
infrastructure construction, production and utilization of clean credit, high cost and
commercial agriculture, productive industry and tourism development and expansion of
trade.
2. Ensure Accessible and Quality Healthcare and Education: At the local level, equitable
access of citizens to health services will be established by developing health infrastructure
including basic health services. The use of the latest technology and the availability
of manpower and efficiency will be ensured to ensure the quality of health services in
medicine and treatment systems, physicians and service effects.
3. Developing Internal and Inland Interdependence and Sustainable Cities/Settlements:
The investment will be concentrated in this area, which is one of the major contributors
to economic growth. Inter-dependency development, production cost reduction and
competitive capacity will be enhanced based on an integrated transport system for
the construction of national, regional and local road networks, tunnelways, highways,
railways, waterways, and airports. It will also help increase domestic and international
trade and quality tourism.
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4. Productivity and Productivity Enhancement: Rapid and intensive expansion of irrigation
facilities, effective implementation of land use policy, integration of land and agitation,
adoption of advanced seed-seeding, fertilizer and modern technology, mechanization,
modernization, commercialization of agriculture with emphasis on low cost/volume high
cost and organic agricultural production and processing.
5. Provide Complete, Sustainable and Productive Social Security and Protection: All
citizens will be provided with the opportunity provided by the Constitution, the services
provided by the state, full security and respect and social protection. For the inclusive
economic growth, elimination of absolute poverty, and equitable distribution of income,
equitable access, distribution and utilization of the means of production, employment and
opportunities will be ensured.
6. To build a Just Society with Poverty Alleviation and Economic Social Equality: Programs
on building a safe, decent and equitable society will be implemented by ending gender
equality and ending all forms of violence, discrimination, exclusion, and perversion.
Emphasis will be given to equal access and distribution on all types of opportunities
including education, health, employment, representation. Emphasis will be given on the
establishment of healthy and vibrant social life through the protection and promotion of
socio-cultural diversity, social and community activities and social capital mobilization.
7. Conservation of Natural Resources and Development of Operations and Sustainability:
The contribution of land, forest, water resources, and mineral resources to agriculture,
industry, and services will be increased and protected. Commercial and agricultural forest
and non-timber forest products will be increased towards the forest area. A strategy will
be adopted to adapt to climate change and reduce the risk of disaster. In order to prepare
for disaster management, rescue, relief, and rehabilitation, basic proof will be given to the
institutional and structural reforms and development processes of the union, state and
local levels.
8. Strengthening Public Service, Promoting Regional Balance and National Unity: On the
basis of cooperation, co-existence and coordination in the federal governance system,
public services provided by the federal, state and local level will be made agile, transparent
and accountable. The services and facilities directly involved with the citizenry will be
provided from the local level. The multidimensional aspects of good governance will be
improved for development and prosperity while strengthening national unity, security,
and dignity. The federal governance system will be strengthened by increasing access to
financial services, inclusion, and literacy.
Priority Areas of 15th periodic planl:
The following are the priority areas of this Plan
a. Development of hydroelectricity and different energies.
b. Increase the profitability, expansion, and commercialization of the farming segment.
c. Development of the tourism, industry and business segments.
d. Development of fundamental instruction and wellbeing, drinking water and sanitation
sectors.
e. Promotion of good administration.
f. Development of roadways and other physical foundations.
g. Protection of natural resources and the environment
i. Involvement of all tiers of government to achieve economic growth.
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Quantitative Targets
The major highlights and quantitative targets of the key indicators for the Fifteenth Plan
are shown in the table given below
S.N Indicators Current Current Plan
Situation Targets
1 Annual average economic growth rate (%) 6.8 10.3
2 GNP Per Capita US $1047 US $1595
3 Population below poverty line (%) 18. 11
4 Gini Co-efficient 0.31 0.29
5 Life expectancy at birth 69.7 years 72 years
6 Unemployment rate 11.4% 6%
7 Roadways 6979 KM 15000 KM
8 Railways 42 KM 200 KM
9 Family with access to electricity (%) 90.7 99
10 Population with access to drinking water (%) 88 99
11 Population with access to internet service (%) 55.4 80
12 Hydropower generation (MW) 1020 5000
13 HDI 0.574 0.624
14 Happiness Index 4.7 5.1
Key Takeaways READING BETWEEN THE LINES
MILLENIUM DEVELOPMENT GOALS
The United Nations Eight Millennium Development Goals which were to be achieved by 2015
by all 191 UN member countries were:
1. to eradicate extreme poverty and hunger;
2. to achieve universal primary education;
3. to promote gender equality and empower women;
4. to reduce child mortality;
5. to improve maternal health;
6. to combat HIV/AIDS, malaria, and other diseases;
7. to ensure environmental sustainability; and
8. to develop a global partnership for development.
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EXTRA READINGS
SUMMARY OF THE FIFTEENTH PLAN
Long Term Vision of 15th plan :
Promote Good Governance, Development, and Prosperity of the country. The main motto
of the current 15th 5-year plan is “Prosperous Nepal, Happy Nepali” To transform Nepal
as a nation of happy, healthy, educated, dignified and high quality living citizens with
equal opportunity, including prosperous, independent and socialist-oriented economies.
Goal:
To increase the economic growth rate to 10.5% and eradicate absolute poverty (reduce to
0%) by 2100 B.S.
National Objectives of 15th periodic plan of Nepal:
a. To provide easily accessible, qualitative and modern infrastructure, productive em-
ployment generation, high sustainable inclusive economic growth through poverty
alleviation.
b. To provide qualitative health and a healthy environment, social justice, accountable
social service and quality of life.
c. To protect the national benefit of democracy, sovereignty and ensure socio-economic
transformation for a strong economic foundation.
Long Term National Objectives:
1. Accessible modern infrastructure and intensive connectivity.
2. Development and full utilization of human capital potentials.
3. High and sustainable production and productivity.
4. High and equitable national income.
5. Well-being and decent life.
6. Safe, civilized and just society.
7. Healthy and balanced environment.
8. Good governance, Comprehensive democracy, National unity, security, and dignity.
Strategies of 15th periodic plan of Nepal:
a. Facilitate accelerated, sustainable and employment-oriented economic growth.
b. Facilitating accessible and quality medical care and education.
c. Internal and non-industrial immobility and development of residence.
d. Increasing production and productivity.
e. Provide comprehensive, effective social security and safety.
f. Alleviating poverty and ensuring equality and justice-based society.
g. Conservation of natural resources and development of sustainability.
h. Strengthening of public service, provincial balancing, and integration of central units.
i. Involvement of all tiers of government to achieve economic growth.
Priority Areas of 15th periodic plan of Nepal:
a. Development of hydroelectricity and different energies.
b. Increase the profitability, expansion, and commercialization of the farming segment.
c. Development of the tourism, industry and business segments.
d. Development of fundamental instruction and wellbeing, drinking water and sanita-
tion sectors.
e. Promotion of good administration.
f. Development of roadways and other physical foundations.
g. Protection of natural resources and the environment.
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KEY CONCEPTS
Economic planning Sectoral planning Priorities
Sustainable growth Biodiversity Good governance
Inclusive development Millenium Development Goals Interim Plan
Poverty alleviation Economic transformation Red tapism
UNIT OVERVIEW
Economic planning with poverty reduction through productive
employment and justifiable distribution
Economic planning is the conscious and oriented economic growth.
deliberate attempt by the state to achieve some
pre determined objectives. Current Plan- Fifteenth Plan (2019/20-
2023/24)
Process of plan formulation Vision
Promote Good Governance, Development,
1. Assessment of Existing Status of and Prosperity of the country. The main
Development motto of the current 15th 5-year plan is
“Prosperous Nepal, Happy Nepali”
2. Objectives Goal
3. Priorities To increase the economic growth rate to
4. Strategies and Policies 10.5% and eradicate absolute poverty (re-
5. Programmes duce to 0%) by 2100 B.S.
6. Monitoring and Evaluation
Long Term National Objectives:
Importance of economic planning 1. Accessible modern infrastructure and
1. Important to increase economic growth intensive connectivity.
rate 2. Development and full utilization of hu-
2. To increase the rate of capital formation man capital potentials.
3. Bring equality in the society by reducing 3. High and sustainable production and
the gap between rich and poor. productivity.
4. Important to increase employment 4. High and equitable national income.
5. Well-being and decent life.
opportunities 6. Safe, civilized and just society.
5. Expand foreign trade and reduce trade 7. Healthy and balanced environment.
8. Good governance, Comprehensive de-
deficit
6. Essential to reduce regional imbalance mocracy, National unity, security, and
dignity.
in development
Fourteenth Plan (2016/17-2018/19)
Vision
The vision of the Fourteenth Plan is to develop
independent, prosperous and socialism
oriented economy and prosperous Nepali
people.
Target
The Fourteenth Plan aims to create a socially
just welfare state and upgrade Nepal to the
level of mIddle income country.
Objective
The Plan has the objective o achieve
economic and social ransformation along
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REVIEW QUESTIONS
Very Short Answer Type Questions
1. What is meant by development planning?
2. When was the systematic development planning started in Nepal
3. What is the objective of the current plan?
4. What is the long term vision of the current plan?
5. What is the economic growth rate target of the current plan?
Short Answer Type Questions
1. Explain the steps of plan formulation.
2. What were the priorities of the thirteenth plan
3. Discuss the objectives and priorities of the current plan?
4. What are the strategy and sectors included in the current plan?
READINGS BETWEEN THE LINES
NATIONAL PLANNING COMMISION
The Planning Commission was first created in Nepal in 1956. It was
soon renamed in accordance with the Yojana Mandal Act of 1957.
Following the introduction of the partyless Panchayat system in 1961,
the National Planning Council was formed under the then King. In
1963, the Council was dissolved and a new planning body, with an
identical name, was constituted under the Chairman of the Council of
Ministers. All the Ministers became ex-officio members of the Council;
and the Ministry of Economic Affairs was renamed the Ministry of
Economic Planning.
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9UNIT STATISTICS IN ECONOMICS
Learning Objectives Weight:23 Lecture Hours
On Completion of this unit the student will be
able to:
• Understand the meaning of Statistics in
singular and plural sense
• Explain the scope and importance of statistics
• Explain the limitations of statistics
• Explain the various bases of classification of
data
• Understand tabulation and explain different
types of table Before you begin
• Present the data in diagrams and graphs Statistics is very important in business
and economics because it helps businesses
make informed and accurate decision
based oncertain trends. It helps the plan-
ning and production process.
Very Short Type Short Type Long Answer Type Total Marks
0 2
0 10
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9.0 INTRODUCTION TO STATISTICS
The word ‘Statistics’ has been derived from the Latin word ‘status’, German word
‘statistik’ and the Italian word ‘statista’. All denote the same meaning that is a
political state. In ancient times, the government used to collect the information
regarding the size of the population in the country, property of the country, military
force, etc. So, in those days, statistics was considered as the science of statecraft. But
at present, statistics are used by the economist, managers, scientist, politicians, etc. So
these days, there is hardly a place where statistics are not used.
Statistics is understood in two senses: singular sense and plural sense. In the singular
sense, statistics is a science which studies the collection, presentation, analysis and
interpretation of numerical data. In the plural sense, it denotes an aggregate of numerical
data. These two aspects are briefly explained below.
A SINGULAR DEFINITION OF STATISTICS
In singular sense, statistics may be defined as science of statistical technique used for
collection, presentation, analysis and drawing conclusion from the data.
According to Croxton and Cowden, “Statistics is defined as the collection, presentation,
analysis and interpretation of numerical data”
The definition of Croxton and Cowden is the most comprehensive definition of
statistics in the singular sense and has the following features which are also the stages
of any statistical enquiry:
a. Collection of Data: The collection of data is first work of any statistical investigation.
The statistical data are collected with proper planning with the use of suitable method
of data collection.
b. Organization and Presentation of Data: The collected data are arranged in a systematic
manner and presented in various forms such as tables, graphs, diagrams, figures etc.
c. Analysis of Data: The organized data are analyzed by using various statistical methods
or tools such as average, correlation, regression, index number, time series etc.
d. Interpretation of Data: In the final step, the result of the analysis is interpreted to draw
correct and valid conclusions.
B PLURAL DEFINITION OF STATISTICS
In the plural sense, statistics refers to the statistical data or numerical facts and figures
collected from various fields of study in a systematic manner for a pre-determined
purpose. In other words, statistics denotes an aggregate of numerical facts and figures.
According to Horace Secrist, “By Statistics we mean aggregate of facts affected to
a marked extent by multiplicity of causes, numerically, expressed, enumerated or
estimated to reasonable standards of accuracy, collected in systematic manner for a
predetermined purpose and placed in relation to each other.”
The definition has the following features:
a. Statistics are Aggregate of Facts: In statistics, a single numerical figure has no meaning.
Statistics is an aggregate of numerical data.
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b. Multiplicity of Causes:Numerical facts are generally affected by various factors. So it
is difficult to isolate the effect of any single factor.
c. Statistical Values are Numerically Expressed: The statistical values are expressed
numerically. Qualitative information doesn’t constitute statistics.
d. Statistics are Collected in a Systematic Manner: The data are collected systematically
with proper planning. Otherwise, interpretation and conclusion may be wrong or
misleading.
e. Statistics are Collected for Pre-determined Purpose: The purpose, specific aims and
objectives of the inquiry have to be well defined before collecting the data.
f. Data Placed in Relation to Each Other: The collected numerical data constitutes
statistics if they are comparable. The data are placed in relation to each other to
facilitate comparison.
9.1 FUNCTIONS OF STATISTICS
The functions of statistics may be enumerated as follows :
1. Present facts in a Definite Form: Numerical expressions are convincing and therefore one
of the most important functions are statistics is to present general statements in a precise
and definite form. Statements or facts conveyed in exact quantitative terms are always
more convincing than vague expressions.
2. Simplify Complex Data: Huge mass of data are simplified with statistics. An average is
used to give a bird’s eye view of the large masses. For example, complex data may be
simplified by presenting them in the form of a table, graph or diagram, or representing it
through an average etc.
3. Technique for Making Comparisons: The significance of certain figures can be better
appreciated when they are compared with others of the same type. The comparison
between two different groups is best represented by certain statistical methods, such as
average, coefficients, rates, ratios, etc.
4. Enlarge Individual Knowledge: Statistics enables one to enlarge his horizon. So when
a person goes through various procedures of statistics, it widens his knowledge pattern.
It also widens his thinking and reasoning power. It also helps him to reach to a rational
conclusion.
5. Formulation of Policies: Statistics helps in formulating plans and policies in different
fields. Statistical analysis of data forms the beginning of policy formulations. Hence,
statistics is essential for planners, economists, scientists and administrators to prepare
different plans and programmes.
6. Forecasting: Plans and policies of organizations are invariably formulated well in advance
of the time of their implementation. A knowledge of future trends is very helpful in framing
suitable policies and plans. Statistical methods provide helpful means of forecasting future
events.
7. Measurement of the Magnitude of a Phenomenon: But for the development of the
statistical science, it would not be possible to estimate the population of a country or
to know the quantity of wheat, rice and other agricultural commodities produced in the
country during any year.
8. Formulation and Testing of Hypothesis: Statistical methods are extremely useful
in formulating and testing hypothesis. With the help of statistical techniques, we can
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know the effect of imposing tax on the exports of tea on the consumption of tea in other
countries.This helps in developing new theories. So statistics examines the truth and
helps in innovating new ideas.
9.2 SCOPE OF STATISTICS
The scope of statistics is very vast. There is almost no human activity where its application
is not needed. As far as scope is concerned it is studied under following heads:
1. Nature of statistics
2. Relation of statistics with other sciences i,e Uses of Statistics
3. Limitations of statistics.
1. NATURE OF STATISTICS
The nature of statistics concerns with statistics as science or an art. Different economists
and statisticians differ on this point.
Statistics as a Science:
Statisticians like Bowley treated Statistics as a science. According to Bowley, “Statistics
is the science of measurement of the social organism regarded as a whole in all its,
manifestations.”
As a science, it studies the statistics in a systematic manner. But it is not a complete
science such as Physics and Chemistry. Because in these all the causes are kept under
control and the observations and results are found similar.
If we take the various statistical methods in consideration, we can define statistics as a
science due to the following facts:
• It gives the scientific manner to compare and present the data in the numerical form.
• By using the formulas we can study the economic problems and their solutions too.
• It helps as a instrument to manage and built up the economic theory.
Statistics as an Art:
Some statisticians defined statistics as an art of applying the science of scientific methods.
As an art, statistics offer a better understanding and solution to problems in real life as it
offers quantitative information. It is concerned with ways and means of presenting and
handling data making inferences logically and drawing relevant conclusions.
We can define statistics as a science due to the following facts:
• It teaches the manner that how we should present our data.
• It may use the graphs, table to show the data and by making them clearly it’s the art to
show it clearly.
• It offers a better understanding and solution to problems in real life as it offers
quantitative information
According to Tippet, “Statistic is both a science and an art. It is a science in that its methods
are basically systematic and have general application and art in that their successful
application depends, to a considerable degree, on the skill and special experience of the
statistician, and on his knowledge of the field of application.”
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9.3 IMPORTANCE AND USES OF STATISTICS
The importance and uses of statistics may be explained in the following headings:
1. Statistics and Economics: Economics is concerned with production and distribution of
wealth as well as with the complex institutional set-up connected with the consumption,
saving and investment of income. Statistical data and statistical methods are of immense
help in the proper understanding of the economic problems and in the formulation of
economic policies. In the field of economics it is almost impossible to find a problem
which does not require an extensive uses of statistical data. The laws of economics like
law of demand, law of supply etc can be considered true and established with the help of
statistical methods.
2. Statistics and Business: Statistics is an aid to business and commerce. When a person
enters business, he enters into the profession of fore casting. Modern statistical devices
have made business forecasting more precise and accurate. A business man needs relevant
fact and figures to prepare the financial plan of the proposed business. In industrial
concern statistical devices are being used not only to determined and control the quality
of products manufactured by also to reduce wastage to a minimum. The technique of
statistical control is used to maintain quality of products.
3. Statistics and Research: Statistics is an indispensable tool of research. Most of the
advancement in knowledge has taken place because of experiments conducted with
the help of statistical methods. Statistical methods are also useful for the research in
medicine and public health. In fact there is hardly any research work today that one can
find complete without statistical data and statistical methods.
4. Statistics in Planning: Statistics is indispensable in planning. The modern age is termed
as the ‘age of planning’ and almost all organisations,business or management resort to
planning for efficient working and for formulating policy decision. To achieve this end,
the statistical data relating to production, consumption, birth, death, investment, income
are of paramount importance. Today efficient planning is a must for almost all countries,
particularly the developing economies for their economic development.
5. Statistics in Mathematics: Statistics is intimately related to and essentially dependent
upon mathematics. The modern theory of Statistics has its foundations on the theory of
probability which in turn is a particular branch of more advanced mathematical theory of
Measures and Integration. Ever increasing role of mathematics into statistics has led to the
development of a new branch of statistics called Mathematical Statistics. Thus Statistics
may be considered to be an important member of the mathematics family. In the words of
Connor, “Statistics is a branch of applied mathematics which specialises in data.”
6. Statistics in Social Sciences: Every social phenomenon is affected by a multiplicity of
factors. Statistical tools of Regression and Correlation Analysis can be used to study and
isolate the effect of each of these factors on the given observation. Sampling Techniques
and Estimation Theory are very powerful and indispensable tools for conducting any
social survey, pertaining to any strata of society and then analysing the results and drawing
valid inferences. The most important application of statistics in sociology is in the field
of Demography for studying mortality (death rates), fertility (birth rates), marriages,
population growth and so on.
7. Statistics in Trade: Business is full of uncertainties and risks. The future trend of the
market can be expected with the use of statistics. Failure in anticipation will mean failure
of business. Changes in demand, supply, habits, fashion etc. can be anticipated with the
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help of statistics. Statistics is of utmost significance in determining prices of the various
products, determining the phases of boom and depression etc. Use of statistics helps
in smooth running of the business, in reducing the uncertainties and thus contributes
towards the success of business.
9.4 LIMITATIONS OF STATISTICS
In spite of the wide scope of the subject, statistics has certain limitations. Some important
limitations of statistics are the following:
1. Statistics does not Study Qualitative Phenomena: Statistics always studies the quantitative
characteristics of the given problems. A qualitative phenomenon like honesty, culture,
love, poverty, etc, can’t be expressed numerically or direct statistical analysis. So the
quality aspect of a variable or the subjective phenomenon falls out of the scope of statistics.
However, that phenomenon can be expressed indirectly of numbers and analyzed in
statistics. Statistics deals with facts and figures.
2. Statistical Laws are not Exact: Statistical laws are not exact as in case of natural sciences.
These laws are true only on average. They hold good under certain conditions. They
cannot be universally applied. Most of the statistical analysis is based on the collected
data that may not be 100% correct. If the data are not correct, then the result obtained from
such data can’t be expected 100% accurate. So statistics has less practical utility.
3. Statistics does not Study Individuals: Statistics deals with the aggregate of facts and doesn’t
give any individual measurement. Individual item does not constitute statistical data and
is meaningless for statistical enquiry. For example, a student’s marks in economics can’t be
considered as statistics but the marks obtained by all the students make statistics. Single
or isolated figures are not statistics. This is considered to be a major handicap of statistics.
4. Statistics can be Misused: Statistical techniques are used to analyze and interpret the
collected information in an enquiry. Statements supported by statistics are more appealing
and are commonly believed. For this, statistics is often misused. Statistical methods rightly
used are beneficial but if misused, these become harmful. Statistical methods used by less
expert hands will lead to inaccurate results.
5. Statistical relies on Estimates and Approximations: Statistical laws are not exact laws
like mathematical or chemical laws. They are derived by taking a majority of cases and are
not true for every individual. Statistics largely deals with averages and these averages may
be made up of individual items radically different from each other. Thus the statistical
inferences are uncertain.
6. Statistical Decisions Attract Errors: One of the shortcomings of statistics is that there are
several errors which occur during statistical decisions. These errors are notably detected
during statistical inference. Also, in measures of variability, a variation between variables
can be calculated using the standard deviation, mean deviation and quartile deviation in
which the results vary. Hence statistics should not be used as the only method of research.
7. To Many Methods to Study a Problem: There are many methods of analyzing a given
problem. For example, variation can be found by quartile deviation, mean deviation or
standard deviations and results vary in each case.
Glossary Comprehensive: Complete or covering all aspects of something
Vague: Indefinite, or unclear character or meaning.
Subjective: Based on or influenced by personal feelings, tastes, or opinions
Deviation: Departing from an established course or accepted standard
Vedanta High School Economics - 10 164
9.5 IMPORTANCE OF STATISTICS IN ECONOMICS
In the field of Economics it is almost impossible to find a problem which does not require
an extensive use of statistical data. The importance of statistics in economics are as
follows:
1. Analysis of Consumption: Statistics of consumption tell us of the relative strength of the
desire of a certain section of the people and its variations from time to time. By statistical
analysis we can study the manner in which people spend their income over various items
of expenditure, namely, food, clothing, house rent, etc.
2. Analysis of Production Function: The relationship Production function is the
between the various factors of input and output is relation relation between
termed as production function. In fact, such a production KEY inputs and output
function is evaluated by the help of various statistical IDEA
tools.
3. Statistics in Exchange: Exchange statistics throw light on the commercial development of
a nation. They tell us about the volume of business done in a country and the amount of
money in circulation.
4. In the Field of Distribution: Distribution statistics disclose the economic conditions of
the various classes of people. They throw light on the distribution of national dividend
amongst the inhabitants of a country.
5. Determination of National Income and Per Capita Income: Statistics help us to calculate
the national income and PCI. PCI is one of the component of national income. It is
accounted for by the help of NI and the size of the population. Statistical techniques are
used in collecting and processing national income data.
6. To solve Production related Economic Problems: Production statistics are very useful
in solving basic economics problems like what to produce, how to produce, for whom to
produce, etc. which are arisen due to the scarcity of resources. It also helps in adjusting
the market supply to market demand.
Pause for Thought
7. Helpful in Formulating Economic Policies: The various Despite its uses, there
statistical tools help in the formulation of economic are limitations of statistics
policies. In fact, economic policies such as fiscal policies ....Explain
and monetary policies are determined by the help of
statistics.
8. Means of Economic Planning: Statistical methods are methods of economic planning.
Statistics helps to evaluate the achievements and problems of the previous plan. Similarly,
they help to fix targets and revenue and expenditure statements of the current plan
CHECKPOINT 1. Explain the singular definition of statistics
2. Explain the plural definition of statistics
3. Explain the relationship of statistics with other sciences
4. Is statistics a science or an art? Explain
165 Vedanta High School Economics - 10
9.6 TYPES AND SOURCES OF DATA
There are two sources of data. These sources also constitutes the types of data:
a. Primary Data
b. Secondary Data
a. Primary Data: The data which are collected by an investigator originally from its basic
source for the first time for any statistical inquiry are known as primary data. The primary
data are also called first-hand data. As it is collected directly from the informants. Primary
data are generally used in those cases where the secondary data do not provide an adequate
basis for analysis. Primary data are also called field source. Example: Data obtained in a
population census by C.B.S (Central Bureau of statistics) are primary data of the same
organization.
b. Secondary Data: Those data which are collected by one agency organization or person
but used by other agency, organization or person are called secondary data. These types of
data are not original for the user. These are also called second-hand data. The data which
are already collected by someone but obtained from some published and unpublished
sources are called secondary data. Example: For Central Bureau of statistics, the census
data are primary whereas, for all others we use, such data are secondary.
Census of population is done by the government. The data collected are known as primary
data. Now a separate department of the government or any other private concern use these
related data for any purpose, then the data will be known as secondary data to them. Data
are primary to the collector, but secondary to the user.
DISTINCTION BETWEEN PRIMARY AND SECONDARY DATA
The distinction between primary data and secondary data is shown in the table given
below:
Primary Data Secondary Data
Data collected the first time from the Data that are already collected and used
field of study are called primary data. by others are called secondary data.
They are first hand or original in nature. They are second hand in nature.
It gives more accurate information. Sometimes secondary data may not be
accurate.
They are like raw materials and they They are found in ready-made form just
have to be processed after collection. like finished goods.
Collection of primary data takes a large Secondary data save money, time and
amount of money and efforts. efforts because these are used from the
existing sources.
There is no need to worry about while Secondary data should be carefully and
using primary data from the investigator. critically examined before they are used.
Primary data are collected directly from the Secondary data are collected from pub-
people to which enquiry is related. lished sources
Keynote • Primary data are raw data which are collected for the first time from the
field of enquiry
• Secondary data are obtained from the already existing sources are second
hand data
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9.7 METHODS OF COLLECTING PRIMARY DATA
The following methods are common in use :
1. Direct Personal Observation: Under this method, the investigator collects the data
personally. He has to go to the spot for conducting enquiry has to meet the persons
concerned. It is essential that the investigator should be polite, tactful and have a sense of
observation.
This method is applicable when the field of enquiry is small and there is an intention of
greater accuracy. This method however, gives satisfactory result provided the investigator
is fully dependable.
2. Indirect Oral Investigation: In this method data are collected through indirect sources.
Persons having some knowledge regarding the enquiry are cross-examined and the desired
information is collected. The investigator does not directly ask the questions to the persons
who are directly concerned with the problem. The investigator obtains the necessary
information by contacting the third person (witness) who is familiar with the problem.
This method is usually adopted by enquiry committees or commissions appointed by
governments or semi- government or private institutions.
3. Mailed Questionnaire Method: In this method, the investigator prepares a questionnaire (a
set of questions). The questionnaire along with a self addressed stamped envelope is sent
to various informants by post or mail. The respondents have to fill up the questionnaire
and mailed it back to the concerned authority. A questionnaire is a list of questions directly
or indirectly connected with the field of enquiry.
The advantage in this method is that it is less costly, as no enumerators are required and
investigations can be completed within a short time. Its greatest drawback is that the
informants may not send back the schedules duly filled in.
4. Schedule Sent through Enumerators: In this method, enumerators go to the informants to
help them in filling the answers. Trained investigators go to all persons or selected persons
connected with the enquiry. This method is useful for extensive enquiries. The method of
collecting data is relatively cheap. Also the information obtained is of good quality.
The main drawback of this method is that the enumerator may be a biased and may not
enter the answer given by the information.
4. Information from Correspondents: Under this method certain correspondent are
appointed in different parts of the field of enquiry, They submit their reports to the Central
Office where the information is processed. With this method, a rough and approximate
estimate is obtained at a very low cost. This method is adopted by news media and various
government departments where regular information is to be collected from a wide area.
9.8 SOURCES OF SECONDARY DATA
Secondary data can be gathered from different sources which can be categorised into two
categories:
A questionnaire is a list of
1. Published sources
questions directly or indirectly
2. Unpublished sources KEY connected with the work of the
IDEA enquiry.
1. Published Sources:
Secondary data is usually gathered from the published (printed) sources. A few major
sources of published information are mentioned below:
167 Vedanta High School Economics - 10
a. Official publication by government bodies such as Central Bureau of Statistics (CBS),
Ministry of Finance, National Planning Commission (NPC) etc.
b. Official publication by international organization such as report of WHO, IMF, UNDP,
ILO, World Bank etc.
c. Semi-official publication by various organization such as Nepal Rastra Bank (NRB),
Nepal Food Corparation etc.
d. Non governmental or private publications like reports of NGOs and INGOs, market
reports of trade associations, financial and economic journals etc.
e. Reports presented by Research Scholars, Bureaus, Economists, etc.,
2. Unpublished Sources:
Statistical data can be obtained from several unpublished references. Some of the major
unpublished sources from which secondary data can be obtained are:
a. Reports of a private office. The earliest writing on
b. Hospital records. statistics was found in a
c. Records of Village Municipality, Municipality etc. 9th-century book entitled:
d. Records of schools and campus administration “Manuscript on Decipher-
e. Thesis, field reports, etc. of University students. ing Cryptographic Mes-
sages”, written by Al-Kindi
9.9 TECHNIQUES OR METHODS OF DATA COLLECTION
There are two types of techniques of data collection: Key Term
1. Census Method
2. Sample Method: Population: A population re-
fers to the set of all observa-
tions under concern.
1. Census Method: Census method is the method of statistical enumeration where all
members of the population are studied. A census is a technique of data collection where
the information is collected from each and every unit of the population associated with
the subject matter of enquiry. In Nepal, census is taken every ten years. In such census,
information about each and every individual of the country is collected. Not a single
individual is left out in such a census.
Key Takeaways
Merits: • Census method takes into
a. It gives complete information about the population. consideration each and
every unit of the popula-
b. This method is more suitable for a limited area. tion
Demerits: • Sample method consid-
ers only a part of the
a. It is more expensive, labour requiring and time-consuming. population taken as rep-
b. This method is impractible if the population size is infinite. resentative
2. Sampling Method: In this method, only the part of population units is selected as a
representative of the whole population. The selected part of the units is called sample
and the method of selecting a sample is called a sample method. The number of items in
the sample is known as sample size. For example, 15 people are drawn from a population
of 250 people from a village to know the drinking habits of those 15 people are the sample
for the study.
Vedanta High School Economics - 10 168
Merits:
a. This method is less time consuming, less labour requiring and cheaper.
b. In the case of infinite population, it is a suitable method.
Demerits:
a. The sample units may not be true representative of the population.
b. Due to the biases of the indicator, the result obtained may be misleading.
9.10 CLASSIFICATION OF DATA
Meaning of Classification of Data
The classification of data is tthe process of arranging data into different classes or
groups according to resemblance and similarities. The arrangement of a huge mass of
heterogeneous data into homogeneous groups facilitates comparison and analysis of
the data. Classification prepares the ground for the proper presentation of statistical
facts. It tries to present the voluminous and heterogeneous data in a condensed and
homogenous form.
According to Secrist, “Classification is the process of arranging data into sequences and
groups according to their common characteristics, or separating them into different but
related parts.”
Classification of data is a function very similar to that Classification is the
of sorting letters in a post- office in accordance with KEY method of arranging data
their destinations such as Kathmandu, Birtamode, IDEA into homogeneous classes
Pokhara, Biratnagar, etc. according to some common
features present in the data
Objectives of Classification
Classification means arranging the data on the basis of similarities of data. The following
are the main purpose of classification of data.
1. To Condense Data by Eliminating Unnecessary Details: By classification of data
voluminous data can be present in condense form by eliminating unnecessary details.
It becomes inconvenient to understand and analysis data if it includes unnecessary
details.
2. To Facilitate Comparisons among various Classified Groups: Statistical data is classified
in various ways such as geographical classification, chronological classification,
qualitative classification etc. Such classification makes easier to compare between
different groups.
3. To Highlight the most Important Characteristics of the Data. Classification of data
arranges the data in easier form on the basis of various factors such as time, geography
etc. This helps to highlight the important characteristics of the data.
4. To Facilitate Statistical Treatment of the Data: Classification of data makes easier for
further statistical treatment such as graphical presentation, calculation of mode, mean,
median etc.
5. To Study the Relationships: Relation between variables can be established only after
the various characteristics of the data have been known. This is possible only through
classification and tabulation.
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Characteristics of Classification
An ideal classification should have the following characteristics:
1. Unambiguous: It is necessary that the various classes should be so defined that there is
no room for confusion.
2. Stable: The classification of a data set into various classes must be done in such a
manner that if each time an investigation is conducted, it remains unchanged and hence
the results of one investigation may be compared with that of another.
3. Flexible: Classification should be flexible so that suitable adjustments can be made in
new situations and circumstances.
4. Exhaustiveness: A classification is said to be exhaustive if there is no item that cannot be
allotted a class.
5. Mutually Exclusive: The classification should be mutually exclusive. When a classification
is mutually exclusive, each item of the data can be placed only in one of the classes.
6. Suitability: Classification should be suitable to the objective of investigation.
7. Homogeneity: A classification is said to homogeneous if similar items are placed in a
class.
8. Revealing: A classification is said to revealing if it brings out essential features of the
collected data.
Glossary Condense: To reduce to a shorter form
Homogenous: Having similar aspects
Heterogenous: Mixed, varied
Exhaustiveness: Complete
9.11 TYPES OF CLASSIFICATION
There are two types of classification depending upon the nature of data. They are:
1. Classification according to attributes
2. Classification according to class interval
1. Classification according to Attribute: When facts are grouped according to the
qualities (attributes) like male, female, religion, literacy, etc., the classification is called
classification according to attribute or qualitative classification. Such classification is
done for data of descriptive nature.
According to attributes or qualities classification is divided into two parts :
a. Simple classification
b. Multiple classification.
a. Simple Classification: When data are divided on the basis of a single attribute, the classification
is called ‘Simple Classification’. For example
In case of simple clas-
Population KEY sification a single attrib-
IDEA ute is considered
Male Female
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b. Manifold or Multiple Classification: When data are divided on the basis of two or more
attributes, the classification is called ‘Manifold Classification’. For example ,
Population Key Takeaways
• Classification is the sys-
tematic arrangement of
Male Female data into different classes
• Classification helps in es-
tablishing relationship be-
tween variables
Literate Illiterate Literate Illiterate
2. Classification according to Class-interval or Variables: The data which is expressed
in numbers (quantitative data), is classified according to class-intervals. While forming
class-intervals each and every item are covered. After finding the least value of an item
and the highest value of an item, the items are classified into different class-intervals.
Key Takeaways
Age (in years) No. of persons
• If the classification is stable,
0-10 4 the result of one investigation
10-20 6 and another can be com-
20-30 8 pared
30-40 5 • When a classification is mu-
tually exclusive, each item of
40-50 2 the data can be placed only
Total 25 in one of the classes
In deciding on the grouping of the data into classes, for the purpose of reducing it to a
manageable form, the number of classes should not be too large. If it were so then the
object of summarization would be defeated. The number of classes should also not be
too small because then we will miss a great deal of detail available and get a distorted
picture. Further, classes should be exhaustive; they should not be overlapping, so
that no observed value falls in more than one class. Apart from exceptions, all classes
should have the same length.
VARIABLE
The term variable refers to the characteristic that varies in amount or magnitude in a
frequency distribution. It increases or decreases over time, or takes different values in
different situations. Variables are divided into two types on the basis of their value.
1. Discrete Variable: Discrete variable is such a variable whose value cannot be expressed
in terms of fraction or decimal but it is expressed in integral or whole number. For
example, number of workers, number of family members, etc are discrete variable and
this should be expressed in whole number. A discrete variable takes a fixed value.
2. Continuous Variable: The variables are said to be continuous variables which can be
expressed in fraction or decimals. It can assume value within a range. For example,
variables such as weight, height, age, temperature in a day etc are continuous variables.
Keynote • Attribute refers to a quality or feature regarded as a characteristic or in-
herent part of someone or something
• Variable refers to an element, feature, or factor that is liable to change
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9.12 FREQUENCY DISTRIBUTION
Frequency refers to the number of times a variate value repeats in a distribution. The
frequencies of variables in a data are to be listed in a table. This table is known as
frequency distribution table and the list is referred as frequency distribution.
Types of Frequency Distribution
Frequency distribution can be categorized as univariate frequency distribution and bi
variate frequency distribution. A frequency distribution formed of a single variable
is called univariate frequency distribution or a simple frequency distribution.
While a frequency distribution formed of two variables is called bivariate frequency
distribution. A simple frequency distribution is of three types:
1. Individual Series: Individual series is such a series where items are listed singly after
observation. In this series items are either arranged in ascending or descending order
of magnitude of items.
Example: Height of 10 students (in cm):
120,140,145,150,160,165,170,180,200
2. Discrete Series: A series formed of a discrete variable is called a discrete series. In
discrete series the value of discrete variable is considered. Then we count how many
times that discrete variable is repeated. Presenting the value of discrete variables and
its repetition in tabular form, discrete series is constructed.
Example:
Weight (Kg) 50 60 70 80 90
4 1
Number of students 10 12 5
3. Continuous Series: The series formed of a continuous variable is called continuous
series. In this classification, the variable values can take fractional values and presented
into certain interval within which the variable value lie. The number of variables
within the interval is taken as a frequency in a tabular form. Age, wages, income,
profit, etc can be taken as continuous variables.
Example:
Weight (Kg) 20-30 30-40 40-50 50-60 60-70
Frequency 4 6 10 5 2
METHODS OF CONSTRUCTING FREQUENCY DISTRIBUTION
A. Discrete Frequency Distribution:
The steps in the formation of discrete frequency distribution are:
1. First note down the values in ascending order
2. Put a vertical line (tally bar) opposite the value to which the item refers.
3. To facilitate counting generally blocks of five bars are prepared (4 bars are kept vertical and
the 5th bar diagonally or horizontally crossing four vertical bars).
4. In the other column count the tally bars and write the value
Vedanta High School Economics - 10 172
Example:
Form a discrete from the given data:
50,40,50,90,90,90,80,40,50,70,70,70,70,50,40,50,90,90,90,80,60,50,70,80,80,70,50,
70,60,60,60,90,60,70,70,70,80,80,90
Solution:
Arranging the data in ascending order
40,40,40,50,50,50,50,50,50,50,60,60,60,60,60,70,70,70,70,70,70,70,70,70,70,80,80,
80,80,80,80,90,90,90,90,90,90,90,90
The data is presented in a frequency distribuion as:
Weight ( Kg) Tally bar Frequency
40 ||| 3
|||| || 7
50 |||| 5
|||| |||| 10
60 ||||| 6
70
80
90 |||| ||| 8
Total 39
B. Continuous Frequency Distribution:
The steps in the formation of continuous frequency disribution are:
1. Determine the class interval by applying the formula:
Where, i= class interval, L= largest value, S= smallest value and k= number of classes to be
formed
2. Count the values lying within the class and put a vertical line (tally bar) in the column to
which the item refers.
3. In the other column count the tally bars and write the value.
Example
The marks obtained by 30 students of a class are given below:
40, 60, 65, 10,70, 72, 30, 15, 54, 38, 20, 5, 25, 42, 48, 18, 50, 58, 59, 46, 78, 80 35, 28,98
Classify the above data taking a class-interval of 20.
Solution
Since the class-interval should be of size 20 and the least item is 5, the first class should
be 0-20. Again as the greatest item is 98, the last class should be 80-100.
Marks (X) Tally Bar Frequency
0-20 //// 4
20-40 //// / 6
40-60 //// /// 8
60-80 //// 5
80-100 // 2
Total 25
173
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We can prepare continuous frequency distribution as exclusive, inclusive and open
end class interval.
a. Exclusive class: In exclusive class interval, only the lower limit is included and upper
limit is excluded. In this classification the value of upper limit of first class is equal to the
lower limit of the second class. For example, in class 30-40, 30 is included but 40 is not.
Example:
Wages (Rs) 40-50 50-60 60-70 70-80 80-90
Number of Workers 15 10 12 9 5
b. Inclusive class interval: If both lower and upper values are included then it is called
inclusive class interval. So there is gap on upper limit of first class and lower limit of
second class.
Example:
Marks 0-9 10-19 20-29 30-39 40-49
Frequency 2 3 4 26
c. Open end class: If there is no fixed lower limit of first class or no fixed upper limit of
last class, it is said to be open end class. If anyone limit is missing then class is open
end class.
Marks 10-20 20-30 30-40 40-50 50 and above
Frequency 5 10 2 10 7
Or,
Marks Below 20 20-30 30-40 40-50 50-60
Frequency 5 10 2 10 7
If the class-intervals are given as the inclusive type, to convert it into the exclusive-type
we require a correction factor.
Correction factor = ( the upper limit of a class - the lower limit of the next class)/2
The correction factor is generally 0.5.Now we subtract it from the lower limits and add it
to the upper limits of the class-intervals given in the inclusive-method. The class-intervals
given above can be written after correction as:
Marks in economics 0-19.5 19.5-39.5 39.5-59.5 59.5-79.5 79.5-99.5
2
No of students 46 85
Glossary Attribute: A quality or feature regarded as a characteristic
Variable: Not consistent or having a fixed pattern; liable to change
Discrete: Individually separate and distinct
Magnitude: Extent or Size
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CUMULATIVE FREQUENCY DISTRIBUTION
A grouped frequency distribution in which frequencies are cumulated either from top to
bottom or from the bottom to top is called cumulative frequency distribution. Cumulative
frequency is obtained by adding the frequencies successively. The distribution made
by such addition is cumulative frequency distribution.
There are two types of cumulative frequency distribution.
a. Less than Cumulative Frequency: The total frequencies of a particular class and all
classes prior to that particular class is called the Less than cumulative frequency.
b. More than Cumulative Frequency: The cumulative frequency of a particular class and
all the classes after that class is called the “greater than” type cumulative frequency.
Example: The following table shows simple cumulative frequency distribution. Prepare a)
less than type and b) more than type cumulative frequency distribution.
Marks 0-20 20-40 40-60 60-80 80-100
Number of students 2 4 6 2 1
Solution:
a. Less than type cumulative frequency distribution is constructed as:
Marks No. of students Cumulative Frequency
Less than 20 2 2
Less than 40 2+4=6 6
Less than 60 6+6=12 12
Less than 80 12+2=14 14
Less than 100 14+1=15 15
b. More than type cumulative frequency distribution is constructed as:
Marks No. of students Cumulative Frequency
More than 0 15 15
More than 20 15-2=13 13
More than 40 13-4=9 9
More than 60 9-6=3 3
More than 80 3-2=1 1
FEW TERMS ASSOCIATED WITH GROUPED FREQUENCY DISTRIBUTION
1. Class: The various groups which are designated to collect the information within the limit are
called classes. For example, 0-20, 20-40, 40-60 etc. as given in the table above are classes.
2. Class Limits: A class is formed within the two values. These values are known as the class-
limits of that class. The lower value is called the lower limit and the higher value is called the
upper limit of the class.
3. Class Frequency: The number of observations (frequency) in a particular class-interval is
known as class-frequency.
4. Mid value: The arithmetical average of the two class limits (i.e. the lower limit and the upper
limit) is called the mid-value.
5. Class-interval: The difference between the upper limit and the lower limit of the class is called
class interval.
175 Vedanta High School Economics - 10
9.13 TABULATION
Tabulation is the process of systematic arrangement of the numerical data in
rows and columns to facilitate comparison and statistical analysis. It facilitates
comparison by bringing related information close to each other and helps in further
statistical analysis and interpretation.
Tabulation prepares the ground for analysis and interpretation. It involves the orderly
and systematic presentation of numerical data in a form designed to explain the problem
under consideration.
Objectives and Importance of Tabulation
1. To Simplify the Complex Data: Tabulation presents the data set in systematic and
concise form avoiding unnecessary details. Such data become more meaningful and
can be easily understood.
2. To Economize Space: By condensing data in a meaningful form, space is saved without
sacrificing the quality and quantity of data.
3. To Facilitate Comparison: Since table is divided into various parts and for each part
tables are given, the relationship between various items in the tables can be easily
compared.
4. To Facilitate Statistical Analysis: Tabulation facilitates statistical analysis. Various
statistical technique such as measures of average and dispersion, correlation and
regression, time series, and so on can be applied to analyze data and then interpreting
the results.
5. To Save Time: It reduces the bulk of information in a simplified and meaningful form
so that it could be easily by a common man in less time.
6. To Depict Trend: Data condensed in the form of table reveal the trend or pattern of data
which otherwise cannot be understood in a descriptive form of presentation.
7. To Help in Future Reference: When data are arranged in a table in a suitable form, they
can be easily identified and can also be used as reference for future needs.
8. To Bring Out Essential Features of the Data: It brings out themain characteristics of
data and presents facts clearly and precisely without textual explanation.
GENERAL RULES OF TABULATION
There are no hard and fast rules for the tabulation of data but for constructing good table,
following general rules should be observed while tabulating statistical data:
1. First of all, there should be a proper title to each table. Table number and title of table
must be written above the table.
2. The table should suit the size of the paper and, therefore, the width of the column should
be decided beforehand.
3. Number of columns and rows should neither be too large nor too small.
4. Captions, heading or sub-headings of columns and heading and sub headings of rows
must be self-explanatory.
5. Each column and row must be given title. Title of column is called caption and title of
the row is called stub.
Vedanta High School Economics - 10 176
6. As far as possible figures should be approximated before tabulation. This would reduce
unnecessary details.
7. The units of measurement under each heading or sub-heading must always be indicated.
8. Foot note can be written if necessary, either use signs like X etc.
9. Ditto marks should not be used in a table because sometimes it creates confusion.
10. Table should be simple and attractive.
PARTS OF STATISTICAL TABLE
The following are the parts of the statistical table that must be in all tables.
1. Table Number: A table should be numbered for easy identification and reference in future.
The table number may be given either in the center or side of the table but above the top of the
title of the table.
2. Title: Title is the main part of the data which gives brief explanation of what data
is.Title should be clear, precise and self-explanatory.
3. Captions and stubs: The table is divided in different columns and rows. The title of
columns (column heading) is said to be caption. The title of rows (row headings) is
stubs.
4. Body of the Table: The body of the table gives the numerical information of the data.
This is the most vital part of the table.
5. Headnote: It is a statement given below the title which clarifies the contents of the
table.Head notes may be used to indicate the units in which the data of the table are
expressed.
6. Footnote: It is a statement which clarifies some specific items given in the table. It is
written to further clarify either the title captions or stubs.
7. Source: The source of the data should be mentioned. It helps the reader to gather
additional information. A blank model table is given below:
Table Number
Title
[Head note or Prefatory Note (if any)]
Stub headings Caption Total (Rows)
Stub entries
Sub head Sub head
Column- Column Column- Column
head head head head
Body of the table
Total (col-
umns)
Foot note :
Source note:
177 Vedanta High School Economics - 10
Requirements of a Good Table Point to Note
A good table is one which fulfils the following requirements: • Tabulation prepares
the data for further sta-
1. It should present the data clearly, highlighting important details. tistical treatment
2. It should save space but be attractively designed. • Body of the table is the
3. The table number and title of the table should be given. main part of the table
4. Row and column headings must explain the figures therein. and contains the statis-
tical data
5. Averages or percentages should be close to the data.
6. Units of the measurement should be clearly stated along the titles or headings.
7. Abbreviations and symbols should be avoided as far as possible.
8. Sources of the data should be given at the bottom of the data.
9. In case irregularities creep in table or any feature is not sufficiently explained, references
and foot notes must be given.
10. The rounding of figures should be unbiased.
9.14 TYPES OF TABLE
Tables can be classified in a number of ways depending on the extent of coverage,
objective and scope of the survey, nature of the survey etc.
1. Attributes and Interval Table
Attribute Table: Attribute table is based on qualitative phenomena such as religion,
gender, poverty, beauty, literacy etc.
Example: The following is the example of attribute table which shows distribution of
population by religion and gender.
S.No. Religion Male Female Total
1. Hinduism 9176144 9153977 18330121
2. Buddhism 1197723 1244797 2442520
3. Islam 492654 461369 954023
4. Kirat 398330 419776 818106
5. Jain
6. Christian 2158 1950 4108
49917 52059 101976
7. Sikhism
8. Bahai 2979 2911 5890
9. Others 537 674 1211
38936 40043 78979
Total 11359378 11377558 22738934
Interval Table: The interval table is made taking class interval. The given numerical
data is divided into various intervals so that it will be easy to analyze.
Example: The following table is interval table which shows the marks obtained by 50
students in class ten taking different class interval.
Vedanta High School Economics - 10 178
Marks No. of students. Point to Note
0-20 2 • Attribute table is based
10
20-40 8 on qualitative phenom-
40-60 16 enon like gender, pov-
60-80 erty, illiteracy
14
80-100 • Interval table is made
50 up of quantitative data
Total by taking class interval
2. One way, Two way and Three way Table
One Way Table: One or simple table describes only one features or character of statistics.
Example: The following table shows the marks obtained by the 50 students of class ten
out of 100 marks.
Marks No. of students Let us Summarize
• A one way table rep-
40-50 7
50-60 8 resents only a single
60-70 6 attribute
70-80 4
80-90 13 • A two way table rep-
90-100 12 resents two attributes
• A three way table rep-
resents three attributes
Total 50
The above table shows the marks obtained by 50 students in class. Here data is
constructed on the basis of one characteristics .i.e. marks. This shows single feature of
the data. So it is said to be one way table.
Two Way Table: Two way table describes two features or characteristics of statistics in
single table.
Example: The following table shows the marks obtained by 50 students both girls and
boys in class.
Marks obtained No. of Students Total
40-50 Boys Girls 7
50-60 8
60-70 43 6
70-80 4
80-90 53 13
90-100 12
Total 33 50
22
76
84
29 21
The above table is two way table. This shows two features: one is marks and other is
gender (boys and girls) in one table.
179 Vedanta High School Economics - 10
Three Way Table: Three way table describes three characteristics or features of statistics
in one table.
Example: The following table shows three way table having three characteristics age
group, gender and literacy.
Age group (in Literate Illiterate All
Years) Female Male Total Female Male Female
Total Male Total
0-20 10 8 18 12 10 22 18 22 40
20-40 4 59 88 14 13 10 23
40-80 8 4 10 85 13 9 14 23
80-80 5 38 64 10 7 11 18
80 and above 8 2 10 10 4 14 8 18 24
Total 33 22 55 42 31 73 48 75 128
Beside the types given above, tables may also be classified as:
General purpose table
a. General purpose and specific purpose table are reference tables that
b. Original and derived table. KEY presents detailed informa-
a. General Purpose and Specific Purpose Table IDEA tion
General Purpose Table: General purpose tables represent the raw data in great detail,
cover variety of information on the same subject and present the data without any
special analytical purpose. They are also called repository tables or reference tables.
Tables published by various government agencies like CBS, Nepal Rastra Bank etc. are
such tables. The sole purpose of such table is to present detailed statistical information
pertaining to national income, population, employment, prices, production, money
supply, taxation etc on a continuing basis.
Special Purpose Table: A special purpose table also known as text table, summary table,
or analytical table. It presents data relating to a specific problem. For example tables
prepared by a firm for managerial decision, a table presenting data related to the sale of
a particular product are termed as specific purpose table. Such tables are usually smaller
than reference table and are generally found in the body of a report.
b. Original and Derived Table
Original table: The table formed from raw data collected for the first time by an
investigator is called original table. It is also known as classification table. Such tables
are initially collected from the original source.
Derivative table: A table which presents results derived from Special purpose table
the original data like averages, coefficients etc. constitutesare prepared for specific
derivative table. It is derived from the original table. Similarly,purpose and are general-
a time series forms a table containing original values but a tablely found in the body of a
report
containing trend values constitutes a derived table.
Vedanta High School Economics - 10 180
EXERCISE
1. What is statistics?Explain.
2. What are the functions of statistics?
3. What are the limitations of statistics?
4. What are the sources of data? Explain.
5. What are the methods of collecting primary data?
6. Distinguish between primary dataa and secondary data.
7. What is classification of data? Write its advantages.
8. What are the characteristics of classification?
9. Explain the methods of classification of data.
10. What do you understand by variable? Explain the types of variable.
11. What is meant by frequency distribution? Explain the different types of series
12. What is tabulation? Mention the advantages of tabulation.
13. What are the requisites of a good table?
14. Distinguish between classification and tabulation.
15. Clarify the different components of a table with the format of a table.
16. Prepare a format of one way, two way and three way table.
17. The marks obtained by 50 students of Class X in economics are given below. Construct a
frequency distribution table taking class interval 20
34, 33, 29, 27, 37, 59, 53, 41, 53, 51, 21, 31, 42, 37, 38, 42, 49, 52, 38, 53, 39, 44, 59, 39,
17, 33, 47, 57, 57, 27, 19, 54, 61, 43, 42, 16, 37, 80, 81, 83, 83,92, 4, 5, 74, 77, 78,20,40,60
18. Prepare a frequency table taking the magnitude of each class interval as 10 by using given
information about daily expenses of group of 50 students.
76, 84, 50, 67, 78, 77, 63, 65, 95, 68, 69, 104, 80, 79, 79, 54, 73, 59, 81, 100, 66, 49, 77, 90,
84, 76, 42, 64, 79, 70, 80, 72, 50, 79, 52, 103, 51, 86, 78, 94, 71, 42, 74, 60, 82, 115, 41,
61, 75, 63.
19. Make a distribution of exclusive classes from the following table.
Marks 10-19 20-29 30-39 40-49 50-59 60-69 70-79
10 18
No. of students 53 6 15 20
20. Make a distribution of inclusive classes from the following table
Marks 10-20 20-30 30-40 40-50 50-60 60-70 70-80
No. of students
53 6 15 20 10 18
181 Vedanta High School Economics - 10
9.15 DIAGRAMS AND GRAPHS
Diagrams and graphs are two of the common means to visually represent information
that is either repetitive in nature or too complex. Like tabulation, diagrammatic
and graphical representation is another way to present the data. But diagrammatic
and graphical presentation makes data more attractive, easy to remember and less
voluminous compared to tabulation. So, diagrammatic and graphical presentation of
statistical data is widely used.
Advantages of Diagrams and Graphs
The presentation of statistics in the form of diagrams and graphs facilitates many
processes in economics. The main advantages of diagrams and graphs are as under:
1. Attractive and Effective Presentation of Data: The statistics can be presented in
attractive and effective way by diagrams and graphs. It is said that a picture is worth a
thousand words.
2. Simple Presentation of Complex Data: Diagrammatic and graphical presentation helps
to present the complex data in a simple and understandable way. It helps to remove the
complex nature of statistics.
3. Remembrance for Long Period: Diagrams and graphs have visual appeal and help to
remember the facts for a long time.
4. Universal Utility: In modern era, diagrams and graphs can be used in all spheres such
as trade, economics, government departments, advertisement, etc.
5. Information as well as Entertainment: Diagrams and graphs are entertaining as well as
informative. There occurs no hindrance in the deep analysis of information.
6. Saves Time: Diagrammatic and graphical presentation provides a bird eye view of the
entire distribution and thus save time and labour in analysis.
7. Helpful in Predictions: Through graphs, tendencies that could occur in near future can
be predicted in a better way. Graphs like time series graphs help to reveal trend which
is helpful for simple forecasting.
8. Useful in Comparison: Graphs also help to compare the statistics. If investment made in
two different ventures is presented through graphs, then it becomes easy to understand
the difference between the two.
Difference between Diagrams and Graphs
There is no clear-cut line of demarcation between a diagram and a graph yet the two may
be distinguished on the following lines:
1. A graph needs a graph paper but a diagram can be drawn on a plain paper.
2. As diagrams are attractive to look at, they are used for publicity and propaganda. Graphs
on the other hand are more useful to statisticians and research workers for the purpose
of further analysis.
3. For representing frequency distribution, diagrams are rarely used when compared with
graphs. For example, for the time series, graphs are more appropriate than diagrams.
4. Graphs are used to present time series data and frequency distributions. Diagrams are
useful in presenting geographical or spatial series. Presentation of data through graphs is
easier than through diagrams.
Vedanta High School Economics - 10
182
Keynote5. Graphs are more precise and accurate than diagrams and are useful in research works.
Diagrams furnish only approximate information on the problem under study. These are
of not much use to a researcher for further analysis.
6. Values of mean and median can be calculated through graphs which is not possible with
diagrams
General Rules of Constructing Diagrams
1. The diagrams should be simple. Even a layman should be able to understand it.
2. Each diagram and graph must be given a clear, concise and suitable title without damaging
clarity.
3. A proper proportion between height and width must be maintained in order to avoid an
unpleasant look. As a general rule, the proportion between height and width is taken as
1:1.414.
4. A proper scale should be selected. It should be in even numbers or in multiples of five or
ten. But there is no fixed rule.
5. In order to clear certain points, footnotes should be provided.
6. An index, explaining different lines, shades and colours should be given.
7. The diagram should be properly constructed to suit the size of the paper where it is
drawn.
8. Diagrams should be absolutely neat, clean and attractive
9.16 TYPES OF DIAGRAMS
The different types of diagrams used to represent data are classified into three types:
1. One dimensional diagrams such as bar diagrams.
2. Two dimensional diagrams such as rectangles, squares, circles.
3. Three dimensional diagrams such as cylinders, cubes.
BAR DIAGRAM
It is most common diagram to represent statistical data. Bar diagram is one dimensional
graph because only its height matters but not width. The data are presented in the
form of rectangular bars (vertical or horizontal). However vertical bar diagrams are in
common use.
The following points need to be considered in drawing bar diagrams:
a. The bars should have the same base line.
b. All bars should have the same width.
c. The gap between successive bars should be same.
d. Appropriate scale should be taken so as to accommodate the highest value of the
distribution.
e. Magnitude of the bar may be represented at the top of each bar.
• Presentation of data by graphs and charts reveal the true significance of the data
• Diagrams and graphs simplify statistical data
• Diagrams are drawn on plain paper
183 Vedanta High School Economics - 10
Types of Bar Diagrams Point to Note
• Bar diagrams may be
The bar diagram can be divided into:
A. Simple bar diagram horizontal or vertical, but
B. Sub divided diagram vertical bar diagrams are
in common use
C. Multiple bar diagram • Bar diagrams are the most
D. Percentage bar diagram commonly used diagrams
for representing data in
A. Simple Bar Diagram diagrammatic form.
Simple bar diagram represent only one variable. The height of the bar is used to
represent one variable such as profit, production or income and width of the bar makes
diagram more attractive. In a simple bar diagram the width of different bar must be
same.
Example: The following table shows the enrollment of students in Class X in a school
in different five years.
Year 2017 2018 2019 2020
No. of Students 35 38 30
40
Simple Bar Diagram of Students Enrollment
Point to Note
No. of Students 45 38 40 • A bar diagram makes it
40 35 30 2020
35 easy to compare sets of
30 2018 2019 data between different
25 groups at a glance
20
15 • Bar diagram can also
10 show big changes in
data over time
5
0 • Simple bar diagram is
very useful when pre-
2017 senting a series of data
over time
Year
B. Subdivided Bar Diagram
The sub divided bar diagram is used when total magnitude of the given variable is to
be divided into various parts. The procedure is given as:
a. The bar is drawn that represents total magnitude of the variable.
b. The bar is divided into different segments and each segment represents a part of
total magnitude.
c. The different color. shades. design etc are used to distinguish different segments.
d. Index should be given along with diagrams to explain each segment.
Example: Represent the following data by sub-divided bar diagram.
Year First Division Second Division Third Division
2017 500 700 350
2018 700 800 600
2019 900 850 650
2020 950 900 600
Vedanta High School Economics - 10 184
Solution Point to Note
Sub-divided Bar Diagram of SEE Passed Students • Sub-divided bar dia-
gram is also called
3000 Stacked bar diagram
2500 • While constructing Sub
divided bar diagram,
2000 the various components
in each bar should be
1500 Third kept in the same order.
Second
1000 First • Sub divided bar dia-
gram is also called
500 component bar dia-
gram
0 2018 2019 2020
2017
Year
C. Multiple Bar Diagram
Two or more than two inter related data can be presented in multiple bar diagram.
In this method the components are shown as separate adjoining bars. The height of
each bar represents the actual value of the component. The components are shown by
different shades or colours.
Example: The following data shows the number of students in different stream science,
humanities and management. Represent this by multiple bar diagram.
Year Science Management Humanities Total
2017
2018 500 700 350 1550
2019
2020 700 800 600 2100
Solution
900 850 650 2400
1000
900 950 900 600 2450
800
700 Multiple Bar Diagram Point to Note
600
500 • A multiple bar diagram
400 shows the relationship
300 between different val-
200 ues of data
100
0No. of Students Science • In a multiple bar dia-
2017 Management gram multiple data
Humanities points for each category
of data are shown with
2018 Year 2019 2020 the addition of columns
• If two or more sets of
inter-related phenom-
enon or variables are
to be presented graphi-
cally, multiple bar dia-
grams are used
185 Vedanta High School Economics - 10
D. Percentage Bar Diagram
Percentage bar diagram is the subdivided bar diagram expressed in percentage terms.
When data should be compared between the group and the variable is composed of
various interrelated components, it is appropriate to present these values by percentage
bar diagrams To construct this diagram the sum total of values is taken as 100. So height
of the each bar is 100. The component values are then expressed in terms of percentage
of the total to obtain the necessary length for each of these in the full length of the bars.
Example: Represent the expenditure of family by percentage bar diagram.
Items Expenditure(Rs.) Point to Note
• The rules regarding the
Food 800
Clothing 500 shades, index, and weight
Education 400 are the same as in multi-
Health 200 ple bar diagram.
Miscellaneous 100
• In a simple bar chart, we
Total 2000 make bars of equal width
but variable length
Solution: To represent above data in percentage bar diagram we have to express the
given figure in percentage form.
Items Expenditure(Rs.) Percentage Cumulative
Percentage
Food 800 2800000 × 100 = 40
Clothing 500 40
Education 400 2500000 × 100 = 25 65
Health 200 2400000 × 100 = 20 85
Miscellaneous 100 2200000 × 100 = 10 95
2000 2100000 × 100 = 5 100
Total
100
Let us Summarize
Vedanta High School Economics - 10 • Simple bar diagram repre-
sents only one variable
• In component bar diagram,
the bar is divided into differ-
ent component
• In multiple bar diagram,
components are shown as
separate adjoining bars
• In percentage bar diagram,
the total magnitude is taken
as 100 percent
186
PIE CHART OR PIE DIAGRAM
Pie diagram is a circle divided into different sectors with each sector representing
a particular component. The total magnitude is taken as 360o and the individual
components are expressed in angular terms. It is a circular diagram which is a circle
(pie) divided by the radii, into sectors (like slices of a cake or pie). The area of a sector
is proportional to the size of each component. Pie diagram is also called an-
The procedure to construct pie diagram is as gular diagram, wheel diagram
follows. KEY or circular diagram
• The sum total of values is taken equal to 360° IDEA
• The each component of total value is converted in to degree using the following formula.
value of component
Degree of component= total value × 360°
• The circle is drawn having appropriate radius.
• After drawing a circle, a radius is drawn to make an angle and the same way angle of
other component is drawn.
• Use different shades to show the different sectors of the circle.
Example. Represent the following data by pie-chart. Point to Note
Usually, the largest
Items Expenditure(Rs.) portion of the data in a
pie-diagram is shown
Food 1600 first at 12 O’clock po-
Clothing 1000 sition on the circle,
Education 800 whereas other obser-
Health 400 vations are shown in
clockwise succession
Miscellaneous 200 in descending order of
Total 4000 magnitude. But they
can be shown in a logi-
Solution: cal order as well.
Converting the above items in degree form.
Items Expenditure(Rs.) Degree
Food 800 2800000 × 360o = 144o
2500000 × 360o = 90o
Clothing 500 2400000 × 360o = 72o
2200000 × 360o = 36o
Education 400 2100000 × 360o = 18o
Health 200 360o
Miscellaneous 100
Total 2000
187 Vedanta High School Economics - 10
Food Let us Summarize
Clothing • Simple bar diagram repre-
Education
Transportation sents only one variable
Health
Miscellaneous • In component bar dia-
gram, the bar is divided
into different component
9.17
• In multiple bar diagram,
components are shown as
separate adjoining bars
• In percentage bar dia-
gram, the total magnitude
is taken as 100 percent
GRAPHS
Graph is used in economics to show the relationship between the variable. Graph is considered to be
the best way when the statistical data are to be present in time series and frequency distribution.
Mainly we describe two types of graph.
a. Graphs of time series
b. Graphs of frequency distribution
A TIME SERIES GRAPH
The types of data series dependent of time are called time series data. A graph of time
series shows the changes in the values of a variable with the changes in the time. It is a very
simple graph which shows the data on the basis of time. General time is measured in terms of year,
month, week etc. For example the population of Nepal in different time periods can be shown in time
series graph.
Example: Construct time series graph of the following data.
Year 2015 2016 2017 2018 2019
Paddy(in Metric Tonnes)
300 450 550 400 750
Solution Points to Note
Graph of Time Series • Time series data are the data
relating to time periods
800 750
• Time series graphs can be
Paddy (in Metric Tonnes 700 2019 used to visualize trends
in numerical values over
600 550 188 time.
500 450 • Time series graph is also
400 called historigram
400 300 • Variables like income, GDP,
GNP, money supply, infla-
300 tion, production, export,
import and so on which
200 changes over time periods.
100
0 2020
2014 2015 2016 2017 2018
Year
Vedanta High School Economics - 10
B GRAPHS OF FREQUENCY DISTRIBUTION
HISTOGRAM
The histogram is the graphical presentation of the continuous frequency distribution
drawn as rectangular vertical bars whose heights represent the frequencies of the
classes. The class interval represents the width of the bar and frequency shows the
height. While constructing a histogram it is necessary to see that the class intervals
are equal. If the class intervals are not equal, adjustment has to be made. Class interval
should represent into the X-axis and corresponding frequencies should be measured on
Y-axis. A histogram is a graphical
Methods to draw a histogram representation of the distribu-
• Represent class interval in X-axis tion of numerical data. It is
• Represent frequency in Y-axis an estimate of the probability
distribution of a continuous
• Construct rectangular bar on x-axis taking the variable and was first intro-
width of the bar equal to class interval and duced by Karl Pearson.
height of the bar is determined by corresponding
frequency.
• Join each rectangular bar to each other.
Example:
Represent the following data by a histogram.
Marks 10–20 20–30 30–40 40–50 50–60
No. of students 5 8 12 10 7
Solution
Let us Summarize
• For a histogram, the
frequency distribution
should be continuous and
exclusive
• In the case of open-end
classes, the histogram can-
not be constructed
• In the case of the unequal
class of frequency distri-
bution, the class interval
must be equal before con-
structing the histogram
Glossary Frequency: The number of times a variate value repeats in a distribution
Variable: Able to be changed or adapted
A dividing line
Demarcation: Numerical width of any class in a particular distribution
Class interval:
189 Vedanta High School Economics - 10
QUESTIONS FOR REVIEW
1. What are the advantages of diagrammatic and graphical representation of data?
2. What are the general rules for constructing diagrams?
3. Represent the following data of number of students enrolled in a school in grade X in a
simple bar diagram
Year 2068 2069 2070 2071 2072
50
No. of Students 30 35 45 40
4. The table shows the monthly expenditure of family A and family B
Particulars Family A Expenses (in Rs.) Family B Expenses (in Rs.)
Rice 1000 1200
Vegetables 800 1000
Clothes 400 600
Tution Fees 600 500
Others 500 400
Represent the information in sub-divided bar diagram
5. Represent the given data in percentage bar diagram
Particulars Family A Expenses (in Rs.) Family B Expenses (in Rs.)
Rice 1000 1200
Vegetables 800 1000
Clothes 400 600
Tution Fees 600 500
Others 500 400
6. Represent the given data of the SLC results of a school in a multiple bar diagram.
Year 1st Division 2nd Division 3rd Division Failed
2069 30 25 10 5
2070 35 20 15 6
2071 40 30 20 8
7. Prepare a time series graph from the growth rate of GDP in Nepal.
Fiscal Year 2009/10 2010/11 2011/12 2012/13 2013/14
Growth rate 4.26 3.85 4.61 3.46 5.15
Vedanta High School Economics - 10 190
10UNIT STATISTICAL TOOLS
Learning Objectives Weight: 11 Lecture Hours
On Completion of this unit the student will be
able to:
• Get acquainted with the various measures of
central tendency
• Explain the merits and demerits of mean
• Explain the merits and demerits of median
• Explain the merits and demerits of mode
• Understand the concept of Price Index Before you begin
Number
The central tendency of a distribution
represents one characteristic of a distri-
bution.Mean, median, and mode are dif-
ferent measures of center in a numerical
data set. They each try to summarize a
dataset with a single number to represent
a “typical” data point from the dataset
Very Short Type Short Type Long Answer Type Total Marks
0 0
1 10
191 Vedanta High School Economics - 10
10.0 MEASURES OF CENTRAL TENDENCY
Ameasure of central tendency is a single value that attempts to describe a set of
data by identifying the central position within that set of data. Measures of central
tendency means the methods of finding out the central value or average value of a
statistical series or any other series of quantitative information. It is also called average.
Measure of central tendency gives the single numerical value representing the entire
distribution. The central value or average lies between two extreme observations
around which other items of the distribution concentrate. Its value lies between the
maximum and the minimum value of a series and represents all the items belonging to
the series.
Types of Average
Central tendency refers
There are three types of averages. to the central value or per-
1. Arithmetic Average or mean KEY haps a typical value which
2. Median IDEA is the representative of the
3. Mode
entire distribution
Characteristics of an Average
1. It is a single figure expressed in some quantitative form.
2. It lies between the extreme values of a series.
3. It is a typical value that represents all the values in a series.
4. It is capable of giving a central idea about the series it represents.
5. It is determined by some method or procedure.
Objectives of an Average
The main objectives of an average are:
1. To determine one single value that may be used to describe the characteristics of the
entire series.
2. To facilitate comparison at a particular point of time or over a period of time.
3. To facilitate statistical inference. An average obtained from a sample is used in
estimating the average of the population.
4. To facilitate quick understanding of complex data.
5. To help the decision-making process. The averages help the managers in decision-
making. An average is a single
Requisites of an Ideal Average value which provides com-
KEY plete idea about the distri-
1. It should be rigidly defined. IDEA bution
2. It should be easy to understand.
3. It should be simple to compute.
4. Its definition should be in the form of mathematical formula.
5. It should be based on all the items in the distribution.
6. Any single item or a group of items should not unduly influence it.
7. It should be capable of further algebraic treatment.
8. It should have sampling stability. 192
Vedanta High School Economics - 10
10.1 ARITHMETIC MEAN
The arithmetic mean is a measure of central tendency and is popularly known as mean.
Arithmetic mean is obtained by dividing the sum of the values of all items of a series
by the number of items of that series. Normally, arithmetic mean is denoted by X which
is read as ‘X bar’. It can be computed for unclassified/ungrouped data or individual series
as well as classified/grouped data i,e discrete or continuous series.
The mean is the most common measure of central tendency used by researchers and
people in all kinds of professions. A mean is the simple mathematical average of a set of
two or more numbers. It is the measure of central tendency that is also referred to as the
average.
COMPUTATION OF SIMPLE ARITHMETIC MEAN
1. Individual Series
a. Direct Method: Let, x1, x2 , x3 ,...............xn be the n values of the variable, then the arithmetic
Points to note
mean X is defined by; ∑X = x1 + x2 + x3 + ........... + xn = X • The mean is the mathe-
Where, matical average of a set of
NN two or more numbers
x=Arithmetic Mean,
• The Mean isthe measure
of central tendency which
∑x =sum of the variable x, is usually reffered to as an
N=the total number of observations. average
b. Short cut Method: When the numerical values of the observations are large, the calculation
of mean by direct method is mathematically complex and time consuming. In such a
situation, we take the deviations of observations from any arbitrary value for computing
the mean. This method is known as assumed mean method or short-cut method. The
formula for calculating the arithmetic mean by using short-cut method is presented below;
X = A+ ∑d Assumed mean is any
arbitrary value which is as-
Where, AN= Assumed mean KEY sumed as mean
d = X - A = Deviations of observations from assumed IDEA
mean
∑ d = Sum of deviations of the items
N = No. of observations.
It is the simplest method to calculate average value of the distribution of the data.
The arithmetic mean or average or simply mean is defined as the sum total of all
observations divided by the number of observations.
Example 1
The marks obtained by 5 students in Economics are given below:
Name of students Ram Shyam Hari Sita Gita
Marks in economics 65 47 88 75 50
Find the mean by direct method and short cut method.
193 Vedanta High School Economics - 10
Direct Method Points to note
We have, X = ∑ X • Arithmetic mean is the
most popular and com-
N monly used average
65 + 47 + 88 + 75 + 50 625 • Assumed mean is any ar-
= 5 =5 bitrary value which is as-
sumed as mean
== 6655
Shortcut Method (Assumed Mean Method)
Solution
Let assumed mean (A) be 50,
Marks (X) d=X-A
65 15
47 -3
88 38
75 25
50 0
Total Σd=75
We have A = 50, ∑d = 75, N= 5 Mean is the most commonly used
measure of central tendency. There
X = A+ ∑d are different types of mean, viz.
arithmetic mean, weighted mean,
N geometric mean (GM) and har-
75 monic mean (HM). If mentioned
= 50 + 5 without an adjective (as mean),
=50+15 it generally refers to the arith-
=65 metic mean.
2. Discrete Series:
Icforxr,e,sxp2o,ndXi3n.g...f.r.e..q..u..e..n..c..ieXs nthaerne n1h items of the series and fl, fZ, f3, ............. f~ are
mean is given by
a. Direct Method
= � f r=equ∑ e f nXcy,
f X = the value of the variable and
Where,
N = total frequency
b. Assumed Mean Method
A � ==AAs+sum∑ e f dd
Mean, d = (x – A) deviation from assumed mean,
Where,
N = total frequency.
fd = Sum of the product of frequency and deviations of the items
Vedanta High School Economics - 10 194
c. Step Deviation Method
� =A+ ∑ fd′ × ℎ
X−A
Where, A= Assumed mean, ′ = =ℎ∑f = Deviations of observations from assumed mean
divided by common factor ‘h’. N (sum of frequency)
Example 1: From the following marks obtained by 50 students calculate arithmetic mean.
Marks(x) 20 25 30 35 40
No. of students
10 12 8 15 5
Solution:
Marks(x) No. of students(f) fx
20 10 200
25 12 300
30 8 240
35 15 525
40 5 200
N=50 ∑fx=1465
Total
Assumed mean method is used
Mean (x) = ∑fx to simplify calculations when the
n KEY numerical values of the observa-
1465 IDEA tions are large
= 50
= 29.3
= 19
Example 2: Calculate arithmetic mean using short cut method.
Weight(kg) 10 15 20 25 30
Persons 5 44 43
Solution:
Assumed mean= 20
Weight(x) Persons(f) d=x-a fd
-10 -50
10 5 -5 -20
15 4 0 0
20 4 5 20
10 30
25 4 ∑fd=-20
30 3
Total N=20
Mean (x) ∑fd
=a+ N
-20
= 20+ 20
195 Vedanta High School Economics - 10
Example 3: Calculate arithmetic mean using Step Deviation Method.
Amount (in Rs) 10 20 30 40 50
4
No. of students 8 12 16 10
Solution
Let, Assume mean be A=30 and h = 10
Amount (in Rs) X Frequency (f) ′ X−A fd'
ℎ
=
10 8 -2 -16
20 12 -1 -12
30 16 00
40 10 1 10
50 4 28
Total N=50
Σfd’= - 10
� = A + ∑ fd′ × ℎ In Step Deviation Meth-
od, the deviation of the
10 KEY variate value from the as-
� = 30 − 50 × 10 IDEA sumed mean is divided by
a common factor
= 28
3. Continuous Series: In continuous series the data is given in different class and each
class constitutes frequency. The mid value(lower limit+ upper limit)/2 of the class
is taken to calculate arithmetic mean of continuous series. Arithmetic mean can be
calculated using direct,assumed mean method and step deviation methods.
a. Direct Method:
Mean(x) = ∑fm
N
Where, x= mean
∑fm = sum of product of frequency and mid value.
N = sum of frequency
m = mid value of corresponding class. In Continuous Series,
midvalue (m) is taken as
b. Assumed Mean Method: KEY the average of the ratio of
IDEA lower limit and upper lim-
Mean(x) = a + ∑fd it of the class
N
Where, x= mean
d = deviation from assumed mean.(d = m-a),
∑fd = sum of product of frequency and deviation.
N = ∑f (sum of frequency)
Vedanta High School Economics - 10 196
c. Step Deviation Method:
Mean(x) = a+ ∑fd’ ×h Where, x = mean
N
a = assumed mean The assumed mean
method is also called
m-a KEY short cut method
d’ = h
IDEA
h = common factor or class width
m = mid value of corresponding class.
Example 1: From the following data calculate arithmetic mean using direct method.
Marks 0-10 10-20 20-30 30-40 40-50 50-60
No. of students 4 6 10 20 6 4
Solution:
Marks Mid value(m) No. of students(f) fm
0-10 5 4 20
10-20 15 6 90
20-30 25 10 250
30-40 35 20 700
40-50 45 6 270
50-60 55 4 220
∑fm =1550
Total N=50
Mean(x) ∑fm In continuous series ‘d’
=N refer to the deviation of
KEY the midvalue from the as-
1550 IDEA sumed mean
= 50
= 31
Example 2: Calculate mean of the following data using short cut method.
Marks 0-20 20-40 40-60 60-80 80-100
No. of students 2 4 6 8 2
Solution:
Assumed mean(a)=50
Marks No. of Mid value(m) d=m-a fd
students(f)
0-20 10 -40 -80
20-40 2 30 -20 -80
40-60 4 50 0 0
60-80 6 70 20 160
80-100 8 90 40 80
2 ∑fd=80
N=22
197 Vedanta High School Economics - 10
Mean(x) = a+ ∑fd In continuous series ‘d’
N refer to the deviation of
80 KEY the midvalue from the as-
= 50 + 22 IDEA sumed mean
= 50+3.63
= 53.63
Example 3: Calculate the mean from the following data by step deviation method.
Marks 0-10 10-20 20-30 30-40 40-50 50-60 60-70
5 12 15 25 8 3 2
No. of
students
Solution:
Assumed mean=35, h=10
Marks No. of students(f) Mid value(m) m-a fd’
5 d’= h
0-10 5 15 -15
10-20 12 25 -3 -24
20-30 15 35 -2 -15
30-40 25 45 -1 0
40-50 55 0 8
50-60 8 65 1 6
60-70 3 2 6
Total 2 3 ∑fd’=-34
N=70
Mean(x) ∑fd’ Key Takeaways
= a + N-34× h
=35 + 70 × 10 • A measure of central tendency is
a number used to represent the
= 35 - 4.86 center or middle of a set of data
values. The mean, median, and
= 30.14 mode are three commonly used
measures of central tendency.
Merits of Arithmetic Mean
• The mean is the most common
1. It is easy to understand. measure of central tendency, but
2. It is simple to calculate. it has a huge downside – it is eas-
3. It is based on all the items of the series. ily affected by extreme observa-
tions
4. It is rigidly defined by a mathematical formula so that the same answer is derived by
everyone who computes it.
5. It is capable of further algebraic treatment and can be extended to compute the combined
average of two or more related series.
6. It has sampling stability. It is least affected by sampling fluctuations.
7. Its computation does not require arrangement of items since it is not based on position
in the series.
8. Arithmetic average can be calculated if we know the number of items and aggregate.
Vedanta High School Economics - 10 198
9. It provides a good basis for comparison.Keynote
10. The mean is an ideal average and a more stable measure of central tendency.
Limitations of Arithmetic Mean
1. Since it includes all the items, its value may be distorted by extreme values.
2. It cannot be calculated if any item of the series is missing.
3. The average may not coincide with any of the actual items in a series.
4. In cases where the items cannot be represented quantitatively, like intelligence, honesty
and character but can be ranked, the arithmetic average is not an appropriate measure of
central tendency.
5. It cannot be located by observation or the graphic method.
6. It gives greater importance to bigger items of a series and lesser importance to smaller
items.
7. It cannot be calculated in a distribution with open-ended class series and cumulative
series without converting the class series into exclusive series.
8. It fails to provide a characteristic value or a representative value where the distribution
of the series is not normal.
• Simple arithmetic mean is the most popular average
• Mean is affected by extreme observations
• The assumed mean method is also called short cut method
• Mean is not a positional average and is based on all observations
10.2 MEDIAN
Median is the central value of the variable that divides the series into two equal
parts in such a way that half of the items lie above this value and the remaining
half lie below this value. If the set of data is arranged either in ascending order or
descending order, the middle value is the median.
According to L.R. Connor, “Median is that value of the variable which divides the group
into two equal parts, one part comprising all the values greater, and the other all values
less than the Median.”
Median is the value
that is in the middle of the
CALCULATION OF MEDIAN KEY data when the values are
1. Individual Series: IDEA put in numerical order.
To find the value of Median in this case the values are arranged in ascending or descending
order first; and then the middle most value is taken as Median.
Steps to Calculate
1. Arrange the terms in ascending or descending order
2. Count the number of terms N
3. Apply the formula:
199 Vedanta High School Economics - 10
M d = Size of the N 2o+b1sethrvitaetmions
= No. Of
Where, N
The calculation of median depends on whether the number of observations is odd or even,
which are discussed below:
Case–1 : When the number of observations is odd
If 40,20, 10, 30, 50 are the marks secured by the students, find the median marks.
Solution Points to note
Arranging the given data into ascending order: • Median is the value which di-
vides the distribution into two
10,20, 30, 40, 50 equal halves
Here, total number of observations (N) = 5 • Median concentrates on the mid-
dle or centre of the distribution
We have, N + 1 th
2 • In computing median in indi-
M d = Size of the item vidual series, the items are ar-
ranged in ascending or descend-
= size of the 5 2+it1em th item
= size of the 3rd
Thus, median marks ( M d ) =30
Case–2: When the number of observations is even
If 20, 40, 10, 30, 50,and 60 are the marks secured by the students, find the median marks.
Solution
Arranging the given data into ascending order:
10,20, 30, 40, 50, 60
Here, total number of observations (N) = 6
We have, N + 1 th Points to note
2
M d = Size of the item • Median is a positional average
• Median can be calculated even
= size of the 6 + 1 th item
2 in open end distribution
• In computing median, classes
have to be converted into
exclusive classes
= size of the 3.5th item • In discrete frequency distribution,
cumulative frequency table
Thus, median lies between 3rd and 4th item has to be prepared to compute
Median
So, Median marks ( M d ) = 30 + 40
= 325
Hence, the required median marks ( M d ) is 35.
Vedanta High School Economics - 10 200
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