Unit 1
Population Sample and Data Condensation
Definition of Statistics:
1. Statistics can be defined as the collection presentation and interpretation of numerical data.-
Croxton and Crowed.
2. Statistics are numerical statement of facts in any department of enquiry placed interrelation to
each other.- Bowley.
3. Statistics are measurement, enumerations or estimates of natural or social phenomena
systematically arrangement to exhibit their inner relation.- Conner.
4. By Statistics we mean quantitative data affected to a marked extend by a multiplicity of causes. –
Youle and Kendal.
5. The science of Statistics is essentially a branch of applied mathematics and can be regarded as a
mathematics applied to observation data.- R.A fisher.
Singular Sense:
In a singular sense, it means the science of counting or science of average. This definition has the
following features:
1. Collection of data:
Most of the statistical analysis is performed on the basis of collected data. The methods of
data collection like primary and secondary, census and sampling, etc. are related to data
collection.
2. Organization of data:
After collecting data, a systematic arrangement is essential. They are organized and
presented in the table on the basis of rows and columns. This process is known as a
presentation of data.
3. Analysis of data:
The organized data presented need to be analyzed. There are various tools of analysis in
statistics like average, co-relation, regression, dispersion, etc.
4. Interpretation of data:
After analysis, results are interpreted and conclusions are drawn. IT is the last and most
essential part of the work. If findings are interpreted wrongly, the wrong conclusion is
obtained.
Plural Sense:
In the plural sense, it refers to the numerical facts and figures systematically collected for some
special purpose. This definition has the following features:
1. Statistics are aggregate of facts:
In statistics, the single numerical figure has no meaning. It is not statistics. The numerical
figures of production, income, price of commodities, students of the class, etc. are statistics.
2. The values of statistics are numerically expressed:
The values of statistics are countable as well as numerically expressed. For example, the
numbers of students at Siddhartha College in grade 11 are 400. Among them 264 are female
and 136 are male, which constitute statistics.
3. Statistics are collected in a systematic manner:
Firstly, we have to think about the field of study. Then, data should be collected by applying
suitable methods and work should be carried out in a systematic manner. Otherwise,
interpretation and conclusion may be wrong or misleading.
4. Statistics are collected for a pre-determined purpose:
We must have a well-defined purpose, specific aims, and objectives before we collect data.
Suppose, if we want to compare the performance of students in grade XI in Siddhartha
, College in one subject or more, we must specify the subject and the year, for which
comparison is carried out.
5. Statistics makes easy to comparison:
The collected numerical data constitute statistics if they are comparable. To make a valid
comparison, the data should be homogeneous. For example, the passed number of students
of Siddhartha College and other College constitute statistics, as they are comparable. But the
weight of the students and their intelligence do not constitute statistics as they are not
comparable.
Scope and importance of Statistics:
1. Statistics and planning: Statistics in indispensable into planning in the modern age which is
termed as “the age of planning”. Almost all over the world the govt. are re-storing to planning for
economic development.
2. Statistics and Economics: Statistical data and techniques of statistical analysis have to
immensely useful involving economical problem. Such as wages, price, time series analysis, demand
analysis.
3. Statistics and Business: Statistics is an irresponsible tool of production control. Business
executive are relying more and more on statistical techniques for studying the much and desire of
the valued customers.
4. Statistics and industry: In industry statistics is widely used inequality control. In production
engineering to find out whether the product is confirming to the specifications or not. Statistical
tools, such as inspection plan, control chart etc.
5. Statistics and Mathematics: Statistics are intimately related recent advancements in
statistical technique are the outcome of wide applications of mathematics.
6. Statistics and Modern science: In medical science the statistical tools for collection,
presentation and analysis of observed facts relating to causes and incidence of dieses and the result
of application various drugs and medicine are of great importance.
7. Statistics, psychology and Education: In education and physiology statistics has found wide
application such as, determining or to determine the reliability and validity to a test, factor analysis
etc.
8. Statistics and War: In war the theory of decision function can be a great assistance to the
military and personal to plan “maximum destruction with minimum effort.”
Statistics in Business and Management:
1. Marketing: Statistical analysis are frequently used in providing information for making decision
in the field of marketing it is necessary first to find out what can be sold and the to evolve suitable
strategy, so that the goods which to the ultimate consumer. A skill full analysis of data on
production purchasing power, man power, habits of compotators, habits of consumer,
transportation cost should be consider to take any attempt to establish a new market.
2. Production: In the field of production statistical data and method play a very important role.
The decision about what to produce? How to produce? When to produce? For whom to produce is
based largely on statistical analysis.
3. Finance: The financial organization discharging their finance function effectively depend very
heavily on statistical analysis of peat and tigers.
3. Banking: Banking institute have found if increasingly to establish research department within
their organization for the purpose of gathering and analysis information, not only regarding their
own business but also regarding general economic situation and every segment of business in which
they may have interest.
, 4. Investment: Statistics greatly assists investors in making clear and valued judgment in his
investment decision in selecting securities which are safe and have the best prospects of yielding a
good income.
5. Purchase: the purchase department in discharging their function makes use of statistical data to
frame suitable purchase policies such as what to buy? What quantity to buy? What time to buy?
Where to buy? Whom to buy?
6. Accounting: statistical data are also employer in accounting particularly in auditing
function, the technique of sampling and destination is frequently used.
7. Control: the management control process combines statistical and accounting method
in making the overall budget for the coming year including sales, materials, labor and other
costs and net profits and capital requirement.
Limitation of Statistics
Statistics has wide applications in almost every sphere of human activities. There is nearly no place
where statistics are not used. In spite of being many applications, the following are a few limitations
of statistics
1. Statistics do not study individual:
It 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.
2. It is not suitable for the study of a qualitative phenomenon:
Statistics always studies the quantitative characteristics of the given problems. A qualitative
phenomenonlike honesty, culture, love, poverty, etc, can‟t be expressed numerically or direct
statistical analysis.However, that phenomenon can be expressed indirectly of numbers and
analyzed in statistics.
3. Statistical relations are not exact:
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. Thus, it just describes the phenomenon on average.
4. Statistics is liable to be misused:
There is a great possibility of the misuse of statistics. Any person can misuse statistics and
draw any type of conclusions he likes. Only the experts can handle statistical data properly.
When statistical data are in the hand of in-expert, at that condition, it may lead wrong
information and most fallacious conclusions. So, statistics might be harmed in the hand of
an unskilled person.
5. One of the methods of solving problem:
There are many methods of solving the given problem. It is one method of solving the
problem. It may not be suitable for all the problems
Function of Statistics
The various functions performed by statistics in modern times are discussed under:
Population Sample and Data Condensation
Definition of Statistics:
1. Statistics can be defined as the collection presentation and interpretation of numerical data.-
Croxton and Crowed.
2. Statistics are numerical statement of facts in any department of enquiry placed interrelation to
each other.- Bowley.
3. Statistics are measurement, enumerations or estimates of natural or social phenomena
systematically arrangement to exhibit their inner relation.- Conner.
4. By Statistics we mean quantitative data affected to a marked extend by a multiplicity of causes. –
Youle and Kendal.
5. The science of Statistics is essentially a branch of applied mathematics and can be regarded as a
mathematics applied to observation data.- R.A fisher.
Singular Sense:
In a singular sense, it means the science of counting or science of average. This definition has the
following features:
1. Collection of data:
Most of the statistical analysis is performed on the basis of collected data. The methods of
data collection like primary and secondary, census and sampling, etc. are related to data
collection.
2. Organization of data:
After collecting data, a systematic arrangement is essential. They are organized and
presented in the table on the basis of rows and columns. This process is known as a
presentation of data.
3. Analysis of data:
The organized data presented need to be analyzed. There are various tools of analysis in
statistics like average, co-relation, regression, dispersion, etc.
4. Interpretation of data:
After analysis, results are interpreted and conclusions are drawn. IT is the last and most
essential part of the work. If findings are interpreted wrongly, the wrong conclusion is
obtained.
Plural Sense:
In the plural sense, it refers to the numerical facts and figures systematically collected for some
special purpose. This definition has the following features:
1. Statistics are aggregate of facts:
In statistics, the single numerical figure has no meaning. It is not statistics. The numerical
figures of production, income, price of commodities, students of the class, etc. are statistics.
2. The values of statistics are numerically expressed:
The values of statistics are countable as well as numerically expressed. For example, the
numbers of students at Siddhartha College in grade 11 are 400. Among them 264 are female
and 136 are male, which constitute statistics.
3. Statistics are collected in a systematic manner:
Firstly, we have to think about the field of study. Then, data should be collected by applying
suitable methods and work should be carried out in a systematic manner. Otherwise,
interpretation and conclusion may be wrong or misleading.
4. Statistics are collected for a pre-determined purpose:
We must have a well-defined purpose, specific aims, and objectives before we collect data.
Suppose, if we want to compare the performance of students in grade XI in Siddhartha
, College in one subject or more, we must specify the subject and the year, for which
comparison is carried out.
5. Statistics makes easy to comparison:
The collected numerical data constitute statistics if they are comparable. To make a valid
comparison, the data should be homogeneous. For example, the passed number of students
of Siddhartha College and other College constitute statistics, as they are comparable. But the
weight of the students and their intelligence do not constitute statistics as they are not
comparable.
Scope and importance of Statistics:
1. Statistics and planning: Statistics in indispensable into planning in the modern age which is
termed as “the age of planning”. Almost all over the world the govt. are re-storing to planning for
economic development.
2. Statistics and Economics: Statistical data and techniques of statistical analysis have to
immensely useful involving economical problem. Such as wages, price, time series analysis, demand
analysis.
3. Statistics and Business: Statistics is an irresponsible tool of production control. Business
executive are relying more and more on statistical techniques for studying the much and desire of
the valued customers.
4. Statistics and industry: In industry statistics is widely used inequality control. In production
engineering to find out whether the product is confirming to the specifications or not. Statistical
tools, such as inspection plan, control chart etc.
5. Statistics and Mathematics: Statistics are intimately related recent advancements in
statistical technique are the outcome of wide applications of mathematics.
6. Statistics and Modern science: In medical science the statistical tools for collection,
presentation and analysis of observed facts relating to causes and incidence of dieses and the result
of application various drugs and medicine are of great importance.
7. Statistics, psychology and Education: In education and physiology statistics has found wide
application such as, determining or to determine the reliability and validity to a test, factor analysis
etc.
8. Statistics and War: In war the theory of decision function can be a great assistance to the
military and personal to plan “maximum destruction with minimum effort.”
Statistics in Business and Management:
1. Marketing: Statistical analysis are frequently used in providing information for making decision
in the field of marketing it is necessary first to find out what can be sold and the to evolve suitable
strategy, so that the goods which to the ultimate consumer. A skill full analysis of data on
production purchasing power, man power, habits of compotators, habits of consumer,
transportation cost should be consider to take any attempt to establish a new market.
2. Production: In the field of production statistical data and method play a very important role.
The decision about what to produce? How to produce? When to produce? For whom to produce is
based largely on statistical analysis.
3. Finance: The financial organization discharging their finance function effectively depend very
heavily on statistical analysis of peat and tigers.
3. Banking: Banking institute have found if increasingly to establish research department within
their organization for the purpose of gathering and analysis information, not only regarding their
own business but also regarding general economic situation and every segment of business in which
they may have interest.
, 4. Investment: Statistics greatly assists investors in making clear and valued judgment in his
investment decision in selecting securities which are safe and have the best prospects of yielding a
good income.
5. Purchase: the purchase department in discharging their function makes use of statistical data to
frame suitable purchase policies such as what to buy? What quantity to buy? What time to buy?
Where to buy? Whom to buy?
6. Accounting: statistical data are also employer in accounting particularly in auditing
function, the technique of sampling and destination is frequently used.
7. Control: the management control process combines statistical and accounting method
in making the overall budget for the coming year including sales, materials, labor and other
costs and net profits and capital requirement.
Limitation of Statistics
Statistics has wide applications in almost every sphere of human activities. There is nearly no place
where statistics are not used. In spite of being many applications, the following are a few limitations
of statistics
1. Statistics do not study individual:
It 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.
2. It is not suitable for the study of a qualitative phenomenon:
Statistics always studies the quantitative characteristics of the given problems. A qualitative
phenomenonlike honesty, culture, love, poverty, etc, can‟t be expressed numerically or direct
statistical analysis.However, that phenomenon can be expressed indirectly of numbers and
analyzed in statistics.
3. Statistical relations are not exact:
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. Thus, it just describes the phenomenon on average.
4. Statistics is liable to be misused:
There is a great possibility of the misuse of statistics. Any person can misuse statistics and
draw any type of conclusions he likes. Only the experts can handle statistical data properly.
When statistical data are in the hand of in-expert, at that condition, it may lead wrong
information and most fallacious conclusions. So, statistics might be harmed in the hand of
an unskilled person.
5. One of the methods of solving problem:
There are many methods of solving the given problem. It is one method of solving the
problem. It may not be suitable for all the problems
Function of Statistics
The various functions performed by statistics in modern times are discussed under:
