Definition, Nature, Functions, Scope and Limitations of Statistics - A Brief Introduction to Statistics
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| Intro to Statistics |
Intro to Statistics:
What do you learn in intro to statistics?
In the modern world of computers and information technology, the importance of statistics is very well recognized by all the disciplines. Topics discussed include Definitions, functions, scope and Limitations.
Why is it important to learn statistics?
Statistics has originated as a
science of statehood and found applications slowly and steadily in Agriculture,
Economics, Commerce, Biology, Medicine, Industry, planning, education and so
on. As on date there is no other human walk of life, where statistics cannot be
applied.
Origin and Growth of Statistics:
Where did statistics come from?
The word ‘Statistics’ and ‘Statistical’
are all derived from the Latin word Status, means a political state. The theory
of statistics as a distinct branch of scientific method is of comparatively
recent growth.
Research particularly into the mathematical theory of statistics is rapidly proceeding and fresh discoveries are being made all over the world.
Research particularly into the mathematical theory of statistics is rapidly proceeding and fresh discoveries are being made all over the world.
Meaning of Statistics:
What is statistics in simple words?
Statistics is concerned with
scientific methods for collecting, organizing, summarizing, presenting and analyzing data as well as deriving valid conclusions and making reasonable decisions
on the basis of this analysis.
Statistics is concerned with the systematic collection of numerical data and its interpretation.
Statistics is concerned with the systematic collection of numerical data and its interpretation.
The word ‘statistic’ is used to
refer to
1. Numerical facts, such as the
number of people living in particular area.
2. The study of ways of
collecting, analyzing and interpreting the facts.
Statistics Definitions:
What are Statistics?
Statistics is defined differently
by different authors over a period of time. In the olden days statistics was
confined to only state affairs but in modern days it embraces almost every
sphere of human activity.
Therefore a number of old definitions, which was confined to narrow field of inquiry were replaced by more definitions, which are much more comprehensive and exhaustive. Secondly, statistics has been defined in two different ways – Statistical data and statistical methods.
Therefore a number of old definitions, which was confined to narrow field of inquiry were replaced by more definitions, which are much more comprehensive and exhaustive. Secondly, statistics has been defined in two different ways – Statistical data and statistical methods.
The following are some of the definitions of statistics as numerical data.
1. Statistics are the classified
facts representing the conditions of people in a state. In particular they are
the facts, which can be stated in numbers or in tables of numbers or in any tabular
or classified arrangement.
2. Statistics are measurements,
enumerations or estimates of natural phenomenon usually systematically
arranged, analysed and presented as to exhibit important interrelationships among
them.
Statistics Definition by A.L. Bowley:
What is the simple definition of statistics?
Statistics are numerical
statement of facts in any department of enquiry placed in relation to each
other. - A.L. Bowley
Statistics may be called the
science of counting in one of the departments due to Bowley, obviously this is
an incomplete definition as it takes into account only the aspect of collection
and ignores other aspects such as analysis, presentation and interpretation.
Bowley gives another definition for statistics, which states ‘statistics may be rightly called the scheme of averages’. This definition is also incomplete, as averages play an important role in understanding and comparing data and statistics provide more measures.
Definition of Statistics by Croxton and Cowden:
What is statistics and its importance?
Statistics may be defined as the
science of collection, presentation analysis and interpretation of numerical
data from the logical analysis. It is clear that the definition of statistics
by Croxton and Cowden is the most scientific and realistic one.
According to this definition
there are four stages:
1. Data Collection:
It is the first step and this is the foundation upon which the entire data set. Careful planning is essential before collecting the data. There are different methods of collection of data such as census, sampling, primary, secondary, etc., and the investigator should make use of correct method.
2. Data Presentation:
The
mass data collected should be presented in a suitable, concise form for further
analysis. The collected data may be presented in the form of tabular or diagrammatic
or graphic form.
3. Analysis of Data:
The data presented should be carefully analysed for making inference from the presented data such as measures of central tendencies, dispersion, correlation, regression etc.,
4. Data Interpretation:
The final step is drawing conclusion from the data collected. A valid conclusion must be drawn on the basis of analysis. A high degree of skill and experience is necessary for the interpretation.
Statistics Definition by Horace Secrist:
Statistics may be defined as the
aggregate of facts affected to a marked extent by multiplicity of causes,
numerically expressed, enumerated or estimated according to a reasonable standard
of accuracy, collected in a systematic manner, for a predetermined purpose and
placed in relation to each other. The above definition seems to be the most
comprehensive and exhaustive.
Functions of Statistics:
What are functions of statistics?
There are many functions of
statistics. Let us consider the following five important functions.
Condensation:
Generally speaking by the word
‘to condense’, we mean to reduce or to lessen. Condensation is mainly applied
at embracing the understanding of a huge mass of data by providing only few observations.
If in a particular class in Chennai School, only marks in an examination are given, no purpose will be served. Instead if we are given the average mark in that particular examination, definitely it serves the better purpose.
Similarly the range of marks is also another measure of the data. Thus, Statistical measures help to reduce the complexity of the data and consequently to understand any huge mass of data.
If in a particular class in Chennai School, only marks in an examination are given, no purpose will be served. Instead if we are given the average mark in that particular examination, definitely it serves the better purpose.
Similarly the range of marks is also another measure of the data. Thus, Statistical measures help to reduce the complexity of the data and consequently to understand any huge mass of data.
Comparison:
Classification and tabulation are
the two methods that are used to condense the data. They help us to compare
data collected from different sources. Grand totals, measures of central
tendency measures of dispersion, graphs and diagrams, coefficient of correlation
etc provide ample scope for comparison.
If we have one group of data, we
can compare within itself. If the rice production (in Tonnes) in Tanjore
district is known, then we can compare one region with another region within
the district.
Or if the rice production (in
Tonnes) of two different districts within Tamilnadu is known, then also a
comparative study can be made. As statistics is an aggregate of facts and
figures, comparison is always possible and in fact comparison helps us to
understand the data in a better way.
Forecasting:
By the word forecasting, we mean
to predict or to estimate before hand. Given the data of the last ten years
connected to rainfall of a particular district in Tamilnadu, it is possible to predict
or forecast the rainfall for the near future. In business also forecasting
plays a dominant role in connection with production, sales, profits etc. The
analysis of time series and regression analysis plays an important role in
forecasting.
Estimation:
One of the main objectives of
statistics is drawn inference about a population from the analysis for the
sample drawn from that population.
The four major branches of statistical inference are
The four major branches of statistical inference are
1. Estimation theory
2. Hypothesis Testing
3. Non Parametric tests
4. Sequential analysis
In estimation theory, we estimate
the unknown value of the population parameter based on the sample observations.
Suppose we are given a sample of heights of hundred students in a school, based
upon the heights of these 100 students, it is possible to estimate the average
height of all students in that school.
Hypothesis Testing:
A statistical hypothesis is some
statement about the probability distribution, characterizing a population on
the basis of the information available from the sample observations. In the formulation
and testing of hypothesis, statistical methods are extremely useful. Whether
crop yield has increased because of the use of new fertilizer or whether the
new medicine is effective in eliminating a particular disease are some examples
of statements of hypothesis and these are tested by proper statistical tools.
Scope of Statistics:
What is nature and scope of statistics?
Statistics is not a mere device
for collecting numerical data, but as a means of developing sound techniques
for their handling, analyzing and drawing valid inferences from them.
Why do we study statistics?
Statistics is applied in every
sphere of human activity – social as well as physical – like Biology, Commerce,
Education, Planning, Business Management, Information Technology, etc. It is
almost impossible to find a single department of human activity where
statistics cannot be applied. We now discuss briefly the applications of statistics
in other disciplines.
What are the benefits of statistics?
Statistics and Industry:
Statistics is widely used in many
industries. In industries, control charts are widely used to maintain a certain
quality level. In production engineering, to find whether the product is
conforming to specifications or not, statistical tools, namely inspection
plans, control charts, etc., are of extreme importance. In inspection plans we
have to resort to some kind of sampling – a very important aspect of
Statistics.
Statistics and Commerce:
Statistics are lifeblood of
successful commerce. Any businessman cannot afford to either by under stocking
or having overstock of his goods. In the beginning he estimates the demand for
his goods and then takes steps to adjust with his output or purchases. Thus
statistics is indispensable in business and commerce.
As so many multinational
companies have invaded into our Indian economy, the size and volume of business
is increasing. On one side the stiff competition is increasing whereas on the
other side the tastes are changing and new fashions are emerging. In this connection,
market survey plays an important role to exhibit the present conditions and to
forecast the likely changes in future.
Statistics and Agriculture:
Analysis of variance (ANOVA) is
one of the statistical tools developed by Professor R.A. Fisher, plays a
prominent role in agriculture experiments. In tests of significance based on small
samples, it can be shown that statistics is adequate to test the significant
difference between two sample means. In analysis of variance, we are concerned
with the testing of equality of several population means.
For an example, five fertilizers
are applied to five plots each of wheat and the yield of wheat on each of the
plots are given. In such a situation, we are interested in finding out whether
the effect of these fertilizers on the yield is significantly different or not.
In other words, whether the
samples are drawn from the same normal population or not. The answer to this
problem is provided by the technique of ANOVA and it is used to test the
homogeneity of several population means.
Statistics and Economics:
Statistical methods are useful in
measuring numerical changes in complex groups and interpreting collective phenomenon.
Nowadays the uses of statistics are abundantly made in any economic study. Both
in economic theory and practice, statistical methods play an important role.
Alfred Marshall said, “Statistics
are the straw only which I like every other economist have to make the bricks”.
It may also be noted that statistical data and techniques of statistical tools
are immensely useful in solving many economic problems such as wages, prices, production,
distribution of income and wealth and so on. Statistical tools like Index
numbers, time series Analysis, Estimation theory, Testing Statistical
Hypothesis are extensively used in economics.
Statistics and Education:
How is statistics used in education?
Statistics is widely used in
education. Research has become a common feature in all branches of activities.
Statistics is necessary for the formulation of policies to start new course, consideration
of facilities available for new courses etc. There are many people engaged in research
work to test the past knowledge and evolve new knowledge. These are possible
only through statistics.
Statistics and Planning:
Statistics is indispensable in
planning. In the modern world, which can be termed as the “world of planning”,
almost all the organisations in the government are seeking the help of planning
for efficient working, for the formulation of policy decisions and execution of
the same.
In order to achieve the above
goals, the statistical data relating to production, consumption, demand,
supply, prices, investments, income expenditure etc and various advanced statistical
techniques for processing, analyzing and interpreting such complex data are of
importance. In India statistics play an important role in planning,
commissioning both at the central and state government levels.
Statistics and Medicine:
In Medical sciences, statistical
tools are widely used. In order to test the efficiency of a new drug or
medicine, t - test is used or to compare the efficiency of two drugs or two
medicines, t test for the two samples is used. More and more applications of statistics
are at present used in clinical investigation.
Statistics and Modern applications:
Recent developments in the fields
of computer technology and information technology have enabled statistics to
integrate their models and thus make statistics a part of decision making procedures
of many organisations. There are so many software packages available for
solving design of experiments, forecasting simulation problems etc. SYSTAT, a
software package offers mere scientific and technical graphing options than any
other desktop statistics package. SYSTAT supports all types of scientific and
technical research in various diversified fields as follows
1. Archaeology: Evolution of skull
dimensions
2. Epidemiology: Tuberculosis
3. Statistics: Theoretical
distributions
4. Manufacturing: Quality improvement
5. Medical research: Clinical investigations.
6. Geology: Estimation of Uranium
reserves from ground
water.
Limitations of statistics:
Statistics with all its wide
application in every sphere of human activity has its own limitations. Some of
them are given below.
- Statistics is
not suitable to the study of qualitative phenomenon:
Since statistics
is basically a science and deals with a set of numerical data, it is
applicable to the study of only these subjects of enquiry, which can be
expressed in terms of quantitative measurements. As a matter of fact,
qualitative phenomenon like honesty, poverty, beauty, intelligence
etc, cannot be expressed numerically and any statistical analysis cannot
be directly applied on these qualitative phenomenons. Nevertheless,
statistical techniques may be applied indirectly by first reducing the
qualitative expressions to accurate quantitative terms. For example, the
intelligence of a group of students can be studied on the basis of
their marks in a particular examination.
- Statistics
does not study individuals:
Statistics does not give any specific importance to the individual items, in fact it deals with an aggregate of objects. Individual items, when they are taken individually do not constitute any statistical data and do not serve any purpose for any statistical enquiry.
- Statistical laws are not exact:
It is well known that mathematical and physical sciences are exact. But statistical laws are not exact and statistical laws are only approximations. Statistical conclusions are not universally true. They are true only on an average.
- Statistics
table may be misused:
Statistics must be used only by experts; otherwise, statistical methods are the most dangerous tools on the hands of the inexpert. The use of statistical tools by the inexperienced and un traced persons might lead to wrong conclusions. Statistics can be easily misused by quoting wrong figures of data. As King says aptly ‘statistics are like clay of which one can make a God or Devil as one pleases’.
- Statistics is
only, one of the methods of studying a
problem:
Statistical method do not provide
complete solution of the problems because problems are to be studied taking the
background of the countries culture, philosophy or religion into consideration.
Thus the statistical study should be supplemented by other evidences.