Why Statistics?
We find different kinds of numerical facts published in news
papers, journals and magazines. Radios and Televisions convey different kinds
of numerical information. Some of them, for example, are “The cost of living index number rose from 230 in
January I970 to 300 in December 1971”.
“This year we expect an
increase of Rs. 50 over the percapita income of last year”. “The
average score of Srikanth in the test matches is 48”.
To understand these and similar other statements and to
analyse and interpret them we require knowledge in Statistical Methods. So a
grasp of Statistics is thus essential in the modern world.
All of us must be aware of statistical content in our
social, economic and political life. It is impossible for the Government to
function without collecting vast amount of information for administration and
for national economic planning. It is impossible to understand Psychology,
Education, Sociology, Economics, Business Management, Physical Sciences, even
at the most elementary level, without some idea of Statistical Methods.
Meaning of Statistics
The word Statistics is understood by different people in
different manner. For some people, if is tables, charts etc. For some, it is a
set of figures. It is a method of studying quantitative information regarding
some phenomena. Thus we see that generally the word is used in two different
senses.
In the first sense it refers to
the numerical facts called statistical data. In the second sense it refers to
some theories, methods, principles etc. In this sense statistics is a body of
methods known as statistical. methods. The methods and techniques provided by
Statistics range from the most elementary devices which may be understood by
even a layman to the complicated mathematical procedures which can be
understood only by experts.
Origin and Growth
of ‘Statistics’
Statistics is a very old branch of knowledge. The word ‘Statistics’ seems to have been derived from the Latin word ‘Status’ or Italian word ‘Statista’ or German word ‘Statistik’ all mean political state. The origin of Statistics
was due to administrative requirements of the state. Administration of the
state required the collection and anal sis of data relating to population. And
material wealth of the country .One of the earliest census of population and
wealth was held 1n Egypt as early as 3050 BC. for the creation of pyramids.
Although Statistics originated as a science of kings, now it
has emerged into a very important and useful science of all human beings. There
is hardly any branch 'of human activity where the statistical methods are not
made use of. Statistics has grown into a very powerful science.
Definition of ‘Statistics’
Statistics has been defined either as a singular noun or as
a plural noun in various ways by different authors.
(a) Definition
of Statistics as plural noun (or as numerical facts)
Statistics as a plural noun stands
for numerical facts collected. Though different anthers have defined the term
Statistics differently, the definition given by Horace Secrist is most
exhaustive.
According to Horace Secrist, “Statistics are aggregates of
facts affected to 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”
(b) Definition
of Statistics as a singular noun (or as a method)
The word Statistics as a singular noun
stands for a body of methods known as statistical methods. Statistics’ is a method
of obtaining and analyzing numerical facts, and figures in order to arrive at the
some decisions. In this sense, the word Statistics has been defined by many We
Of these definitions, the definition given by Seligman is short and simple and
yet quite comprehensive.
According to Seligman, “Statistics is the science which
deals with the methods of collecting, classifying, comparing and interpreting numerical
data collected, to throw some light on any sphere of enquiry”
The definition points out the
Various Statistical methods or features of science of Statistics. They are
collection of data classification of data, presentation of data and analysis
and interpretation of these presented data.
Characteristics of Statistics
As per the definition given by Horace Secrist, Statistics
should possess the following characteristics.
(1) Statistics should be aggregate of facts: Single and
unconnected figures are not statistics. A single motor accident in a city is
not statistics. But the total or aggregate number of motor accidents that have
occurred in a city during a month or an year are statistics.
(2) They should be affected to a marked extent by
multiplicity of causes: Statistical facts are affected or influenced by a
number of factors. For example, if Rajesh gets good marks in the examination
the following factors might have influenced (i) he is intelligent (ii) he is
hard working (iii) his parents took‘keen
interest in his studies (iv) he is a disciplined boy etc. Therefore Statistical
facts are influenced by many factors. (3) They must be numerically expressed:
Qualitative expressions like good, bad, young, old etc., do not form part of
statistical studies. Facts which are expressed in figures can only be called
Statistics. For example, when we say that this year the rainfall is poor, it is
not statistics. But when we say the average rainfall, in the last year was 10
cm and this year it is only 4 cm then it becomes a statistical statement. '
(4) They should be enumerated or estimated according to
reasonable standard of accuracy: The data may be collected by enumeration or by
estimation. Statistician must observe reasonable standard of accuracy in
collection of data. Heights of students are measured to the nearest centimeter
while distance of a place is measured to the nearest kilometer.
(5) They should be collected in a systematic manner: The
data should be collected in a systematic manner according to a well prepared
plan.
(6) They should be collected for a predetermined purpose:
The purpose for which the data are to be collected should be specific and well
defined. Investigator should be fully aware of the purpose of the enquiry
before he proceeds to collect the data. Otherwise he may ignore facts which are
relevant.
(7) They should be placed in relation to each other:
Statistics collected should facilitate comparison. Therefore they must be
homogeneous. Unrelated data cannot constitute Statistics. For example, the
height of a person cannot be compared with the money spent by him.
Functions of Statistics (Why is Statistics important?) Main
functions of Statistics are
(1) It Simplifies complexity: In our studies' we collect
huge facts and figures. They cannot be easily understood. Statistical methods
make these large number of facts easily ' intelligible and readily
understandable. In Statistics there are methods like Graphs and Diagrams,
classification, Averages etc which render complex data very simple.
(2) It presents facts in a definite and precise form:
Statistics presents facts numerically and thus gives definite and precise form
to the data. Statement of facts conveyed in quantitative terms are always
convincing.
(3) It helps condensation: Statistics helps in condensing
mass of data into a few significant figures. Average provides a single
significant figure summarizing the entire data. Percapita income, for example,
is the essence of the individual incomes.
(4) It enables comparison of data: Unless figures‘are compared with others of
the same kind, they are of no use. When we say that the price of a commodity
has increased very much, the statement does not make the position very clear.
But when we say that last year price was Rs. 10 but now it is Rs. 11 the
comparison becomes easy. Statistics provides a number of suitable methods like
ratios, percentages, averages etc for comparison.
(5) It helps in testing: Statistical methods are extensively
useful in testing hypothesis. They also help to develop new theories.
Statistics help in testing laws of other sciences. For example, Law of demand,
Law of 'supply etc can be verified with the help of Statistics.
(6) It helps prediction (or forecasting): Plans and policies
‘of organizations are
formulated well in advance of the time of their implementation. A knowledge of
future trends is always necessary in framing policies and plans. Statistical
methods provide helpful means of forecasting future events.
(7) It helps' In formulating policies. Statistics provide
the basic material for framing suitable policies. The statistical tools like
collection of data help much in this regard.
(8) Statistics studies the relationship between different
groups: In all types of studies the importance of observing relationship
between different phenomena is very great. The relationship between price and supply
or price and demand can be studied with the help of Statistical methods like
correlation.
(9) It enlarges human experience: The science of Statistics
enlarges human experience and knowledge. Statistical methods can be applied to
make vague and indefinite‘ideas to
become clear and definite. Many conclusions and information can be verified and
established with the help Statistics.
Importance and utility of Statistics (or Scope of Statistics)
In the early period of development of Statistics, it had
only limited scope. But in modern times, the scope of Statistics has become so
wide that it includes all quantitative studies and analysis relating to any
department of enquiry.
Thus it is hardly possible to find a field where statistical
methods are not used. This universality of statistics is enough to indicate its
importance, utility and indispensability to the modern world.
We shall discuss below the importance of statistics in
various fields.
1. Business and Industry:
Statistics is an aid to business and commerce. When a person
enters business, he enters into the profession of forecasting. Modern
statistical devices have made business forecasting more precise and accurate.
A business man needs Statistics right from the time he
proposes to start business. He should have relevant facts and figures to
prepare the financial plan of the proposed business. Statistical methods are
necessary for these purposes.
Before putting his product in the market the business man
should know the probable demand of the commodity. So he must make careful
studies of seasonal variations in the habits and tastes of the people. He should
also take into consideration the changes in purchasing power of money. Statistical
methods are very useful in this regard. When a businessman wants to explore the
demand for his product, he has to conduct market research which is nothing but
a type of statistical investigation.
In industrial concerns statistical devices are being used
not only to determine and control the quality of products manufactured but also
to reduce wastage to a minimum. The technique of statistical quality control is
used to maintain the quality of products.
2. Business Management
One of the important functions of business management is to
coordinate the activities of the various departments so as to secure maximum
efficiency with minimum effort. To discharge this function efficiently,
management is making wise decisions in the face of uncertainty. Modern
Statistics has developed certain general principles and devices to deal with
uncertainties wisely. Modern statistical tools of collection, classification,
tabulation, analysis and interpretation of data, have been found to be an
important aid in making wise decisions at various levels of management
function.
The success of production programming both in the short as
well as long period depends to a great extent on the quality of sales
forecasts. Statistical methods can be applied to have better sales forecasts.
Effective control on sales can also be exercised through regional allocations.
Market research consumer preference studies etc. are some other methods of
sales control, which make an extensive use of statistical tools.
3. Economics
The science of Economics is becoming statistical in its
method. In me field of Economies it is almost impossible to find a problem
which does not require an extensive use of statistical data. As economic theory
advances, use of statistical methods also increases. The laws of Economics like
Law of demand, Law of supply etc. can be considered true and established with
the help of statistical methods. Statistics of consumption tell us about the
relative strength of the desire of a section of people. Statistics of production
describe the ‘wealth of a
nation. Exchange statistics throw light on commercial development of a nation.
Distribution Statistics disclose the economic conditions of the various classes
of people Therefore statistical methods are necessary for proving economic
laws. Marshall observes that “statistics
are the straw out of which I like every other economist to make bricks”.
Index number like Cost of living index number, Whole sale
price index number etc. and analysis of time series are important statistical
concepts in economic theory. Thus one can say that without Statistics many
theories of Economics would have remained closed to mankind.
4. Administration (or to the Government)
Statistics are the eyes of government administration. For efficient
administration, Government have to depend on Statistics. The Government has to
collect statistical data whenever they adopt measures to achieve the objectives
like reducing inequalities in the distribution of wealth, income etc. The
Government administration is run through budgets which are formulated on the
basis of statistics. The commissions and committees appointed by the
Governments base their reports on statistics. The government requires
statistics for carrying on their commercial activities. The government
formulates policies concerning family planning, establishment of new industries
etc. On the basis of statistical information. Our five year plans are
formulated with the help of statistical methods.
5. Research
Modern statistical methods and statistical data are being
found increasingly useful in research in different fields. In the field of
science, in the literary field, in the field of business activities and in the lied
of economic activities, research work are being undertaken with the help of
statistical methods.
6. Planning Modem age is an age of planning
For planning to be successful, statistical data are
necessary. So planning cannot be managed without statistics. National sample
survey scheme was primarily started to collect statistical data.
7. Bankers, brokers and Insurance companies
Statistical methods help various economic entities. A banker
has to make statistical study of business cycles. The stock exchange brokers
speculators and investors etc. Have to rely on statistical data for precise
forecasting. The success of insurance company depends on the accurate basic
data that it uses for the calculation of premium rates etc.
Limitation of Statistics (1) Statistics studies only
numerical facts: Statistics are numerical statements of facts. Therefore such
characteristics which cannot be expressed in numbers are not capable of
statistical analysis. Thus qualitative characteristics like honesty,
intelligence etc, cannot be studied directly with Statistics. '
(2) Statistics does not study individual cases: Statistics
studies only the aggregate of facts. It does not study any particular unit.
Suppose the percapita income of an American is 10000 dollars. Then this is only
the average income of people of America and it does not reveal the poverty and
misery of individuals in America. The reason for this is that the high incomes
of some people offset the low incomes.
(3) Statistical results are true only on an average:
Law of Statistics are not universally true like the laws of Physics
or Astronomy. They are true only in general.
(4) Statistics does not reveal the entire story of the
problem:
Since many problems are affected by such factors which are
incapable of statistical analysis it is not always possible to examine a problem
in all its aspects by a statistical approach.
(5) Statistics is only one of the methods of studying a
problem:
In many cases, Statistics fails to suggest solution to
certain problems. These are problems which are to be considered in the light of
many qualitative aspects like country’s
culture, religion and philosophy. Statistics cannot ~ be of much help in
studying such problems.
(6) Statistics can be misused (Statistical methods can be
used only by experts):
Any person can misuse statistics and draw any type of
conclusion he likes. In reality statistical methods can be properly used only
by trained people. It requires skill and experience to draw sensible
conclusions from the data.
(7) Only means and not a solution:
Statistics are only a means for finding the solution of any
problem. It is not a solution to the problem,
Distrust of Statistics
By distrust of Statistics we mean lack of confidence in
statistical statements and statistical methods.
It is often commented by people, “Statistics can prove anything”. There are three
types of lies: “lies, damned
lies and Statistics”. “An ounce of Statistics will
produce tons of statistics”.
Some have condemned statistics as “tissues
of falsehood”. Statistics
is also called “a rainbow of
lies”. These and similar statements
indicate the extent to which the science of statistics is not trusted even in
modem times when its use has spread over all types of human activities. Due to
the ignorance of the public as well as the misuse of Statistics by interested
parties, this useful science has been blamed. We are often misled by skilful
talkers and writers who deceive us with incorrect facts. Therefore we come to
distrust Statistics. The distrust of Statistics cannot be attributed to this
science as it is mainly due to the deliberate manipulation of statistics by
unscrupulous persons to support their views.
Figures are innocent and easily believable. Sp men believe
statistical statement, usually without questioning it. There is great danger in
this way of approach since figures which support a particular statement need
not be true. Arriving at wrong conclusions by incorrect figures condemn
statistics in the strongest possible language. The fault in such cases does not
lie with Statistics. It lies with those who use it.
Statistical methods are most dangerous tools in the hands of
the inexpert. The science of Statistics is a most useful servant but only of a
great value to those who understand it properly.
Misuse of Statistics
By Misuse of Statistics we mean using incomplete and
incorrect information and using inappropriate statistical method. Quoting
figures without knowing their context, applying figures or statistical measure
to such phenomena to which they do not relate, generalizing from the pan to the
whole, listing out only those events which are favorable to an argument etc.
are some of the ways of misusing Statistics and Statistical methods. Misuses
unfortunately are as common as valid uses of Statistics. Many people misuse
statistical data and statistical methods and draw fallacious conclusions. In
reality statistical methods can be properly used only by trained people.
Divisions of Statistics The science of statistics can be
divided into three broad divisions.
(1) Theoretical Statistics (2) Statistical methods (3)
Applied Statistics
When Mathematical theory forms e basis of the science of
statistics, it is called Theoretical Statistics. Statistical methods are
methods by which data recollected and they are organized presented analyzed and
interpreted. Statistical methods can be divided into two groups (a) Descriptive
Statistics (b) Inferential or inductive Statistics.
Descriptive statistics and Inferential Statistics. The term
descriptive statistics is conformed to the treatment of data for the purpose of
describing their characteristics. It involves techniques for summarizing data
and presenting them in a usable form. Inferential statistics involves making
forecasts, estimations or judgments about some larger group of data than that
actually observed or about future happening based on a study of historical
data. They project from the known to the unknown. If we find the average marks
obtained by the students in a class to study the efficiency of the students, it
is descriptive statistics. But when we use the average marks obtained by a
section of students to estimate the average marks of the entire students, it is
inferential statistics.
SOME QUOTATIONSAND THEIR MEANING
‘Statistics is the Science of averages’
Statistics as “Science
of averages” Average is
a single figure which can effectively describe the general trend of statistical
data and can be used to compare two or more singular situations. Many of the
statistical conclusions are based on statistical average. Therefore it is
justifiable if Statistics is defined as “science
of averages”. But the
definition is insufficient as the science of Statistics has many other
functions.
‘Statistics
is the Science of counting’
“The elements
of Statistics” defines
Statistics as ‘science of
counting’. Counting in Statistics has a
greater significance. It, in fact, means collection of data through counting or
measuring the objects under study. Collection of data is an extremely important
problem in Statistics. But from the present points of view, the definition is
inadequate and it touches only the function of Statistics.
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