1.1
Nature and Scope of Statistical Methods
Statistics gave it real birth when man first began to count the possession things in and around him
to assertion his strength and weakness. Today’s progress that we notice in all walks of life could
have been in the bay but for the discovery of number theory. The use of statistics dates back
Pharaohs and Hebrews. They used census method to obtained population and wealth related data
collections. Ancient kings maintained records on population, military strength, wealth, cultivated
area, crop yield, livestock, birth and death rates etc. Since statistical data were collected for
governmental purposes only in those days, statistics was then identified as the ‘Science of Kings’
or the ‘Science of State Craft’.
The word statistics is derived form the Latin word ‘Status’ and Italian word ‘Statista’. In
both the cases it means, ‘an organized political state’. The definition of statistics got widened
overtime due its phenomenal growth and use. In fact, statistics constitutes a vital part in each and
every scientific enquiry today. No field of study is complete without the use of statistics.
Statistics thus plays a multifarious role as Tippet has rightly remarked “it affects everybody and
touches life at many points”.
1.2
Definition of Statistics
Statisticians define statistics both in singular and plural sense to emphases their own viewpoints
regarding statistics. For a common man, the word statistics normally means facts and figures of a
particular phenomenon in numerical numbers. In modern life, statistics has different meanings to
different people largely based on its usage. For example, (i) for the census department, statistics
refers the death and birth rates per one thousand population; (ii) for cricket fans statistics means
numerical facts about runs scored by batsman; (iii) for a share broker statistics means the current
price of shares; (iv) for a politician statistics means the eligible voters in his or her constituency.
Thus when we say that a particular statistical abstract contains a large number of facts and figures
then we are clearly referring to statistics in its plural meaning.
(a) Plural definition
Yule and Kendall’s have observed, “By statistics we mean quantitative data affected to a marked
extend by multiplicity of causes.”
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Statistical Methods for Management
Bowley define statistics as, “Numerical statements of facts in any department of enquiry placed in
relation to each other”.
Conner is of the opinion that, “Statistics are measurements, enumerations or estimates of natural
or social phenomenon systematically arranged so as to exhibit their inter-relations.”
Horce Secrist defined statistics as “By statistics we mean aggregate of facts affected to a marked
extent by multiplicity of causes, numerically expressed, enumerated or estimated according to
reasonable standard of accuracy, collected in a systematic manner for a pre determined purpose
and placed in relation to each other.”
Most of the definitions given above except the last one are not fully satisfactory in the sense
that each one of them is defined having a particular usefulness in mind.
(b) Singular definition
Statistics used in the singular sense highlights the importance of methodological issues rather
than mere collection of facts and figures. In this meaning statistics is defined as the body of
knowledge covering the techniques like collection, classification, presentation, analysis and
interpretation of data. Thus, in both the sense it deals with the quantitative aspect of the study
under reference. In the singular sense the term statistics is widely accepted as “a body of
knowledge providing techniques for making decisions when there is uncertainly arising from the
incompleteness or the instability of the information available”.
According to Bowly, “Statistics may rightly be called the science of averages.”
According to Seligman, “Statistics is the science which deals with the methods of collecting,
presenting and interpreting numerically collected data to through light on any spear of enquiry”.
Thus statistics in plural sense are numerical statements of facts capable of some meaningful
analysis and interpretation; in singular sense, it relates to methods of collection, classification,
presentation and interpretation of numerical data.
Functions of statistics:
• Statistics perform many functions like converting a large data base into a manageable and
comprehensive data base.
• It analyse the typical relationships between the variables under study.
• The average behaviour of data mass is identified. Such a reduction is often called the
average.
• Many theories are often obtained after surpassing the relevant statistical tests.
1.3
(i)
(ii)
(iii)
Nature and Scope of Statistics
Nature: Statistics is no doubt both a science and arts. As science, it study the subject
matter in a systematic manner. As an art it provides solutions to the real life problems.
Subject matter: The study of statistics provides all essential like methods of data
collection, methods of data processing and data presentation, data analysis, and data
interpretation. In addition it also provides enough testing tolls for fact theorizing in all the
fields of enquiry.
Relationship with other subjects: The importance of statistics is now being felt in almost
every field of inquiry. In fact it is difficult to find a subject which does not have any
Introduction to Statistical Methods
3
relationship with statistics. Nowadays, even most of the subjects under humanities use
statistical methods in testing their theories. Thus, statistics occupy the dominant position
in the heart of other sciences. Every field of enquiry may be business, natural, physical or
social science; statistics bring-in perfection into it.
(a) Importance of statistical methods in economics
The classical economists, headed by Adam Smith, were too much optimistic about their good
results that they were getting by using merely the standard deductive logical reasoning. They
needed no support either from a large mass of data in the plural sense or statistical methods in
singular sense in deriving their economic laws. In this context it is worth to quote J.S. Mill, “in
some cases instead of deducing our conclusions from reasoning and verifying them using
observations, we begin by obtaining them provisionally from specific experience and afterwards
connect them with the principles of human nature on apriori reasoning”.
It was W.S. Jevons who clearly highlighted the importance of statistics in economic
theorizing. By adopting inductive methods in the place of deductive reasoning he ascertained
certain important economic laws. Later, it is the historical school that played a greater role and
brought about a high degree of integration between economics and statistics. The Marshallian
statement that “statistics are the straw out of which, I, like every other economist, make my
bricks” highlights the importance of statistics in economics.
The numerical information available to economists is classified into two main types, the time
series data and cross-section data. The time series data gives the value of the variables like
income, employment etc., under study overtime. The cross-section data, on the other hand, is
obtained by taking variables like income, employment etc., at a given point of time. Economists
use both the types as complimentary in establishing their economic theories. Economic theories
are in a way establishes a certain kind of relationship among variables like price, quantity,
income, consumption etc., Economists use ‘correlation analysis’ to test the strength of relation
between the theoretically connected variables. Similarly they use ‘regression analysis’ to establish
the exact relationships between concerned variables.
(b) Importance of statistical methods in business
Modern business involves risk and uncertainty everywhere. Decision making under such
uncertain circumstances is rather a difficult task. In this context the probability theory developed
in statistics play a crucial role in solving the real life problems. According to Boddingten, “A
successful businessman is one whose estimates must closely approach accuracy”. The next
associated problem in business is forecasting the future on the basis of past experience. Statistics
provides enough forecasting methods to solve some of these problems.
(c) Importance of statistics in politics
In olden day’s statistics was considered as ‘Science of Kings’. To begin with, the then kings were
collecting and maintaining the military strength related data for himself and their rivals. Latter
they too collected statistics regarding population, irrigated land etc., on welfare grounds. Modern
governments, being welfare oriented states; statistics is collected to solve some of the basic
welfare oriented problems. As technology advanced, today we collect statistical data relating to
earth through satellite image scanning methods. The definition given by Bowly “Statistics is the
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Statistical Methods for Management
science of measurement of social organism regarded as a whole in all its manifestations” is worth
to note in this context.
(d) Statistics in economic planning
Less developed countries often go for planning to achieve high rate of growth. Whether planning
is at the cross root level or at the high layer level statistical data play a crucial role in achieving
the desired level of targets. According to Tippet “Planning is the order of the day and without
statistics, planning is inconceivable”. The success of planning could be evaluated only through
collected statistical data before and after the planning.
(e) Use of statistics in other fields
Besides certain important fields as mentioned above statistical tools are of great help in baking,
industry, social works, trade associations, educational institutions etc. In all these fields’ statistics
helps a lot in solving practical problems. Often individual politicians collect statistics about his
vote bank before filing his application. Thus, the use of statistics is inevitable in all fields.
(f) Use of statistics in mathematics
According to F.C. Mills “Statistics is an offspring of Mathematics”. The ‘Law of inertia of large
numbers’ otherwise called the ‘Law of statistical regularity’ is the brain child of mathematical
statistics. Both mathematics and statistics use each other for their mutual benefits.
(g) Relationship with econometrics
In recent times another quantitative approach, called econometrics, has emerged as an important
tool in economic theorizing. The empirical content and policy significance are the two important
faces of this new approach. Osker Lange defines econometrics as “the science, which deals with
the determination of quantitative laws occurring in economic life.”
Mathematical economics play an important role in translating the verbal economics theories
into its mathematical form. Econometrics, on the other hand, provides the necessary tools in
testing the so obtained mathematical statements of the concerned theory. Thus it is a branch of
knowledge that deals with the empirical measurement of the economic relationships listed out in
economic theories. For example, the linear demand equation given in the previous section is only
a restatement of the date old demand law in its mathematical form.
Econometrics proceeds further in this direction by measuring the tightness of this inverse
relationship using the statistical tools like correlation, regression etc. It is also used to test the
reliability of the inverse demand law by using statistical tools. Once the reliability of the
relationship is established the so obtained relationship is used to forecast the likely changes in the
quantity demanded for an expected price change on a future date. This is the practical utility of
econometrics.
One must remember that before testing a theory for its reliability, it must be first translated
into a suitable mathematical form. It is also true that the statistical tools are commonly used in
econometrics. Thus the basic relationships, which are analyzed in econometrics, are economic
relationships expressed in mathematical form. Hence, for a good understanding of the subject
“econometrics” one must be good enough in economic theory, in addition to mathematical and
statistical tools. In other words we would say that econometrics is a combination of economics,
mathematics and statistics.
Introduction to Statistical Methods
5
1.4 Limitation of Statistics
Though statistical methods are now being used almost in all walks of life, it suffers from a few
limitations. Some of them are listed hereunder.
1. Absence of uniformity: In any statistical enquiry the data obtained are normally
heterogeneous in nature. Though very often we undertake some corrective measures to
overcome this defect, the statistical methods alone can not bring in perfect uniformity in the
data series. Under such circumstances, results obtained need not be uniform and hence will
serve as a representative figure. This is really a severe limitation to the use of statistics in
other fields of enquiry.
2. It does not study individuals: Statistics broadly macro in nature. Thus we give more
importance to aggregates rather than individuals. Hence, isolated or single figures, however
important they might be, can not be considered within the preview of statistics.
3. They speak about only averages: The statistical laws are true only on an average. For
example, if we say that the per capita income in India is Rs. 6500 per annum currently then, it
does not mean that the per capita income of the members of the Tata’s family and the income
of the poor fellows who sleeps in the street are equal. Therefore, sometimes averages give
only fallacious and contradicting results.
4. They cannot be applied to qualitative studies: The statistical studies are not amenable to
qualitative attributes like good, bad, beautiful etc. For a wholesome coverage of the inquiry
the tools must be applicable for both qualitative and quantitative data.
5. Statistical laws are not stable and universal: The statistical laws are obtained on the basis
of information available at one point of time need not be true at some future date. Since over
time the basic data changes, the basic laws governing them also changes. Moreover, what is
applicable to one country on the basis of observed statistics need not be true and hence
applicable in another country. Hence, at least in certain cases, the statistically derived laws
need not be universal.
6. Statistical methods are often biased: The presence of inevitable personal bias with the
individuals who collects the statistical data often gives abnormal and obscured results.
7. Possibility of misuse: Statistics is misused very often in the sense that a dishonest man can
always prove all that he wants to do by using false and cooked up statistics. “Statistics are
like clay of which you can make either a God or Devil as you please” is the right quote in this
context. “Statistical analysis has considerable accomplishments to its credits but at the same
time it is not a panacca, and hence has occasional danger of being oversold.”
EXERCISES
1.
2.
3.
4.
5.
Discuss fully the limitations of statistics in economics.
Discuss in detail the importance of statistics with special reference to economics.
Explain the usefulness of statistics in economic analysis and planning in particular.
“Statistics can prove any thing”. Explain.
“Statistics are like clay of which you can make either a God or Devil as you please”. Give
your comment on the above statement.
6. Describe the role of both mathematical and statistical methods in economics.
7. “Statistical analysis has considerable accomplishments to its credits but at the same time it is
not a panacca, and hence is in occasional danger of being oversold”. Discuss.
❍❍
2.1 Statistical Enquiry
The flow of information for executives responsible for the operations of a business has become an
important part of management. In this context the entire process of collection of quantitative facts
and figures. about the problem under reference play an important role. Since statistical materials
are numerical, it is important to collect only fact that can be quantitatively expressed.
Objective and scope of statistical enquiry
Before entering into data collection, the scope and objectivity of the data must be well defined to
avoid unnecessary and irrelevant information.
An enquiry may be either specific to an issue under reference or general purpose oriented.
For example, an enquiry relating to the academic involvement of teachers in the Indian
Universities is a specific enquiry. Instead, the population census that is being taken once in 10
years in India comes under the general purpose enquiry.
Official and non-official enquiries
Enquiries undertaken on behalf of government are often called the official enquiries. Those
undertaken by private individuals or institutions are called non-official enquiries. Often some
private institutions undertake enquiries with the support of the government as well.
Confidential or non-confidential
Enquiries that are not to be disclosed to the public is called confidential enquiries. On the other
hand non-confidential enquiries, results are made known to public.
Direct or indirect enquiries
In direct enquiries the facts collected are quantitative in nature. For instance, income, employment, etc., are measurable in quantitative terms. But certainly, matters like honesty, intelligence
etc., can not be measured in quantitative terms. However, they are measured indirectly from
related matters. For example, the intelligence of the student could be measured indirectly from his
examination performances.
2.2
Census versus Sampling
A census is an all-inclusive exhaustive type in which each and every aspect of the subject under
reference is examined. The results thus provide an accurate picture of subject under reference.
Collection and Classification of Statistical Data
7
But definitely it is time-consuming and tedious as well. In a sample, instead we take only few
elements of the subject and draw conclusions about the population. If sample is selected
intelligently by following sampling principles, one could expect not only high quality results but
also with minimum time cost.
Statistical units
Thing are measured in quantity by using well defined units. The unit of measurement thus must
be well defined before the start of the enquiry process itself. For example, if we want to collect
data relating to educated persons in the society then the educational qualification must be well
defined, it may be matriculation, or undergraduate or postgraduate.
1. So the definition must be intelligible, clear-cut, rigid and finally unambiguous.
2. It should be relevant to the subject of enquiry,
3. It should have stability throughout the investigation period.
Kinds of units
The units of measurements may be mere counting in certain cases like number of bricks used.
Sometimes it is measured in terms of weights like tons of cement consumed. Someother occasion
the units may be areas like square meters of play wood taken out from the shop. In all the cases
we have well defined standard units. They are all simple units. When a simple unit is qualified by
addition like kilometer per litter of petrol then the number of kilometers given by the vehicle
under reference depends upon the quantity of petrol consumed. Such units are called composite
units. For easy data comparison it is always preferable to have comparable units in percentage,
ratios and rates.
Accuracy and approximation
In any kind of statistical enquiry investigators must aim for reasonable high degree of accuracy.
This does not mean 100% accuracy in all fields of enquiry. The degree of accuracy often depends
upon the nature of the problem addressed. For example for an investigation of distance between
Bangalore and Chennai it is enough to state it in terms of nearest rounded off kilometers. On the
other hand, if it is the question of sending manned space shuttle to moon, the distance estimate
must be at least nearest to meters and definitely the nearest to kilometers.
2.3
Statistical Errors
By error in statistics we mean the difference between the estimated statistics and the true value of
the parameter. Thus in statistical sense error should not be confused with the common usage term
“mistake”. Statistical errors are measured in absolute and relative terms. For example if the
actual profit is Rs. 3500 and the estimated profit is Rs. 3400 then the absolute error in this case is
Rs.100. However, the relative error is (100/3500)100 = 2.8571%. Normally relative errors are
often used in statistics.
Biased errors
These errors are totally attributed to the concerned enumerator. Sometimes informants, enumerators, or investigators under-estimate or over-estimate the concerned parameter. Thus such errors
are committed by biased or prejudiced minds of the persons concerned at the time of estimation.
Obviously, these errors are cumulative in the sense more the number of prejudiced minds more
will be the quantum of error.
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Statistical Methods for Management
Unbiased error
The unbiased errors are due to chance. The error that under-estimates or over-estimates the
parameter concerned due to sampling belongs to this type.
Possible errors
The error that occurs due to approximation is often called as possible error. For example, the
number 123.05321 is approximated to 123.1. The error due to this approximation is called the
possible error.
Probable error
This stands for the numerical term by which the error can be more or less. If the correlation
coefficient between X and Y is r = 0.54 and its probable error is 0.01 then the allowable error for
the correlation coefficient 0.54 – 0.01 to 0.54 + 0.01. This is to say that the correlation coefficient
should lie between 0.53 to 0.55.
2.4 Internal and External Data
The data that emerges from the very factory or the institution is often called the internal data. This
vital information is the source for the development of the concerned institution. The data that tells
something outside the institution concerned is called the external data. Though the internal data is
the vital part in any developmental planning, the external happenings like the strategy of
competitors, investment environment are to be given due consideration. Thus, the ultimate
success of the institution depends upon its ability to generate both internal and external database.
In many respects the process of collection and tabulation are interrelated. Internal data are usually
recorded in the concerned official documentation section of the institution. Thus, its availability
and accuracy heavily depends upon the systematic filing methods that are in practice. External
data however is not available within the institution concerned; facts must be secured either by
making observations or by asking questions outside its own business. In collecting external data,
the process of collection and tabulation are treated differently. If the facts are to be obtained by
observation, it is essential that the observer have to follow some systematic method of recording.
If the facts are to be collected by questioning, then a rightly prepared questionnaire is to be used.
2.5 Primary and Secondary Data
The data that is collected for the first time is called the primary data. Such first hand information
is obtained by variety of methods. The following are some of the important method of collecting
the primary data. A substantial amount of data is collected and published by non-profit agencies,
such as governmental departments, trade associations, research institutions etc., banks,
newspapers, periodicals and public utilities also collect and publish the data. Often some private
agencies also collect and supply the data to the needy, of course, for a price. All these items
constitute the secondary data pool. Thus, collecting secondary data does not involve enumeration.
Since it is already collected in ready-to-use form without much additional cost one can utilize
them as complimentary to the primary data source. Once primary data is collected and used in a
research study it becomes secondary for other users. Thus, demarcation of data into primary and
secondary is only illustrative.
A clear distinction between recorded source and other sources must be stated. In the case of
public records getting the data is relatively easier. However information on the records of
Collection and Classification of Statistical Data
9
individual business will not be made available to the public or even to the researcher. On the
other hand, a great deal of information, such as data on sales, production, employment and profits
may be collected from individual concerned by public agencies or trade associations. Sometimes
most of the information collected by business concerns exists in the minds and memories of
individuals rather than formal records. Information like trading habit, television viewing habits
etc., collected from consumers are really from the memories of the consumer and not from any
formal record.
2.6 Sources of Secondary Data
•
•
•
•
•
Central and State Government Publications.
Publications brought by UN, UNESCO, WHO, WTO etc.
Foreign Government Publications.
Official publications such as Municipalities, District Boards etc.
Reports and Publications Commissions like UGC, Education Commission, Tariff
Commissions, Cooperative Societies, Trade Associations, Banks, Stock Exchanges, and
Business Houses etc.
• News Papers, Journals and Periodicals like Economic Times, The Financial Express,
Economica, Indian Economic Journal, Labour Economic Journal, Political Economy,
Eastern Economics, Times of India Year Book etc.
• Publications brought out by Research Institutions, Research Scholars etc.
Verification of secondary data
Since secondary data by definition is the resource of somebody else, its reliability must be
checked before putting them into actual use.
2.7 Methods of Collecting Primary Statistical Data
1. Observation method
Observation method is mostly viable in experimental data collection. When all other factors other
than the relevant ones are controlled in the said experiment then the observed results are normally
attributed to the changes in the relevant referred variables only. For example, if we are interested
in traffic studies to get some useful information in highway planning then one will have to follow
observation method only. Observers may count the number of different types of vehicles pass
through in a specific time interval, or he may go for a sophisticated counting machine. In either
case, observation is the rule of the game. The amount of data that one can get, of course, is
limited because so many needed facts can be obtained only by asking direct questions and not by
mere observation.
2. Questioning method
Because of the limitations of the observation method, often statisticians prefer the questioning
method. For questioning, however statisticians can use several methods of communication.
Probably, the most commonly used methods are mailing the questionnaire method, telephonic
interview method and personal interview method. Among the three the best could be the one that
secures the needed information with greatest degree of accuracy with lowest money and time
cost. Mailing the questionnaire is the cheapest and expeditious method of collecting the data. This
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Statistical Methods for Management
method could be advantageously used whenever the field of enquiry is vast. But unfortunately,
the response through this method proved to very weak. Whatever may be the urgency some
respondents may not care to reply. If questions are not wisely advocated, some respondents may
go wrong and provide unwanted and incorrect information.
The telephonic method is the next cheapest alternative. But here again one cannot get all the
information needed. Some times even in this method respondent can evade the information
especially when they are sensitive. Some times getting the phone connection itself is a big
problem. Thus, one will have to try several times to get the needed data information.
Often statistical data collection is done directly by the concerned investigator himself by
personally approaching the people concerned. In this method the investigator makes on the spot
observations of customs, traditions, habits and behaviour of the people concerned and explains
the object, scope and practical utility of the investigation. It has been amply demonstrated that the
personal interviewer is able to get much higher percentage response than other methods.
However, high cost interviewing has induced statisticians to opt for combination of methods in an
attempt to reduce the cost. For example, first they prefer to mail and as many response as
possible. Individuals fail to respond in the mailing method will be contacted through telephone
next. If this step also fails they go for third stage of personal interviewing.
If a report is needed periodically then needed information for the first time is collected by
personal interview method. The subsequent details are obtained my mailing method periodically.
This method is being practiced by agencies collecting information on current business. However,
there are no hard and fast rules regarding the type of methods to be adopted. The needed accuracy
could be the one of the important criterion in opting the method of data collection. If sample
survey is the goal then one must use the methods that guarantee each respondent’s involvement in
the enquiry.
2.8
Essentials of a Good Questionnaire
A questionnaire is simply a sheet of paper containing set of judiciously prepared questions
relating to the investigation in hand. These questions are prepared with lot of care by keeping the
objectives, nature and scope of the study in mind. Since the questionnaire and schedule are often
used interchangeably a clear distinction between them is appropriate at this stage. Schedules are
usually blank forms with blank columns under relevant heads. The interviewer or the enumerator
usually fills the schedule after lessening reply of the respondents. Questionnaires on the other had
is designed suitably so that the respondents themselves fills the answers. Thus, questionnaires are
necessarily made simple with necessary instructions so that the respondent can fill it by himself.
The following are some the essential characteristics of a good questionnaire:
1. Questions should be simple, brief and few in number.
2. Questions should be free from ambiguity, easily intelligible and readily answerably.
3. Questions must be answerable simply by ‘yes’ or ‘no’, if not, it must be answerable in
numerical numbers.
4. It should avoid sensitive and confidential information.
5. Questions should be capable of directly eliciting the desired information without prejudice.
6. Wherever possible, questions should be courteous.