Business statistics solutions PDF

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OBJECTIVE: The aim of the present lesson is to enable the students to understand
the meaning, definition, nature, importance and limitations of statistics.
“A knowledge of statistics is like a knowledge of foreign
language of algebra; it may pr ove of use at any time under
any circumstance”.............................................Bowley.
STRUCTURE:
1.1 Introduction
1.2 Meaning and Definitions of Statistics
1.3 Types of Data and Data Sources
1.4 Types of Statistics
1.5 Scope of Statistics
1.6 Importance of Statistics in Business
1.7 Limitations of statistics
1.8 Summary
1.9 Self-Test Questions
1.10 Suggested Readings
1.1 INTRODUCTION
For a layman, ‘Statistics’ means numerical information expressed in quantitative
terms. This information may relate to obj ects, subjects, activities, phenomena, or
regions of space. As a matter of fact, data have no limits as to their reference,
coverage, and scope. At the macro level, these are data on gro ss national product and
shares of agriculture, manufacturing, and services in GDP (Gross Domestic Product).
SUBJECT: BUSINESS STATISTICS
COURSE CODE: MC-106 AUTHOR: SURINDER KUNDU
LESSON: 01 VETTER: DR. B. S. BODLA
AN INTRODUCTION TO BUSINESS STATISTICS

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At the micro level, individual firms, howso ever small or large, produce extensive
statistics on their operations. The annual repo rts of companies cont ain variety of data
on sales, production, expenditure , inventories, capital em ployed, and other activities.
These data are often field data, collected by employing scientific survey techniques.
Unless regularly updated, such data are the product of a one-time effort and have
limited use beyond the situation that may ha ve called for their collection. A student
knows statistics more intimately as a subj ect of study like economics, mathematics,
chemistry, physics, and others. It is a discipline, which scientifically deals with data,
and is often described as the science of data. In dealing with statistics as data,
statistics has developed a ppropriate methods of collec ting, presenting, summarizing,
and analysing data, and thus consists of a body of these methods.
1.2 MEANING AND DEFINITIONS OF STATISTICS
In the beginning, it may be noted that the word ‘statistics’ is used rather curiously in
two senses plural and singular. In the plural sense, it refers to a set of figures or data.
In the singular sense, statis tics refers to the whole body of tools that are used to
collect data, organise and interpret them a nd, finally, to draw conclusions from them.
It should be noted that both the aspects of statistics are important if the quantitative
data are to serve their purpose. If statistics, as a subject, is inadequate and consists of
poor methodology, we could not know the right procedure to extract from the data the
information they contain. Similarly, if our data are defective or that they are
inadequate or inaccurate, we could not reach the right conclusions even though our
subject is well developed.
A.L. Bowley has defined statistics as: (i) statis tics is the science of counting, (ii)
Statistics may rightly be called the science of averages, and (iii) statistics is the
science of measurement of social organism regarded as a whole in all its mani-

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festations. Boddington defined as: Statistics is the science of estimates and
probabilities. Further, W.I. King has defined Statistics in a wider context, the science
of Statistics is the method of judging collective, natural or social phenomena from the
results obtained by the analysis or enumeration or collection of estimates.
Seligman explored that statistics is a science that deals with the methods of collecting,
classifying, presenting, comparing and interp reting numerical data collected to throw
some light on any sphere of enquiry. Spiegal defines statistics highlighting its role in
decision-making particularly under uncertain ty, as follows: statistics is concerned
with scientific method for collecting, organising, summa rising, presenting and
analyzing data as well as drawing valid co nclusions and making reasonable decisions
on the basis of such analysis. According to Prof. Horace Secrist , Statistics is the
aggregate of facts, affected to a marked extent by multiplicity of causes, numerically
expressed, enumerated or estimated accordi ng to reasonable standards of accuracy,
collected in a systematic manner for a pre- determined purpose, and placed in relation
to each other.
From the above definitions, we can highlight the major characteristics of statistics as
follows:
(i) Statistics are the aggregates of facts . It means a single figu re is not statistics.
For example, national income of a country for a single year is not statistics but
the same for two or more years is statistics.
(ii) Statistics are affected by a number of factors. For example, sale of a product
depends on a number of factors such as its price, quality, competition, the
income of the consumers, and so on.

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(iii) Statistics must be reasonably accurate. Wrong figures, if analysed, will lead to
erroneous conclusions. Hence, it is nece ssary that conclusions must be based
on accurate figures.
(iv) Statistics must be collected in a systematic manner. If data are collected in a
haphazard manner, they will not be re liable and will lead to misleading
conclusions.
(v) Collected in a systematic manner for a pre-determined purpose
(vi) Lastly, Statistics should be placed in relation to each other. If one collects data
unrelated to each other, then such data will be confusing and will not lead to
any logical conclusions. Data should be comparable over time and over space.
1.3 TYPES OF DATA AND DATA SOURCES
Statistical data are the basic raw material of statistics. Data may relate to an activity of
our interest, a phenomenon, or a problem situation under study. They derive as a
result of the process of measuring, counting and/or ob serving. Statistical data,
therefore, refer to those aspects of a problem situation that can be measured,
quantified, counted, or classi fied. Any object subject phe nomenon, or activity that
generates data through this proc ess is termed as a variable. In other words, a variable
is one that shows a degree of variability when successive measurements are recorded.
In statistics, data are classified into two broad categories: quantitative data and
qualitative data. This classification is base d on the kind of characteristics that are
measured.
Quantitative data are those that can be quantified in definite units of measurement.
These refer to characteristics whose successive measurements yield quantifiable
observations. Depending on the nature of the variable observed for measurement,
quantitative data can be further categor ized as continuous and discrete data.

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Obviously, a variable may be a continuous variable or a discrete variable.
(i) Continuous data represent the numerical values of a continuous variable. A
continuous variable is th e one that can assume a ny value between any two
points on a line segment, thus representin g an interval of values. The values
are quite precise and close to each othe r, yet distinguishably different. All
characteristics such as weight, length, height, thickness, velocity, temperature,
tensile strength, etc., represent continuous variables. Thus, the data recorded
on these and similar other characteristic s are called continuous data. It may be
noted that a continuous va riable assumes the finest unit of measurement.
Finest in the sense that it enables m easurements to the maximum degree of
precision.
(ii) Discrete data are the values assumed by a di screte variable. A discrete
variable is the one whose outcomes are m easured in fixed numbers. Such data
are essentially count data. These are derived from a process of counting, such
as the number of items possessing or not possessing a certai n characteristic.
The number of customers visiting a departmental store everyday, the incoming
flights at an airport, and the defective items in a consignment received for sale,
are all examples of discrete data.
Qualitative data refer to qualitative characteristics of a subject or an object. A
characteristic is qualitative in nature when its observations are defined and noted in
terms of the presence or abse nce of a certain attribute in discrete numbers. These data
are further classified as nominal and rank data.
(i) Nominal data are the outcome of classification into two or more categories of
items or units comprising a sample or a population according to some quality
characteristic. Classification of stude nts according to sex (as males and

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females), of workers according to skill (as skilled, semi-skilled, and unskilled),
and of employees according to the level of education (as matriculates,
undergraduates, and post-graduates), a ll result into nominal data. Given any
such basis of classificati on, it is always possible to assign each item to a
particular class and make a summation of items belonging to each class. The
count data so obtained are called nominal data.
(ii) Rank data, on the other hand, are the resu lt of assigning ranks to specify order
in terms of the integers 1,2,3, ..., n. Ra nks may be assigned according to the
level of performance in a test. a contest, a competition, an interview, or a
show. The candidates appearing in an interview, for example, may be assigned
ranks in integers ranging from I to n, depending on their performance in the
interview. Ranks so assigned can be vi ewed as the continuous values of a
variable involving performance as the quality characteristic.
Data sources could be seen as of two type s, viz., secondary and primary. The two can
be defined as under:
(i) Secondary data: They already exist in some form: published or unpublished -
in an identifiable secondary source. They are, generally, available from
published source(s), though not necessarily in the form actually required.
(ii) Primary data: Those data which do not alread y exist in any form, and thus
have to be collected for the first time from the primary source(s). By their very
nature, these data require fresh and first-time collection covering the whole
population or a sample drawn from it.
1.4 TYPES OF STATISTICS
There are two major divisions of statistics such as descriptive statistics and inferential
statistics. The term descriptive statistics deals with collecting, summarizing, and

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simplifying data, which are otherwise quite unwieldy and voluminous. It seeks to
achieve this in a manner that meaningful conclusions can be readily drawn from the
data. Descriptive statistics may thus be s een as comprising methods of bringing out
and highlighting the latent characteristics pr esent in a set of numerical data. It not
only facilitates an understand ing of the data and systematic reporting thereof in a
manner; and also makes them amenable to further discussion, analysis, and
interpretations.
The first step in any scientific inquiry is to collect data relevant to the problem in
hand. When the inquiry relates to physical and/or biologic al sciences, data collection
is normally an integral part of the experime nt itself. In fact, the very manner in which
an experiment is designed, determines the kind of data it w ould require and/or
generate. The problem of identif ying the nature and the kind of the relevant data is
thus automatically resolved as soon as th e design of experiment is finalized. It is
possible in the case of physical sciences. In the case of social sciences, where the
required data are often collected through a questionnaire from a number of carefully
selected respondents, the problem is not that simply resolved. For one thing,
designing the questionnaire itself is a critical initial pr oblem. For another, the number
of respondents to be accessed for data colle ction and the criteria for selecting them
has their own implications and importance fo r the quality of results obtained. Further,
the data have been collected, these are assembled, organized, and presented in the
form of appropriate tables to make th em readable. Wherever needed, figures,
diagrams, charts, and graphs are also used for better presentation of the data. A useful
tabular and graphic presentation of data wi ll require that the raw data be properly
classified in accordance with the objectives of investigation and the relational analysis
to be carried out. .

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A well thought-out and sharp data classifica tion facilitates easy description of the
hidden data characteristics by means of a variety of summary measures. These include
measures of central tendency, dispersion, skewness, and kurtosis, which constitute the
essential scope of descriptive statistics. Th ese form a large part of the subject matter
of any basic textbook on the s ubject, and thus they are bein g discussed in that order
here as well.
Inferential statistics , also known as inductive statis tics, goes beyond describing a
given problem situation by means of co llecting, summarizing, and meaningfully
presenting the related data. Instead, it consis ts of methods that are used for drawing
inferences, or making broad generalizations , about a totality of observations on the
basis of knowledge about a part of that to tality. The totality of observations about
which an inference may be drawn, or a gene ralization made, is cal led a population or
a universe. The part of totality, which is obs erved for data collection and analysis to
gain knowledge about the population, is called a sample.
The desired information about a given popul ation of our interest; may also be
collected even by observing all the units comprising the population. This total
coverage is called census. Getting the desi red value for the population through census
is not always feasible and practical for various reasons. Apart from time and money
considerations making the census operations prohibitive, observing each individual
unit of the population with refe rence to any data characteri stic may at times involve
even destructive testing. In such cases, obviously, the only recourse available is to
employ the partial or incomplete information gathered through a sample for the
purpose. This is precisely what inferential st atistics does. Thus, obtaining a particular
value from the sample information and using it for drawing an inference about the
entire population underlies the subject matter of inferentia l statistics. Consider a