QUANTITATIVE
TECHNIQUES
LECTURE NOTES
, CONTENTS
Chapter Title Page No.
I INTRODUCTION TO STATISTICS 5
II MORE ABOUT THE COLLECTION OF DATA 18
III PRESENTATION OF DATA: TABLES 29
IV PICTORIAL REPRESENTATION OF STATISTICAL
DATA 1: PICTOGRAMS AND OTHER DIAGRAMS 36
V PICTORIAL REPRESENTATION OF STATISTICAL
DATA 2: GRAPHS 51
VI AVERAGES: MEASURES OF CENTRAL TENDENCY 54
VII MEASURES OF DISPERSION 68
VIII ELEMENTS OF PROBABILITY 81
, CHAPTER - I
INTRODUCTION TO STATISTICS
OBJECTIVE
Statistics is a mathematical science pertaining to the collection, analysis, interpretation or expla-
nation, and presentation of data. It is applicable to a wide variety of academic disciplines, from the
physical and social sciences to the humanities. Statistics are also used for making informed decisions –
and misused for other reasons – in all areas of business and government.
Statistical methods can be used to summarize or describe a collection of data; this is called
descriptive statistics. In addition, patterns in the data may be modeled in a way that accounts for
randomness and uncertainty in the observations, and then used to draw inferences about the process or
population being studied; this is called inferential statistics. Both descriptive and inferential statistics
comprise applied statistics. There is also a discipline called mathematical statistics, which is concerned
with the theoretical basis of the subject.
The meaning of statistics
The word statistics was originally applied to numerical facts collected for the state and was
concerned initially with population, tax revenue, government expenditure, agricultural output, and so
on. Today its meaning has been widened to include not only any set of numerical data, but also the
processes used in the collection, presentation, analysis and interpretation of this data.
Statistics can therefore denote either a collection of numerical data, which provides the raw
material for the statistician (such as population statistics or production statistics) or a body of scientific
methods, which can be applied to a study of the data. In this module we shall be largely concerned
with the procedures chiefly used in statistics. They will be considered under two heads.
Descriptive statistics
This is the term given to the techniques, which are used to organize and present the data.
These include tabulation, diagrams, graphs and certain numerical procedures, all of which have as
their objective the orderly summarization of the material in a form, which will display its distinctive
features and aid its analysis.
Inferential statistics
This branch of statistics is largely concerned with the analysis and interpretation of data
obtained from samples. It is most unlikely that, the data being used by the statistician will comprise
the entire relevant data (called the population or universe), but rather a small part of it (called a sample).
Yet on the basis of this sample, providing that it is representative of the population, inferences can be
drawn about the population as a whole. Such inferences cannot be absolutely certain because they
will be based on part of the data only, and so will have to be expressed in terms of probability. It is
5
, this aspect of statistical work which has developed so much during this century, and has led to its
expansion into many fields of human endeavour, and to an increasing appreciation of the value of
statistical techniques in ever increasing fields of activity.
The importance of statistics
No one today can afford to be without some knowledge of statistical methods. As citizens
we will be expected to contribute numerical facts to the state, the local authority, the bank, insurance
company, etc., and we should be aware of the use to which they are put and by whom. In any working
situation you will have placed before you considerable information obtained from samples, e.g. market
research polls, whose value you should be able to assess. The hospital patient, the consumer of
cigarettes, the motorist, all may have to depend for their lives on the validity of inferences drawn
from statistical investigations. The factory worker may be faced with activity sampling, or be offered
wages negotiated with reference to the index of retail prices. Statistical relationships between training
and earning prospects may be a feature of recruitment in some industries. All these topics vitally affect
your standard of living, and some understanding of statistical techniques would be useful in evaluating
them.
If statistics are important to us in our individual lives, how much more important must they
be in industry and in government, where enormous projects have to be undertaken, affecting the interests
of great companies and entire nations. Vast sums of money are allocated to projects which later prove
totally abortive, e.g. in such fields as defence, scientific research, new town development, agricultural
development, forestry, etc. Blocks of flats, now being blown up as unfit for human habitation, were
only 20 years ago being awarded architectural prizes for their innovative techniques. A more careful
statistical analysis of these projects would probably have revealed at least some of the weaknesses
inherent in them. Scarce capital could have been put to other, more profitable uses.
Criticisms of statistics
We live in a cynical age and it is fashionable to be particularly cynical about statistics. The
well-known phrase, attributed to Disraeli, ‘There are lies, damned lies, and statistics’ may no longer
generate amusement, but it is widely believed. Professional statisticians are entitled to be unhappy
about this, since they take great pains to ensure that the pronouncements they make are as accurate
as they possibly can be, given the resources that have been devoted to the exercise. Why then is
there such a public distrust of statistics? The answer lies in the difficulties that must be faced in the
collection and interpretation of data. In this introductory chapter it is advisable to mention some of
the pitfalls facing the statistician, both in the collection of data and their interpretation. You will find it
helpful in preparing your own statistical material if you critically appraise all the statistics presented to
you, and examine them for the faults listed in the following section. An appreciation of the difficulties
others have faced, or the weaknesses they have failed to overcome, will improve your own chances
of presenting reliable data and of giving considered reports about any enquiry you are asked to conduct.
6
TECHNIQUES
LECTURE NOTES
, CONTENTS
Chapter Title Page No.
I INTRODUCTION TO STATISTICS 5
II MORE ABOUT THE COLLECTION OF DATA 18
III PRESENTATION OF DATA: TABLES 29
IV PICTORIAL REPRESENTATION OF STATISTICAL
DATA 1: PICTOGRAMS AND OTHER DIAGRAMS 36
V PICTORIAL REPRESENTATION OF STATISTICAL
DATA 2: GRAPHS 51
VI AVERAGES: MEASURES OF CENTRAL TENDENCY 54
VII MEASURES OF DISPERSION 68
VIII ELEMENTS OF PROBABILITY 81
, CHAPTER - I
INTRODUCTION TO STATISTICS
OBJECTIVE
Statistics is a mathematical science pertaining to the collection, analysis, interpretation or expla-
nation, and presentation of data. It is applicable to a wide variety of academic disciplines, from the
physical and social sciences to the humanities. Statistics are also used for making informed decisions –
and misused for other reasons – in all areas of business and government.
Statistical methods can be used to summarize or describe a collection of data; this is called
descriptive statistics. In addition, patterns in the data may be modeled in a way that accounts for
randomness and uncertainty in the observations, and then used to draw inferences about the process or
population being studied; this is called inferential statistics. Both descriptive and inferential statistics
comprise applied statistics. There is also a discipline called mathematical statistics, which is concerned
with the theoretical basis of the subject.
The meaning of statistics
The word statistics was originally applied to numerical facts collected for the state and was
concerned initially with population, tax revenue, government expenditure, agricultural output, and so
on. Today its meaning has been widened to include not only any set of numerical data, but also the
processes used in the collection, presentation, analysis and interpretation of this data.
Statistics can therefore denote either a collection of numerical data, which provides the raw
material for the statistician (such as population statistics or production statistics) or a body of scientific
methods, which can be applied to a study of the data. In this module we shall be largely concerned
with the procedures chiefly used in statistics. They will be considered under two heads.
Descriptive statistics
This is the term given to the techniques, which are used to organize and present the data.
These include tabulation, diagrams, graphs and certain numerical procedures, all of which have as
their objective the orderly summarization of the material in a form, which will display its distinctive
features and aid its analysis.
Inferential statistics
This branch of statistics is largely concerned with the analysis and interpretation of data
obtained from samples. It is most unlikely that, the data being used by the statistician will comprise
the entire relevant data (called the population or universe), but rather a small part of it (called a sample).
Yet on the basis of this sample, providing that it is representative of the population, inferences can be
drawn about the population as a whole. Such inferences cannot be absolutely certain because they
will be based on part of the data only, and so will have to be expressed in terms of probability. It is
5
, this aspect of statistical work which has developed so much during this century, and has led to its
expansion into many fields of human endeavour, and to an increasing appreciation of the value of
statistical techniques in ever increasing fields of activity.
The importance of statistics
No one today can afford to be without some knowledge of statistical methods. As citizens
we will be expected to contribute numerical facts to the state, the local authority, the bank, insurance
company, etc., and we should be aware of the use to which they are put and by whom. In any working
situation you will have placed before you considerable information obtained from samples, e.g. market
research polls, whose value you should be able to assess. The hospital patient, the consumer of
cigarettes, the motorist, all may have to depend for their lives on the validity of inferences drawn
from statistical investigations. The factory worker may be faced with activity sampling, or be offered
wages negotiated with reference to the index of retail prices. Statistical relationships between training
and earning prospects may be a feature of recruitment in some industries. All these topics vitally affect
your standard of living, and some understanding of statistical techniques would be useful in evaluating
them.
If statistics are important to us in our individual lives, how much more important must they
be in industry and in government, where enormous projects have to be undertaken, affecting the interests
of great companies and entire nations. Vast sums of money are allocated to projects which later prove
totally abortive, e.g. in such fields as defence, scientific research, new town development, agricultural
development, forestry, etc. Blocks of flats, now being blown up as unfit for human habitation, were
only 20 years ago being awarded architectural prizes for their innovative techniques. A more careful
statistical analysis of these projects would probably have revealed at least some of the weaknesses
inherent in them. Scarce capital could have been put to other, more profitable uses.
Criticisms of statistics
We live in a cynical age and it is fashionable to be particularly cynical about statistics. The
well-known phrase, attributed to Disraeli, ‘There are lies, damned lies, and statistics’ may no longer
generate amusement, but it is widely believed. Professional statisticians are entitled to be unhappy
about this, since they take great pains to ensure that the pronouncements they make are as accurate
as they possibly can be, given the resources that have been devoted to the exercise. Why then is
there such a public distrust of statistics? The answer lies in the difficulties that must be faced in the
collection and interpretation of data. In this introductory chapter it is advisable to mention some of
the pitfalls facing the statistician, both in the collection of data and their interpretation. You will find it
helpful in preparing your own statistical material if you critically appraise all the statistics presented to
you, and examine them for the faults listed in the following section. An appreciation of the difficulties
others have faced, or the weaknesses they have failed to overcome, will improve your own chances
of presenting reliable data and of giving considered reports about any enquiry you are asked to conduct.
6
