ICAI Notes- Statistical Representation of data | Quantitative Aptitude for CA Foundation PDF Download

 Page 1


UNIT 1: STATISTICAL DESCRITPION 
OF DATA
After reading this chapter, students will be able to understand:
? Have a broad overview of the subject of statistics and application thereof.
? Know about  data collection technique including the distinction of primary and
secondary data.
? Know how to present data in textual and tabular format including the technique of
creating frequency distribution and working out cumulative frequency.
? Know how to present data graphically using histogram, frequency polygon and pie
chart.
13
CHAPTER
Collection
of Data
Present Data
Graphically
Primary
Data
Secondary
Data
Applications of Statistics
Broad overview of the subject of statistics
Present data in Textual
and Tabular form
Frequency
Distribution
Cumulative
Frequency
Line Chart or
Histogram
Pie Chart
Frequency
Polygon
© The Institute of Chartered Accountants of India
Page 2


UNIT 1: STATISTICAL DESCRITPION 
OF DATA
After reading this chapter, students will be able to understand:
? Have a broad overview of the subject of statistics and application thereof.
? Know about  data collection technique including the distinction of primary and
secondary data.
? Know how to present data in textual and tabular format including the technique of
creating frequency distribution and working out cumulative frequency.
? Know how to present data graphically using histogram, frequency polygon and pie
chart.
13
CHAPTER
Collection
of Data
Present Data
Graphically
Primary
Data
Secondary
Data
Applications of Statistics
Broad overview of the subject of statistics
Present data in Textual
and Tabular form
Frequency
Distribution
Cumulative
Frequency
Line Chart or
Histogram
Pie Chart
Frequency
Polygon
© The Institute of Chartered Accountants of India
STATISTICS
13.2
The modern development in the field of not only Management, Commerce, Economics, Social
Sciences, Mathematics and so on but also in our life like public services, defence, banking, insurance
sector, tourism and hospitality, police and military etc. are dependent on a particular subject
known as statistics. Statistics does play a vital role in enriching a specific domain by collecting
data in that field, analysing the data by applying various statistical techniques and finally making
statistical inferences about the domain. In the present world, statistics has almost a universal
application. Our government applies statistics to make the economic planning in an effective
and a pragmatic way. The businessman plan and expand their horizons of business on the basis
of the analysis of the feedback data. The political parties try to impress the general public by
presenting the statistics of their performances and accomplishments. Most of the research scholars
of today also apply statistics to present their research papers in an authoritative manner. Thus
the list of people using statistics goes on and on and on. Due to these factors, it is necessary to
study the subject of statistics in an objective manner.
History of Statistics
Going through the history of ancient period and also that of medieval period, we do find the mention
of statistics in many countries. However, there remains a question mark about the origin of the
word ‘statistics’. One view is that statistics is originated from the Latin word ‘status’. According to
another school of thought, it had its origin in the Italian word ‘statista’. Some scholars believe that
the German word ‘statistik’ was later changed to statistics and another suggestion is that the French
word ‘statistique’ was made as statistics with the passage of time.
In those days, statistics was analogous to state or, to be more precise, the data that are collected
and maintained for the welfare of the people belonging to the state. We are thankful to Kautilya
who had kept a record of births and deaths as well as some other precious records in his famous
book ‘Arthashastra’ during Chandragupta’s reign in the fourth century B.C. During the reign of
Akbar in the sixteenth century A.D. We find statistical records on agriculture in Ain-i-Akbari
written by Abu Fazl. Referring to Egypt, the first census was conducted by the Pharaoh during
300 B.C. to 2000 B.C.
Definition of Statistics
We may define statistics either in a singular sense or in a plural sense Statistics, when used as a
plural noun, may be defined as data qualitative as well as quantitative, that are collected, usually
with a view of having statistical analysis.
However, statistics, when used as a singular noun, may be defined, as the scientific method that
is employed for collecting, analysing and presenting data, leading finally to drawing statistical
inferences about some important characteristics it means it is ‘science of counting’ or ‘science of
averages’.
Application of statistics
Among various applications of statistics, let us confine our discussions to the fields of Economics,
Business Management and Commerce and Industry.
Economics
Modern developments in Economics have the roots in statistics. In fact, Economics and Statistics
are closely associated. Time Series Analysis, Index Numbers, Demand Analysis etc. are some
© The Institute of Chartered Accountants of India
Page 3


UNIT 1: STATISTICAL DESCRITPION 
OF DATA
After reading this chapter, students will be able to understand:
? Have a broad overview of the subject of statistics and application thereof.
? Know about  data collection technique including the distinction of primary and
secondary data.
? Know how to present data in textual and tabular format including the technique of
creating frequency distribution and working out cumulative frequency.
? Know how to present data graphically using histogram, frequency polygon and pie
chart.
13
CHAPTER
Collection
of Data
Present Data
Graphically
Primary
Data
Secondary
Data
Applications of Statistics
Broad overview of the subject of statistics
Present data in Textual
and Tabular form
Frequency
Distribution
Cumulative
Frequency
Line Chart or
Histogram
Pie Chart
Frequency
Polygon
© The Institute of Chartered Accountants of India
STATISTICS
13.2
The modern development in the field of not only Management, Commerce, Economics, Social
Sciences, Mathematics and so on but also in our life like public services, defence, banking, insurance
sector, tourism and hospitality, police and military etc. are dependent on a particular subject
known as statistics. Statistics does play a vital role in enriching a specific domain by collecting
data in that field, analysing the data by applying various statistical techniques and finally making
statistical inferences about the domain. In the present world, statistics has almost a universal
application. Our government applies statistics to make the economic planning in an effective
and a pragmatic way. The businessman plan and expand their horizons of business on the basis
of the analysis of the feedback data. The political parties try to impress the general public by
presenting the statistics of their performances and accomplishments. Most of the research scholars
of today also apply statistics to present their research papers in an authoritative manner. Thus
the list of people using statistics goes on and on and on. Due to these factors, it is necessary to
study the subject of statistics in an objective manner.
History of Statistics
Going through the history of ancient period and also that of medieval period, we do find the mention
of statistics in many countries. However, there remains a question mark about the origin of the
word ‘statistics’. One view is that statistics is originated from the Latin word ‘status’. According to
another school of thought, it had its origin in the Italian word ‘statista’. Some scholars believe that
the German word ‘statistik’ was later changed to statistics and another suggestion is that the French
word ‘statistique’ was made as statistics with the passage of time.
In those days, statistics was analogous to state or, to be more precise, the data that are collected
and maintained for the welfare of the people belonging to the state. We are thankful to Kautilya
who had kept a record of births and deaths as well as some other precious records in his famous
book ‘Arthashastra’ during Chandragupta’s reign in the fourth century B.C. During the reign of
Akbar in the sixteenth century A.D. We find statistical records on agriculture in Ain-i-Akbari
written by Abu Fazl. Referring to Egypt, the first census was conducted by the Pharaoh during
300 B.C. to 2000 B.C.
Definition of Statistics
We may define statistics either in a singular sense or in a plural sense Statistics, when used as a
plural noun, may be defined as data qualitative as well as quantitative, that are collected, usually
with a view of having statistical analysis.
However, statistics, when used as a singular noun, may be defined, as the scientific method that
is employed for collecting, analysing and presenting data, leading finally to drawing statistical
inferences about some important characteristics it means it is ‘science of counting’ or ‘science of
averages’.
Application of statistics
Among various applications of statistics, let us confine our discussions to the fields of Economics,
Business Management and Commerce and Industry.
Economics
Modern developments in Economics have the roots in statistics. In fact, Economics and Statistics
are closely associated. Time Series Analysis, Index Numbers, Demand Analysis etc. are some
© The Institute of Chartered Accountants of India
13.3 STATISTICAL DESCRIPTION OF DATA
overlapping areas of Economics and Statistics. In this connection, we may also mention
Econometrics – a branch of Economics that interact with statistics in a very positive way.
Conducting socio-economic surveys and analysing the data derived from it are made with the
help of different statistical methods. Regression analysis, one of the numerous applications of
statistics, plays a key role in Economics for making future projection of demand of goods, sales,
prices, quantities etc. which are all ingredients of Economic planning.
Business Management
Gone are the days when the managers used to make decisions on the basis of hunches, intuition or
trials and errors. Now a days, because of the never-ending complexity in the business and industry
environment, most of the decision making processes rely upon different quantitative techniques which
could be described as a combination of statistical methods and operations research techniques. So far
as statistics is concerned, inferences about the universe from the knowledge of a part of it, known as
sample, plays an important role in the development of certain criteria. Statistical decision theory is
another component of statistics that focuses on the analysis of complicated business strategies with a
list of alternatives – their merits as well as demerits.
Statistics in Commerce and Industry
In this age of cut-throat competition, like the modern managers, the industrialists and the
businessmen are expanding their horizons of industries and businesses with the help of statistical
procedures. Data on previous sales, raw materials, wages and salaries, products of identical
nature of other factories etc are collected, analysed and experts are consulted in order to maximise
profits. Measures of central tendency and dispersion, correlation and regression analysis, time
series analysis, index numbers, sampling, statistical quality control are some of the statistical
methods employed in commerce and industry.
Limitations of Statistics
Before applying statistical methods, we must be aware of the following limitations:
I Statistics deals with the aggregates. An individual, to a statistician has no significance except
the fact that it is a part of the aggregate.
II Statistics is concerned with quantitative data. However, qualitative data also can be converted
to quantitative data by providing a numerical description to the corresponding qualitative
data.
III Future projections of sales, production, price and quantity etc. are possible under a specific
set of conditions. If any of these conditions is violated, projections are likely to be inaccurate.
IV The theory of statistical inferences is built upon random sampling. If the rules for random
sampling is not strictly adhered to, the conclusion drawn on the basis of these
unrepresentative samples would be erroneous. In other words, the experts should be
consulted before deciding the sampling scheme.
We may define ‘data’ as quantitative information about some particular characteristic(s) under
consideration. Although a distinction can be made between a qualitative characteristic and a
quantitative characteristic but so far as the statistical analysis of the characteristic is concerned,
© The Institute of Chartered Accountants of India
Page 4


UNIT 1: STATISTICAL DESCRITPION 
OF DATA
After reading this chapter, students will be able to understand:
? Have a broad overview of the subject of statistics and application thereof.
? Know about  data collection technique including the distinction of primary and
secondary data.
? Know how to present data in textual and tabular format including the technique of
creating frequency distribution and working out cumulative frequency.
? Know how to present data graphically using histogram, frequency polygon and pie
chart.
13
CHAPTER
Collection
of Data
Present Data
Graphically
Primary
Data
Secondary
Data
Applications of Statistics
Broad overview of the subject of statistics
Present data in Textual
and Tabular form
Frequency
Distribution
Cumulative
Frequency
Line Chart or
Histogram
Pie Chart
Frequency
Polygon
© The Institute of Chartered Accountants of India
STATISTICS
13.2
The modern development in the field of not only Management, Commerce, Economics, Social
Sciences, Mathematics and so on but also in our life like public services, defence, banking, insurance
sector, tourism and hospitality, police and military etc. are dependent on a particular subject
known as statistics. Statistics does play a vital role in enriching a specific domain by collecting
data in that field, analysing the data by applying various statistical techniques and finally making
statistical inferences about the domain. In the present world, statistics has almost a universal
application. Our government applies statistics to make the economic planning in an effective
and a pragmatic way. The businessman plan and expand their horizons of business on the basis
of the analysis of the feedback data. The political parties try to impress the general public by
presenting the statistics of their performances and accomplishments. Most of the research scholars
of today also apply statistics to present their research papers in an authoritative manner. Thus
the list of people using statistics goes on and on and on. Due to these factors, it is necessary to
study the subject of statistics in an objective manner.
History of Statistics
Going through the history of ancient period and also that of medieval period, we do find the mention
of statistics in many countries. However, there remains a question mark about the origin of the
word ‘statistics’. One view is that statistics is originated from the Latin word ‘status’. According to
another school of thought, it had its origin in the Italian word ‘statista’. Some scholars believe that
the German word ‘statistik’ was later changed to statistics and another suggestion is that the French
word ‘statistique’ was made as statistics with the passage of time.
In those days, statistics was analogous to state or, to be more precise, the data that are collected
and maintained for the welfare of the people belonging to the state. We are thankful to Kautilya
who had kept a record of births and deaths as well as some other precious records in his famous
book ‘Arthashastra’ during Chandragupta’s reign in the fourth century B.C. During the reign of
Akbar in the sixteenth century A.D. We find statistical records on agriculture in Ain-i-Akbari
written by Abu Fazl. Referring to Egypt, the first census was conducted by the Pharaoh during
300 B.C. to 2000 B.C.
Definition of Statistics
We may define statistics either in a singular sense or in a plural sense Statistics, when used as a
plural noun, may be defined as data qualitative as well as quantitative, that are collected, usually
with a view of having statistical analysis.
However, statistics, when used as a singular noun, may be defined, as the scientific method that
is employed for collecting, analysing and presenting data, leading finally to drawing statistical
inferences about some important characteristics it means it is ‘science of counting’ or ‘science of
averages’.
Application of statistics
Among various applications of statistics, let us confine our discussions to the fields of Economics,
Business Management and Commerce and Industry.
Economics
Modern developments in Economics have the roots in statistics. In fact, Economics and Statistics
are closely associated. Time Series Analysis, Index Numbers, Demand Analysis etc. are some
© The Institute of Chartered Accountants of India
13.3 STATISTICAL DESCRIPTION OF DATA
overlapping areas of Economics and Statistics. In this connection, we may also mention
Econometrics – a branch of Economics that interact with statistics in a very positive way.
Conducting socio-economic surveys and analysing the data derived from it are made with the
help of different statistical methods. Regression analysis, one of the numerous applications of
statistics, plays a key role in Economics for making future projection of demand of goods, sales,
prices, quantities etc. which are all ingredients of Economic planning.
Business Management
Gone are the days when the managers used to make decisions on the basis of hunches, intuition or
trials and errors. Now a days, because of the never-ending complexity in the business and industry
environment, most of the decision making processes rely upon different quantitative techniques which
could be described as a combination of statistical methods and operations research techniques. So far
as statistics is concerned, inferences about the universe from the knowledge of a part of it, known as
sample, plays an important role in the development of certain criteria. Statistical decision theory is
another component of statistics that focuses on the analysis of complicated business strategies with a
list of alternatives – their merits as well as demerits.
Statistics in Commerce and Industry
In this age of cut-throat competition, like the modern managers, the industrialists and the
businessmen are expanding their horizons of industries and businesses with the help of statistical
procedures. Data on previous sales, raw materials, wages and salaries, products of identical
nature of other factories etc are collected, analysed and experts are consulted in order to maximise
profits. Measures of central tendency and dispersion, correlation and regression analysis, time
series analysis, index numbers, sampling, statistical quality control are some of the statistical
methods employed in commerce and industry.
Limitations of Statistics
Before applying statistical methods, we must be aware of the following limitations:
I Statistics deals with the aggregates. An individual, to a statistician has no significance except
the fact that it is a part of the aggregate.
II Statistics is concerned with quantitative data. However, qualitative data also can be converted
to quantitative data by providing a numerical description to the corresponding qualitative
data.
III Future projections of sales, production, price and quantity etc. are possible under a specific
set of conditions. If any of these conditions is violated, projections are likely to be inaccurate.
IV The theory of statistical inferences is built upon random sampling. If the rules for random
sampling is not strictly adhered to, the conclusion drawn on the basis of these
unrepresentative samples would be erroneous. In other words, the experts should be
consulted before deciding the sampling scheme.
We may define ‘data’ as quantitative information about some particular characteristic(s) under
consideration. Although a distinction can be made between a qualitative characteristic and a
quantitative characteristic but so far as the statistical analysis of the characteristic is concerned,
© The Institute of Chartered Accountants of India
STATISTICS
13.4
we need to convert qualitative information to quantitative information by providing a numeric
descriptions to the given characteristic. In this connection, we may note that a quantitative
characteristic is known as a variable or in other words, a variable is a measurable quantity. Again,
a variable may be either discrete or continuous. When a variable assumes a finite or a countably
infinite number of isolated values, it is known as a discrete variable. Examples of discrete variables
may be found in the number of petals in a flower, the number of misprints a book contains, the
number of road accidents in a particular locality and so on. A variable, on the other hand, is
known to be continuous if it can assume any value from a given interval. Examples of continuous
variables may be provided by height, weight, sale, profit and so on. Finally, a qualitative
characteristic is known as an attribute. The gender of a baby, the nationality of a person, the
colour of a flower etc. are examples of attributes.
We can broadly classify data as
(a) Primary;
(b) Secondary.
Collection of data plays the very important role for any statistical analysis. The data which are
collected for the first time by an investigator or agency are known as primary data whereas the
data are known to be secondary if the data, as being already collected, are used by a different
person or agency. Thus, if Prof. Das collects the data on the height of every student in his class,
then these would be primary data for him. If, however, another person, say, Professor Bhargava
uses the data, as collected by Prof. Das, for finding the average height of the students belonging
to that class, then the data would be secondary for Prof. Bhargava.
Collection of Primary Data
The following methods are employed for the collection of primary data:
(i) Interview method;
(ii) Mailed questionnaire method;
(iii) Observation method;
(iv) Questionnaires filled and sent by enumerators.
Interview method again could be divided into (a) Personal Interview method, (b) Indirect
Interview method and (c) Telephone Interview method.
In personal interview method, the investigator meets the respondents directly and collects the
required information then and there from them. In case of a natural calamity like a super cyclone
or an earthquake or an epidemic like plague, we may collect the necessary data much more
quickly and accurately by applying this method.
If there are some practical problems in reaching the respondents directly, as in the case of a rail
accident, then we may take recourse for conducting Indirect Interview where the investigator
collects the necessary information from the persons associated with the problems.
Telephone interview method is a quick and rather non-expensive way to collect the primary data
where the relevant information can be gathered by the researcher himself by contacting the
interviewee over the phone. The first two methods, though more accurate, are inapplicable for
covering a large area whereas the telephone interview, though less consistent, has a wide coverage.
© The Institute of Chartered Accountants of India
Page 5


UNIT 1: STATISTICAL DESCRITPION 
OF DATA
After reading this chapter, students will be able to understand:
? Have a broad overview of the subject of statistics and application thereof.
? Know about  data collection technique including the distinction of primary and
secondary data.
? Know how to present data in textual and tabular format including the technique of
creating frequency distribution and working out cumulative frequency.
? Know how to present data graphically using histogram, frequency polygon and pie
chart.
13
CHAPTER
Collection
of Data
Present Data
Graphically
Primary
Data
Secondary
Data
Applications of Statistics
Broad overview of the subject of statistics
Present data in Textual
and Tabular form
Frequency
Distribution
Cumulative
Frequency
Line Chart or
Histogram
Pie Chart
Frequency
Polygon
© The Institute of Chartered Accountants of India
STATISTICS
13.2
The modern development in the field of not only Management, Commerce, Economics, Social
Sciences, Mathematics and so on but also in our life like public services, defence, banking, insurance
sector, tourism and hospitality, police and military etc. are dependent on a particular subject
known as statistics. Statistics does play a vital role in enriching a specific domain by collecting
data in that field, analysing the data by applying various statistical techniques and finally making
statistical inferences about the domain. In the present world, statistics has almost a universal
application. Our government applies statistics to make the economic planning in an effective
and a pragmatic way. The businessman plan and expand their horizons of business on the basis
of the analysis of the feedback data. The political parties try to impress the general public by
presenting the statistics of their performances and accomplishments. Most of the research scholars
of today also apply statistics to present their research papers in an authoritative manner. Thus
the list of people using statistics goes on and on and on. Due to these factors, it is necessary to
study the subject of statistics in an objective manner.
History of Statistics
Going through the history of ancient period and also that of medieval period, we do find the mention
of statistics in many countries. However, there remains a question mark about the origin of the
word ‘statistics’. One view is that statistics is originated from the Latin word ‘status’. According to
another school of thought, it had its origin in the Italian word ‘statista’. Some scholars believe that
the German word ‘statistik’ was later changed to statistics and another suggestion is that the French
word ‘statistique’ was made as statistics with the passage of time.
In those days, statistics was analogous to state or, to be more precise, the data that are collected
and maintained for the welfare of the people belonging to the state. We are thankful to Kautilya
who had kept a record of births and deaths as well as some other precious records in his famous
book ‘Arthashastra’ during Chandragupta’s reign in the fourth century B.C. During the reign of
Akbar in the sixteenth century A.D. We find statistical records on agriculture in Ain-i-Akbari
written by Abu Fazl. Referring to Egypt, the first census was conducted by the Pharaoh during
300 B.C. to 2000 B.C.
Definition of Statistics
We may define statistics either in a singular sense or in a plural sense Statistics, when used as a
plural noun, may be defined as data qualitative as well as quantitative, that are collected, usually
with a view of having statistical analysis.
However, statistics, when used as a singular noun, may be defined, as the scientific method that
is employed for collecting, analysing and presenting data, leading finally to drawing statistical
inferences about some important characteristics it means it is ‘science of counting’ or ‘science of
averages’.
Application of statistics
Among various applications of statistics, let us confine our discussions to the fields of Economics,
Business Management and Commerce and Industry.
Economics
Modern developments in Economics have the roots in statistics. In fact, Economics and Statistics
are closely associated. Time Series Analysis, Index Numbers, Demand Analysis etc. are some
© The Institute of Chartered Accountants of India
13.3 STATISTICAL DESCRIPTION OF DATA
overlapping areas of Economics and Statistics. In this connection, we may also mention
Econometrics – a branch of Economics that interact with statistics in a very positive way.
Conducting socio-economic surveys and analysing the data derived from it are made with the
help of different statistical methods. Regression analysis, one of the numerous applications of
statistics, plays a key role in Economics for making future projection of demand of goods, sales,
prices, quantities etc. which are all ingredients of Economic planning.
Business Management
Gone are the days when the managers used to make decisions on the basis of hunches, intuition or
trials and errors. Now a days, because of the never-ending complexity in the business and industry
environment, most of the decision making processes rely upon different quantitative techniques which
could be described as a combination of statistical methods and operations research techniques. So far
as statistics is concerned, inferences about the universe from the knowledge of a part of it, known as
sample, plays an important role in the development of certain criteria. Statistical decision theory is
another component of statistics that focuses on the analysis of complicated business strategies with a
list of alternatives – their merits as well as demerits.
Statistics in Commerce and Industry
In this age of cut-throat competition, like the modern managers, the industrialists and the
businessmen are expanding their horizons of industries and businesses with the help of statistical
procedures. Data on previous sales, raw materials, wages and salaries, products of identical
nature of other factories etc are collected, analysed and experts are consulted in order to maximise
profits. Measures of central tendency and dispersion, correlation and regression analysis, time
series analysis, index numbers, sampling, statistical quality control are some of the statistical
methods employed in commerce and industry.
Limitations of Statistics
Before applying statistical methods, we must be aware of the following limitations:
I Statistics deals with the aggregates. An individual, to a statistician has no significance except
the fact that it is a part of the aggregate.
II Statistics is concerned with quantitative data. However, qualitative data also can be converted
to quantitative data by providing a numerical description to the corresponding qualitative
data.
III Future projections of sales, production, price and quantity etc. are possible under a specific
set of conditions. If any of these conditions is violated, projections are likely to be inaccurate.
IV The theory of statistical inferences is built upon random sampling. If the rules for random
sampling is not strictly adhered to, the conclusion drawn on the basis of these
unrepresentative samples would be erroneous. In other words, the experts should be
consulted before deciding the sampling scheme.
We may define ‘data’ as quantitative information about some particular characteristic(s) under
consideration. Although a distinction can be made between a qualitative characteristic and a
quantitative characteristic but so far as the statistical analysis of the characteristic is concerned,
© The Institute of Chartered Accountants of India
STATISTICS
13.4
we need to convert qualitative information to quantitative information by providing a numeric
descriptions to the given characteristic. In this connection, we may note that a quantitative
characteristic is known as a variable or in other words, a variable is a measurable quantity. Again,
a variable may be either discrete or continuous. When a variable assumes a finite or a countably
infinite number of isolated values, it is known as a discrete variable. Examples of discrete variables
may be found in the number of petals in a flower, the number of misprints a book contains, the
number of road accidents in a particular locality and so on. A variable, on the other hand, is
known to be continuous if it can assume any value from a given interval. Examples of continuous
variables may be provided by height, weight, sale, profit and so on. Finally, a qualitative
characteristic is known as an attribute. The gender of a baby, the nationality of a person, the
colour of a flower etc. are examples of attributes.
We can broadly classify data as
(a) Primary;
(b) Secondary.
Collection of data plays the very important role for any statistical analysis. The data which are
collected for the first time by an investigator or agency are known as primary data whereas the
data are known to be secondary if the data, as being already collected, are used by a different
person or agency. Thus, if Prof. Das collects the data on the height of every student in his class,
then these would be primary data for him. If, however, another person, say, Professor Bhargava
uses the data, as collected by Prof. Das, for finding the average height of the students belonging
to that class, then the data would be secondary for Prof. Bhargava.
Collection of Primary Data
The following methods are employed for the collection of primary data:
(i) Interview method;
(ii) Mailed questionnaire method;
(iii) Observation method;
(iv) Questionnaires filled and sent by enumerators.
Interview method again could be divided into (a) Personal Interview method, (b) Indirect
Interview method and (c) Telephone Interview method.
In personal interview method, the investigator meets the respondents directly and collects the
required information then and there from them. In case of a natural calamity like a super cyclone
or an earthquake or an epidemic like plague, we may collect the necessary data much more
quickly and accurately by applying this method.
If there are some practical problems in reaching the respondents directly, as in the case of a rail
accident, then we may take recourse for conducting Indirect Interview where the investigator
collects the necessary information from the persons associated with the problems.
Telephone interview method is a quick and rather non-expensive way to collect the primary data
where the relevant information can be gathered by the researcher himself by contacting the
interviewee over the phone. The first two methods, though more accurate, are inapplicable for
covering a large area whereas the telephone interview, though less consistent, has a wide coverage.
© The Institute of Chartered Accountants of India
13.5 STATISTICAL DESCRIPTION OF DATA
The nuculer of non-responses is maximum for this third method of data collection.
Mailed questionnaire method comprises of framing a well-drafted and soundly-sequenced
questionnaire covering all the important aspects of the problem under consideration and sending
them to the respondents with pre-paid stamp after providing all the necessary guidelines for
filling up the questionnaire. Although a wide area can be covered using the mailed questionnaire
method, the amount of non-responses is likely to be maximum in this method.
In observation nuculer, data are collected, as in the case of obtaining the data on the height and
weight of a group of students, by direct observation or using instrument. Although this is likely to be
the best method for data collection, it is time consuming, laborious and covers only a small area.
Questionnaire form of data collection is used for larger enquiries from the persons who are
surveyed. Enumerators collects information directly by interviewing the persons having
information : Question are explained and hence data is collected.
Sources of Secondary Data
There are many sources of getting secondary data. Some important sources are listed below:
(a) International sources like WHO, ILO, IMF, World Bank etc.
(b) Government sources like Statistical Abstract by CSO, Indian Agricultural Statistics by the
Ministry of Food and Agriculture and so on.
(c) Private and quasi-government sources like ISI, ICAR, NCERT etc.
(d) Unpublished sources of various research institutes, researchers etc.
Scrutiny of Data
Since the statistical analyses are made only on the basis of data, it is necessary to check whether
the data under consideration are accurate as well as consistence. No hard and fast rules can be
recommended for the scrutiny of data. One must apply his intelligence, patience and experience
while scrutinising the given information.
Errors in data may creep in while writing or copying the answer on the part of the enumerator. A
keen observer can easily detect that type of error. Again, there may be two or more series of
figures which are in some way or other related to each other. If the data for all the series are
provided, they may be checked for internal consistency. As an example, if the data for population,
area and density for some places are given, then we may verify whether they are internally
consistent by examining whether the relation
  holds.
A good statistician can also detect whether the returns submitted by some enumerators are exactly
of the same type thereby implying the lack of seriousness on the part of the enumerators. The bias
of the enumerator also may be reflected by the returns submitted by him. This type of error can be
rectified by asking the enumerator(s) to collect the data for the disputed cases once again.
Density =
Area 
Population
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