Introduction to Statistics
UNIT 1 INTRODUCTION TO STATISTICS
Structure
1.0 Introduction
1.1 Objectives
1.2 Meaning of Statistics
1.2.1 Statistics in Singular Sense
1.2.2 Statistics in Plural Sense
1.2.3 Definition of Statistics
1.3 Types of Statistics
1.3.1 On the Basis of Function
1.3.2 On the Basis of Distribution of Data
1.4 Scope and Use of Statistics
1.5 Limitations of Statistics
1.6 Distrust and Misuse of Statistics
1.7 Let Us Sum Up
1.8 Unit End Questions
1.9 Glossary
1.10 Suggested Readings
1.0 INTRODUCTION
The word statistics has different meaning to different persons. Knowledge of
statistics is applicable in day to day life in different ways. In daily life it means
general calculation of items, in railway statistics means the number of trains
operating, number of passenger’s freight etc. and so on. Thus statistics is used by
people to take decision about the problems on the basis of different type of
quantitative and qualitative information available to them.
However, in behavioural sciences, the word ‘statistics’ means something different
from the common concern of it. Prime function of statistic is to draw statistical
inference about population on the basis of available quantitative information.
Overall, statistical methods deal with reduction of data to convenient descriptive
terms and drawing some inferences from them. This unit focuses on the above
aspects of statistics.
1.1 OBJECTIVES
After going through this unit, you will be able to:
Define the term statistics;
Explain the status of statistics;
Describe the nature of statistics;
State basic concepts used in statistics; and
Analyse the uses and misuses of statistics.
5
,Introduction to Statistics
1.2 MEANING OF STATISTICS
The word statistics has been derived from Latin word ‘status’ or Italian ‘Statista’
meaning statesman. Professor Gott Fried Achenwall used it in the 18th century.
During early period, these words were used for political state of the region. The
word ‘Statista’ was used to keep the records of census or data related to wealth
of a state. Gradually, its meaning and usage extended and thereonwards its nature
also changed.
The word statistics is used to convey different meanings in singular and plural
sense. Therefore it can be defined in two different ways.
1.2.1 Statistics in Singular Sense
In singular sense, ‘Statistics’ refers to what is called statistical methods. It deals
with the collection of data, their classification, analysis and interpretations of
statistical data. Therefore, it is described as a branch of science which deals with
classification, tabulation and analysis of numerical facts and make decision as
well. Every statistical inquiry should pass through these stages.
1.2.2 Statistics in Plural Sense
‘Statistics’ used in plural sense means that quantitative information is available
called ‘data’. For example, information on population or demographic features,
enrolment of students in Psychology programmes of IGNOU, and the like.
According to Websters “Statistics are the classified facts representing the
conditions of the people in a State specifically those facts which can be stated in
number or in tables of number or classified arrangement”.
Horace Secrist describes statistics in plural sense as follows : “ By Statistics we
mean aggregates 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.” Thus Secrist’s definition highlights following
features of statistics:
i) Statistics are aggregate of facts: Single or unrelated items are not considered
as statistics.
ii) Statistics are affected by multiplicity of causes: In statistics the collected
information are greatly influenced by a number of factors and forces working
together.
iii) Statistics are numerical facts: Only numerical data constitute statistics.
iv) Statistics are enumerated or estimated with a reasonable standard of
accuracy: While enumerating or estimating data, a reasonable degree of
accuracy must be achieved.
v) Statistics are collected in a systematic manner: Data should be collected by
proper planning by utilising tool/s developed by trained personnel.
vi) Statistics are collected for a predetermined purpose : It is necessary to define
the objective of enquiry, before collecting the statistics. The objective of
enquiry must be specific and well defined.
6
,vii) Statistics should be comparable: Only comparable data will have some Introduction to Statistics
meaning. For statistical analysis, the data should be comparable with respect
to time, place group, etc.
Thus, it may be stated that “ All statistics are numerical statements of facts but
all numerical statements of facts are not necessarily statistics ”.
1.2.3 Definition of Statistics
In this unit emphasis is on the term statistics as a branch of science. It deals with
classification, tabulation and analysis of numerical facts. Different statistician
defined this aspect of statistics in different ways. For example.
A. L. Bowley gave several definitions of Statistics:
i) “Statistics may be called the science of counting” . This definition emphasises
enumeration aspect only.
ii) In another definition he describes it as “ Statistics may rightly be called the
science of average”.
iii) At another place Statistics is defined as, “Statistics is the science of
measurement of social organism regarded as a whole in all its manifestations”.
All three definitions given by Bowely seem to be inadequate because these do
not include all aspects of statistics.
According to Selligman “Statistics is the science which deals with the methods
of collecting, classifying, presenting , comparing and interpreting numerical data
collected to throw some light on any sphere of enquiry”.
Croxton and Cowden defined “statistics as the collection , presentation, analysis
,and interpretation of numerical data”.
Among all the definitions , the one given by Croxton and Cowden is considered
to be most appropriate as it covers all aspects and field of statistics.
These aspects are given below:
Collection of Data : Once the nature of study is decided , it becomes essential to
collect information in form of data about the issues of the study. Therefore, the
collection of data is the first basic step. Data may be collected either from primary
source or secondary or from both the sources depending upon the objective/s of
the investigation
Classification and Presentation : Once data are collected , researcher has to
arrange them in a format from which they would be able to draw some
conclusions. The arrangement of data in groups according to some similarities is
known as classification.
Tabulation is the process of presenting the classified data in the form of table. A
tabular presentation of data becomes more intelligible and fit for further statistical
analysis. Classified and Tabulated data can be presented in diagrams and graphs
to facilitate the understanding of various trends as well as the process of
comparison of various situations.
Analysis of Data : It is the most important step in any statistical enquiry . Statistical
analysis is carried out to process the observed data and transform it in such a
manner as to make it suitable for decision making. 7
, Introduction to Statistics Interpretation of Data : After analysing the data, researcher gets information
partly or wholly about the population. Explanation of such information is more
useful in real life. The quality of interpretation depends more and more on the
experience and insight of the researcher.
Self Assessment Questions
1) Complete the following statements
i) The word statistics has been derived from Latin word .....................
ii) Statistics in plural means ................................................................
iii) Statistics in singular means .............................................................
iv) The first step in statistics is .............................................................
v) The last step in statistics is .............................................................
2) Tick () the correct answer
Statistical data are:
i) Aggregates of facts
ii) Unsystematic data
iii) Single or isolated facts or figure
iv) None of these
3) Which one of the following statement is true for statistics in singular
sense?
i) Statistics are aggregate of facts.
ii) Statistics are numerical facts.
iii) Statistics are collected in a systematic manner.
iv) Statistics may be called the science of counting.
1.3 TYPES OF STATISTICS
After knowing the concept and definition of statistics, let us know the various
types of statistics.
Though various bases have been adopted to classify statistics, following are the
two major ways of classifying statistics: (i) on the basis of function and (ii) on
the basis of distribution.
1.3.1 On the Basis of Functions
As statistics has some particular procedures to deal with its subject matter or
data, three types of statistics have been described.
A) Descriptive statistics: The branch which deals with descriptions of obtained
data is known as descriptive statistics. On the basis of these descriptions a
particular group of population is defined for corresponding characteristics.
The descriptive statistics include classification, tabulation measures of central
tendency and variability. These measures enable the researchers to know
about the tendency of data or the scores, which further enhance the ease in
description of the phenomena.
8
UNIT 1 INTRODUCTION TO STATISTICS
Structure
1.0 Introduction
1.1 Objectives
1.2 Meaning of Statistics
1.2.1 Statistics in Singular Sense
1.2.2 Statistics in Plural Sense
1.2.3 Definition of Statistics
1.3 Types of Statistics
1.3.1 On the Basis of Function
1.3.2 On the Basis of Distribution of Data
1.4 Scope and Use of Statistics
1.5 Limitations of Statistics
1.6 Distrust and Misuse of Statistics
1.7 Let Us Sum Up
1.8 Unit End Questions
1.9 Glossary
1.10 Suggested Readings
1.0 INTRODUCTION
The word statistics has different meaning to different persons. Knowledge of
statistics is applicable in day to day life in different ways. In daily life it means
general calculation of items, in railway statistics means the number of trains
operating, number of passenger’s freight etc. and so on. Thus statistics is used by
people to take decision about the problems on the basis of different type of
quantitative and qualitative information available to them.
However, in behavioural sciences, the word ‘statistics’ means something different
from the common concern of it. Prime function of statistic is to draw statistical
inference about population on the basis of available quantitative information.
Overall, statistical methods deal with reduction of data to convenient descriptive
terms and drawing some inferences from them. This unit focuses on the above
aspects of statistics.
1.1 OBJECTIVES
After going through this unit, you will be able to:
Define the term statistics;
Explain the status of statistics;
Describe the nature of statistics;
State basic concepts used in statistics; and
Analyse the uses and misuses of statistics.
5
,Introduction to Statistics
1.2 MEANING OF STATISTICS
The word statistics has been derived from Latin word ‘status’ or Italian ‘Statista’
meaning statesman. Professor Gott Fried Achenwall used it in the 18th century.
During early period, these words were used for political state of the region. The
word ‘Statista’ was used to keep the records of census or data related to wealth
of a state. Gradually, its meaning and usage extended and thereonwards its nature
also changed.
The word statistics is used to convey different meanings in singular and plural
sense. Therefore it can be defined in two different ways.
1.2.1 Statistics in Singular Sense
In singular sense, ‘Statistics’ refers to what is called statistical methods. It deals
with the collection of data, their classification, analysis and interpretations of
statistical data. Therefore, it is described as a branch of science which deals with
classification, tabulation and analysis of numerical facts and make decision as
well. Every statistical inquiry should pass through these stages.
1.2.2 Statistics in Plural Sense
‘Statistics’ used in plural sense means that quantitative information is available
called ‘data’. For example, information on population or demographic features,
enrolment of students in Psychology programmes of IGNOU, and the like.
According to Websters “Statistics are the classified facts representing the
conditions of the people in a State specifically those facts which can be stated in
number or in tables of number or classified arrangement”.
Horace Secrist describes statistics in plural sense as follows : “ By Statistics we
mean aggregates 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.” Thus Secrist’s definition highlights following
features of statistics:
i) Statistics are aggregate of facts: Single or unrelated items are not considered
as statistics.
ii) Statistics are affected by multiplicity of causes: In statistics the collected
information are greatly influenced by a number of factors and forces working
together.
iii) Statistics are numerical facts: Only numerical data constitute statistics.
iv) Statistics are enumerated or estimated with a reasonable standard of
accuracy: While enumerating or estimating data, a reasonable degree of
accuracy must be achieved.
v) Statistics are collected in a systematic manner: Data should be collected by
proper planning by utilising tool/s developed by trained personnel.
vi) Statistics are collected for a predetermined purpose : It is necessary to define
the objective of enquiry, before collecting the statistics. The objective of
enquiry must be specific and well defined.
6
,vii) Statistics should be comparable: Only comparable data will have some Introduction to Statistics
meaning. For statistical analysis, the data should be comparable with respect
to time, place group, etc.
Thus, it may be stated that “ All statistics are numerical statements of facts but
all numerical statements of facts are not necessarily statistics ”.
1.2.3 Definition of Statistics
In this unit emphasis is on the term statistics as a branch of science. It deals with
classification, tabulation and analysis of numerical facts. Different statistician
defined this aspect of statistics in different ways. For example.
A. L. Bowley gave several definitions of Statistics:
i) “Statistics may be called the science of counting” . This definition emphasises
enumeration aspect only.
ii) In another definition he describes it as “ Statistics may rightly be called the
science of average”.
iii) At another place Statistics is defined as, “Statistics is the science of
measurement of social organism regarded as a whole in all its manifestations”.
All three definitions given by Bowely seem to be inadequate because these do
not include all aspects of statistics.
According to Selligman “Statistics is the science which deals with the methods
of collecting, classifying, presenting , comparing and interpreting numerical data
collected to throw some light on any sphere of enquiry”.
Croxton and Cowden defined “statistics as the collection , presentation, analysis
,and interpretation of numerical data”.
Among all the definitions , the one given by Croxton and Cowden is considered
to be most appropriate as it covers all aspects and field of statistics.
These aspects are given below:
Collection of Data : Once the nature of study is decided , it becomes essential to
collect information in form of data about the issues of the study. Therefore, the
collection of data is the first basic step. Data may be collected either from primary
source or secondary or from both the sources depending upon the objective/s of
the investigation
Classification and Presentation : Once data are collected , researcher has to
arrange them in a format from which they would be able to draw some
conclusions. The arrangement of data in groups according to some similarities is
known as classification.
Tabulation is the process of presenting the classified data in the form of table. A
tabular presentation of data becomes more intelligible and fit for further statistical
analysis. Classified and Tabulated data can be presented in diagrams and graphs
to facilitate the understanding of various trends as well as the process of
comparison of various situations.
Analysis of Data : It is the most important step in any statistical enquiry . Statistical
analysis is carried out to process the observed data and transform it in such a
manner as to make it suitable for decision making. 7
, Introduction to Statistics Interpretation of Data : After analysing the data, researcher gets information
partly or wholly about the population. Explanation of such information is more
useful in real life. The quality of interpretation depends more and more on the
experience and insight of the researcher.
Self Assessment Questions
1) Complete the following statements
i) The word statistics has been derived from Latin word .....................
ii) Statistics in plural means ................................................................
iii) Statistics in singular means .............................................................
iv) The first step in statistics is .............................................................
v) The last step in statistics is .............................................................
2) Tick () the correct answer
Statistical data are:
i) Aggregates of facts
ii) Unsystematic data
iii) Single or isolated facts or figure
iv) None of these
3) Which one of the following statement is true for statistics in singular
sense?
i) Statistics are aggregate of facts.
ii) Statistics are numerical facts.
iii) Statistics are collected in a systematic manner.
iv) Statistics may be called the science of counting.
1.3 TYPES OF STATISTICS
After knowing the concept and definition of statistics, let us know the various
types of statistics.
Though various bases have been adopted to classify statistics, following are the
two major ways of classifying statistics: (i) on the basis of function and (ii) on
the basis of distribution.
1.3.1 On the Basis of Functions
As statistics has some particular procedures to deal with its subject matter or
data, three types of statistics have been described.
A) Descriptive statistics: The branch which deals with descriptions of obtained
data is known as descriptive statistics. On the basis of these descriptions a
particular group of population is defined for corresponding characteristics.
The descriptive statistics include classification, tabulation measures of central
tendency and variability. These measures enable the researchers to know
about the tendency of data or the scores, which further enhance the ease in
description of the phenomena.
8
