DESCRIPTIVE
STATISTICS
BY
TANUJIT CHAKRABORTY
Indian Statistical Institute
Mail :
,1
AN INTRODUCTION TO STATISTICS
STEPS AT A GLANCE:
Collection of Data −> Summarization of Data −> Analysis of Data −> Interpretation of Data
towards a VALID DECISION.
WHAT IS THE MAIN PROBLEM IN STATISTICS?
Answer: Given a sample (a set of outcomes), we are to say (infer) about the population or
the model. Statistics primarily deals with situations in which the occurrence of some event
can’t be predicted with certainty.
WHAT ARE THE MAJOR OBJECTIVES OF STATISTICS?
Answer: 1. To make inference about a population from an analysis of information
contained in the sample data.
2. To make assessments of the extent of uncertainty involved in these inferences.
3. A third objective, no less important, is to design the process & the extent of sampling so
that the observations from a basis for drawing valid & accurate inferences.
GIVE THE DEFINITION OF STATISTICS?
Answer: “Statistics” is a science of decision making on the basis of sample observations
drawn from a population under uncertainty. That is, it is a mathematical discipline
concerned with the collection of data, summarization of data, analysis of data &
interpretation of data toward a valid decision.
Encyclopedia Americana: As a name of a field of study, Statistics refers to the science &
arts of obtaining & analyzing quantitative data with a view to make sound inferences in the
face of uncertainty.
Encyclopedia Britannica: As is commonly understood nowadays, Statistics is a
mathematical discipline concerned with the study of masses of quantitative data of any
kind.
Have Doubts? Mail:
,2
WHAT IS THE MEANING OF THE TERM ‘STATISTICS’?
Answer: As a singular noun it refers the science of collecting, analyzing & interpreting
numerical data relating to an aggregate of individuals. As a plural noun it denotes the
numerical & quantitative information, e.g., labor statistics, vital statistics.
IS STATISTCS A SCIENCE?
Answer: Any Science has for its objectives the formulation of laws for explaining
phenomena in some part of the real world with a deterministic viewpoint. As Kendall
explained, “Statistics is the branch of scientific method which deals with the data obtained
by counting or measuring the properties of population of natural phenomena”. Indeed, we
can call Statistical Methodology as Scientific Method. It is noted that STATISTICS is
sometimes called the study of variation, i.e., a population or group without any variation &
uncertainty is no interest to Statistics. So, Statistics is the scientific methodology which
deals with the collection, classification & tabulation of numerical facts as a basis for
explanation, description & comparison of social phenomena.
Some Useful Definitions
Statistical Data: The numerical data or measurements obtained in case of an enquiry into
a phenomenon, marked by uncertainty & variability, constitute Statistical Data. Uncertainty
& variability are two major characteristics of Statistical Data. Not all quantitative data is
statistical data. Example of statistical data – Suppose we study the ‘Heights of students in a
particular college’. Here we can’t predict the height of an individual with certainty & there
will be variation in heights of students. Counter Example: Multiplication table in a tabular
form is a quantitative data, but since there is no uncertainty & variability involved in the
data so it’s not a Statistical Data.
Population: A set or group of observations relating to a phenomenon under statistical
investigation is known as statistical population or simply population. However, the term
‘population’ implies an aggregate or collection of measurements on a given variable(s).
Population is said to be finite or infinite according to whether the set contains a finite or
infinite number of observations. Example – Measurements of heights in your college. Note
that: 1. Characteristics of a population are called parameters. 2. A population contains
finite or infinite no of observations on a given variable(s).
Sample: The set of data actually collected through a process of observation from selected
items of any source is called a Sample. However, “Sample” is a subset of population or a
true representation of population. Example − Measurements of heights of students of
Statistics department in your college. Note that: 1. Characteristics of sample are called as
Statistic. 2. A sample is taken in order to gather information about a population.
Have Doubts? Mail:
, 3
WRITE DOWN THE LIMITATIONS OF STATISTICS?
Answer: 1. Statistics deals with quantitative data only. 2. Statistical law holds good only for
aggregate of items or average individuals. It may not be true for a particular individual or
item. 3. Inadequate knowledge of data interpretation may lead to invalid decision. There
are some saying: “There are three kinds of lies –lies, white lies & Statistics”, “Figure won’t
lie, but liars figure”, “Statistics is like a clay of which you can make a god or devil”.
COMMENT ON THE FOLLOIWNGS:
1. “In a study of ages & professions of deceased men, it was found that the
profession with the lowest average age of death was ‘student’. So it appears that
student profession is very dangerous.”
Answer: It is obvious that every profession must have some basic education & it happens
that the average age of every professional men must be higher than the age of the students.
But it can happen that profession with lowest age of death was student. So the given
statement is TRUE. But the conclusion made from the fact is incorrect. It can never be told
that the student profession is dangerous. To conclude properly, we must have data for
computing the proportions or percentages of deceased men in different professions.
Therefore the conclusion made here is absurd.
2. “A study of fighting in bars in which someone was killed found that 90% of the
cases, the person who started fighting was the one who died”.
Answer: It is very obvious that the data is collected from the persons who has survived in
fighting, not from the dies persons; as a matter of fact the survived persons will not accept
the guilt of killing his opponent fighters. If the data is collected from eye witnesses, it is
expected to say something in favor of the survived person as the opponent fighter has
already been dead, from the sympathetic ground. Hence, the data collected may not be
reliable at all. This is an examples of situation where inadequate information takes into bad
decisions.
3. “Blindly using any data happened to be available can lead to misleading
information & bad decision.”
Answer: There are two kinds of people: Some of them believe that the inferences based on
statistical data are very reliable & trusty. And others don’t believe statistical results at all,
they think it as a damned lies. But the fact is statistics is sometimes misused either
deliberately or often due to lack of knowledge. Making conclusions based on inadequate
information, deliberate manipulation & personal bias may lead to bad decision. Statistics
are not to be blamed for all these. Statistics is like a clay of which you can make a god or a
devil.
Have Doubts? Mail:
STATISTICS
BY
TANUJIT CHAKRABORTY
Indian Statistical Institute
Mail :
,1
AN INTRODUCTION TO STATISTICS
STEPS AT A GLANCE:
Collection of Data −> Summarization of Data −> Analysis of Data −> Interpretation of Data
towards a VALID DECISION.
WHAT IS THE MAIN PROBLEM IN STATISTICS?
Answer: Given a sample (a set of outcomes), we are to say (infer) about the population or
the model. Statistics primarily deals with situations in which the occurrence of some event
can’t be predicted with certainty.
WHAT ARE THE MAJOR OBJECTIVES OF STATISTICS?
Answer: 1. To make inference about a population from an analysis of information
contained in the sample data.
2. To make assessments of the extent of uncertainty involved in these inferences.
3. A third objective, no less important, is to design the process & the extent of sampling so
that the observations from a basis for drawing valid & accurate inferences.
GIVE THE DEFINITION OF STATISTICS?
Answer: “Statistics” is a science of decision making on the basis of sample observations
drawn from a population under uncertainty. That is, it is a mathematical discipline
concerned with the collection of data, summarization of data, analysis of data &
interpretation of data toward a valid decision.
Encyclopedia Americana: As a name of a field of study, Statistics refers to the science &
arts of obtaining & analyzing quantitative data with a view to make sound inferences in the
face of uncertainty.
Encyclopedia Britannica: As is commonly understood nowadays, Statistics is a
mathematical discipline concerned with the study of masses of quantitative data of any
kind.
Have Doubts? Mail:
,2
WHAT IS THE MEANING OF THE TERM ‘STATISTICS’?
Answer: As a singular noun it refers the science of collecting, analyzing & interpreting
numerical data relating to an aggregate of individuals. As a plural noun it denotes the
numerical & quantitative information, e.g., labor statistics, vital statistics.
IS STATISTCS A SCIENCE?
Answer: Any Science has for its objectives the formulation of laws for explaining
phenomena in some part of the real world with a deterministic viewpoint. As Kendall
explained, “Statistics is the branch of scientific method which deals with the data obtained
by counting or measuring the properties of population of natural phenomena”. Indeed, we
can call Statistical Methodology as Scientific Method. It is noted that STATISTICS is
sometimes called the study of variation, i.e., a population or group without any variation &
uncertainty is no interest to Statistics. So, Statistics is the scientific methodology which
deals with the collection, classification & tabulation of numerical facts as a basis for
explanation, description & comparison of social phenomena.
Some Useful Definitions
Statistical Data: The numerical data or measurements obtained in case of an enquiry into
a phenomenon, marked by uncertainty & variability, constitute Statistical Data. Uncertainty
& variability are two major characteristics of Statistical Data. Not all quantitative data is
statistical data. Example of statistical data – Suppose we study the ‘Heights of students in a
particular college’. Here we can’t predict the height of an individual with certainty & there
will be variation in heights of students. Counter Example: Multiplication table in a tabular
form is a quantitative data, but since there is no uncertainty & variability involved in the
data so it’s not a Statistical Data.
Population: A set or group of observations relating to a phenomenon under statistical
investigation is known as statistical population or simply population. However, the term
‘population’ implies an aggregate or collection of measurements on a given variable(s).
Population is said to be finite or infinite according to whether the set contains a finite or
infinite number of observations. Example – Measurements of heights in your college. Note
that: 1. Characteristics of a population are called parameters. 2. A population contains
finite or infinite no of observations on a given variable(s).
Sample: The set of data actually collected through a process of observation from selected
items of any source is called a Sample. However, “Sample” is a subset of population or a
true representation of population. Example − Measurements of heights of students of
Statistics department in your college. Note that: 1. Characteristics of sample are called as
Statistic. 2. A sample is taken in order to gather information about a population.
Have Doubts? Mail:
, 3
WRITE DOWN THE LIMITATIONS OF STATISTICS?
Answer: 1. Statistics deals with quantitative data only. 2. Statistical law holds good only for
aggregate of items or average individuals. It may not be true for a particular individual or
item. 3. Inadequate knowledge of data interpretation may lead to invalid decision. There
are some saying: “There are three kinds of lies –lies, white lies & Statistics”, “Figure won’t
lie, but liars figure”, “Statistics is like a clay of which you can make a god or devil”.
COMMENT ON THE FOLLOIWNGS:
1. “In a study of ages & professions of deceased men, it was found that the
profession with the lowest average age of death was ‘student’. So it appears that
student profession is very dangerous.”
Answer: It is obvious that every profession must have some basic education & it happens
that the average age of every professional men must be higher than the age of the students.
But it can happen that profession with lowest age of death was student. So the given
statement is TRUE. But the conclusion made from the fact is incorrect. It can never be told
that the student profession is dangerous. To conclude properly, we must have data for
computing the proportions or percentages of deceased men in different professions.
Therefore the conclusion made here is absurd.
2. “A study of fighting in bars in which someone was killed found that 90% of the
cases, the person who started fighting was the one who died”.
Answer: It is very obvious that the data is collected from the persons who has survived in
fighting, not from the dies persons; as a matter of fact the survived persons will not accept
the guilt of killing his opponent fighters. If the data is collected from eye witnesses, it is
expected to say something in favor of the survived person as the opponent fighter has
already been dead, from the sympathetic ground. Hence, the data collected may not be
reliable at all. This is an examples of situation where inadequate information takes into bad
decisions.
3. “Blindly using any data happened to be available can lead to misleading
information & bad decision.”
Answer: There are two kinds of people: Some of them believe that the inferences based on
statistical data are very reliable & trusty. And others don’t believe statistical results at all,
they think it as a damned lies. But the fact is statistics is sometimes misused either
deliberately or often due to lack of knowledge. Making conclusions based on inadequate
information, deliberate manipulation & personal bias may lead to bad decision. Statistics
are not to be blamed for all these. Statistics is like a clay of which you can make a god or a
devil.
Have Doubts? Mail:
