Introductory & Basic Statistics
Definition of Statistics:
Statistics is concerned with scientific methods for collecting, organizing, summarizing,
presenting and analyzing sample data as well as drawing valid conclusions about
population characteristics and making reasonable decisions on the basis of such analysis.
According to Lovitt, Statistics is the science which deals with collection, classification
and tabulation of numerical facts as the basis for explanation, description and comparison
of phenomenon.
Characteristics/ Salient features of Statistics:
Statistics should possess the following characteristics:
(i) Statistics should deal with aggregate of individuals rather than with individual
alone.
(ii) Statistics should be expressed as numerical figures.
(iii) Statistics should have the property of being varied by multiplicity of causes.
(iv) Statistics should be collected with reasonable standards of accuracy.
(v) Statistics should be obtained for pre-determined purposes.
(vi) Statistics collected should allow comparison with other data.
Scope and Use of Statistics:
The scope and use of statistics are so wide and universal that they cannot be enumerated
instantly in a few words. Statistics is used in researches of almost all disciplines. In fact,
there is hardly any field where statistical methods can not be applied, whether it may be
human population or agriculture, business, economics, planning, education, health,
industry, sociology, management, biometry, physics, chemistry, astronomy, meteorology,
environment, insurance, accounting, auditing, medicine, psychology etc.
Limitation of Statistics:
The drawbacks of the statistics are:
(i) Statistics is not suited to the study of qualitative phenomenon.
(ii) Statistics does not study individuals.
(iii) Statistical laws are not exact.
(iv) Statistics is liable to misused.
Page 1 of 7
,Types of Statistics:
Statistics deals with both statistical data and statistical methods. Statistical methods are
again divided into two branches like
(i) Descriptive Statistics and
(ii) Inductive Statistics
Descriptive Statistics:
Descriptive Statistics deals with collection, tabulation, presentation and analysis of data
without considering the theory of probability. The study of frequency distribution is an
aspect of tabulation. The analytical aspects deal with the measures of central tendency,
measures of dispersion, skewness and kurtosis. The shape of the frequency curve is
studied by skewness and kurtosis. All the above measures are used for univariate, bi-
variate and multivariate data. The study of correlation, regression and association of
attributes are included in the bi-variate descriptive statistics.
Inductive Statistics:
Statistics is based on inductive logic. Inductive Statistics is concerned with making
estimates, predictions and generalizations, or reaching decisions about population based
on sample observations. The method of taking decision is known as statistical inference.
The inference is made by sampling, sampling distribution, estimation of parameter and
test regarding any hypothesis on parameter.
Statistical data:
Any measurement of one or more characteristics recorded (as a result of observation,
interview and so on) either from population or sample units are called data. Data are the
raw, disorganized facts and figures collected from any field of inquiry.
For example, the heights of 14 randomly selected persons from a group of N = 100
persons are as follows: 152, 160, 158, 155, 150, 152, 151, 150, 153, 154, 153, 154, 151,
155. This information on height of people constitutes a data.
Types of data
Statistical data depending upon the sources are of two types, they are:
(i) Primary data
(ii) Secondary Data
Primary Data:
The data, which are collected from the main sources by basic investigation or direct
observation of the experimental units, are called primary data.
Page 2 of 7
,Secondary data:
The data that are collected from indirect sources such as from any institution or
organization, publication, report, journal etc. is called secondary data.
Collected data are stored in two fashions, they are:
(i) Raw data
(ii) Classified data
Raw data:
The data which are collected from sampling units and stored or recorded without any
systematic fashion are known as raw data.
For example: The number of road accident in 5 selected days in high ways in a year: 12,
10. 4, 12, 5
Classified data:
The primary data which are presented in a systematic fashion in rows or columns or even
in ordered way are known as classified data.
For example, the following data represent the number of some selected private
universities according to their number of students:
C.I. of number of Students Number of Universities
<500 5
500-1000 15
1000-1500 4
1500-2000 3
2000+ 2
Continuous Data:
A set of data is said to be continuous if the observations belonging to it may take on any
value within a finite or infinite interval. For example height, weight, temperature, the
amount of sugar in an orange, the time required to run a mile.
Measurement of Data:
Data are also be classified as the followings:
Categorical Data:
A set of data is said to be categorical if the values or observations belonging to it can be
sorted according to category. For example, people have the characteristic of 'gender' with
categories 'male' and 'female'.
Page 3 of 7
,Nominal Data:
A set of data is said to be nominal if the observations belonging to it can be assigned a
code in the form of a number where the numbers are simply labels. One can count but not
order or measure nominal data. For example, in a data set males could be coded as 0,
females as 1; marital status of an individual could be coded as Y if married, N if single
Ordinal Data:
A set of data is said to be ordinal if the observations belonging to it can be ranked (put in
order) or have a rating scale attached. One can count and order, but not measure, ordinal
data. For example, suppose a group of people were asked to taste varieties of biscuit and
classify each biscuit on a rating scale of 1 to 5, representing strongly dislike, dislike,
neutral, like, strongly like. A rating of 5 indicates more enjoyment than a rating of 4, for
example, so such data are ordinal.
Interval data:
An interval scale is a scale of measurement where the distance between any two adjacent
units of measurement (or 'intervals') is the same but the zero point is arbitrary. Scores on
an interval scale can be added and subtracted but cannot be meaningfully multiplied or
divided. For example, the time interval between the starts of years 1981 and 1982 is the
same as that between 1983 and 1984, namely 365 days. The zero point, year 1 AD, is
arbitrary; time did not begin then. Other examples of interval scales include the heights of
tides, and the measurement of longitude.
Ratio data:
Ratio variable is one, which can take numeric values that are actual as well as absolute.
The zero value on this scale is absolutely zero. The variable height, weight, family size
etc. are examples of ratio variable
Sources of Statistical data:
Statistical data may be collected in a variety of ways. These sources may broadly be
categorized as primary source and secondary source. Primary data come mainly from
direct field operations, which may either be a census or a specially designed survey. On
the other hand, secondary data are usually procured from already published or
unpublished documents rather than undertaking first-hand field investigations. So the
primary data collected by an agency or organization, constitute the secondary data in the
hands of other agencies. Bangladesh Bureau of Statistics (BBS), for example, conducts
occasional surveys on various aspects, such as health, migration, marriage and morbidity.
Such data in their hands are regarded as primary data. They are compiling, analyzing and
preparing periodic reports on the issues. If these data are used by some other interested
groups to serve their own purpose, the BBs data become secondary in nature to them.
Page 4 of 7
,Population
An aggregate of all individuals or items under investigation defined on some common
characteristics is called a population.
For example, first year honours students in statistics (session: 2007-2008) of SUST
constitute a population. Here, the common characteristics are:
(i) Students of SUST
(ii) Students of first year honours students in statistics and
(iii) Students of the session 2007-2008
Or, An aggregate of all individuals or items under investigation according to some pre-
determined objective and are available in a specified area at a specified time period.
For example, if the objective is to estimate the per capita salary of female employees
working in different garments industries in Bangladesh, then all female employees in all
industries of Bangladesh during a particular time period constitute the population.
Types of Population:
A population can be classified in different types which is shown by the following
diagram:
Population
Finite Population Infinite Population
Finite Existent Finite Non-existent Infinite Existent Infinite Non-existent
Finite Population:
A population consisting of a finite number of individuals or items is called a finite
population. For example, first year honours students in statistics (session: 2007-2008) of
SUST constitute a finite population.
Infinite Population:
A population consisting of an infinite number of individuals or items is called an infinite
population. For example, if we toss a coin for an infinite number of times and write down
the upturned face of the coin then the sequence of Head (H) and Tail (T) (like
HHHTTHT-----) will constitute an infinite population.
Page 5 of 7
, Sample
A small but representative part with finite number individuals or items of a population
which is under investigation is called a sample.
For example, a group of students, representing the first year first semester honours
students of Shahjalal University of Science and Technology is called a sample.
Random Sample:
If each individual or item in the population from which a sample has been drawn or
selected, has an equal chance of being included in the sample, then the sample is called a
random sample.
For example, If we have a complete list of 100 students and if we select a sample of 20
students from these 100 students completely at random, then each of the students has an
equal chance of being included in the sample. Therefore, the sample 20 students is a
random sample.
Variable:
A variable is a characteristic whose value can vary from person to person, object to object
or from phenomenon to phenomenon.
For example, (i) Sex is variable which is composed of two categories, male and female
and it varies from one to another, (ii) Age is a variable which may vary from person to
person and may assume values 10 years, 15 years 20 years and so on.
Types of variable:
There are two types of variables, they are
(i) Qualitative variable: A qualitative variable is one for which numerical
measurement is not possible, such as hair colour, religion, race, sex etc.
(ii) Quantitative variable: A quantitative variable is one for which the resulting
observations are numeric and thus possesses a natural ordering. Example: Age,
Height, Family size etc.
Quantitative variable can also be classified as
(i) Discrete variable: When the variable can assume only the isolated values, the
variable is called discrete variable. Example: - the number of children in a family.
(ii) Continuous variable: A variable is said to be continuous if it assumes any value
within a certain range. Example: - Age, Height, Temperature etc.
Page 6 of 7
Definition of Statistics:
Statistics is concerned with scientific methods for collecting, organizing, summarizing,
presenting and analyzing sample data as well as drawing valid conclusions about
population characteristics and making reasonable decisions on the basis of such analysis.
According to Lovitt, Statistics is the science which deals with collection, classification
and tabulation of numerical facts as the basis for explanation, description and comparison
of phenomenon.
Characteristics/ Salient features of Statistics:
Statistics should possess the following characteristics:
(i) Statistics should deal with aggregate of individuals rather than with individual
alone.
(ii) Statistics should be expressed as numerical figures.
(iii) Statistics should have the property of being varied by multiplicity of causes.
(iv) Statistics should be collected with reasonable standards of accuracy.
(v) Statistics should be obtained for pre-determined purposes.
(vi) Statistics collected should allow comparison with other data.
Scope and Use of Statistics:
The scope and use of statistics are so wide and universal that they cannot be enumerated
instantly in a few words. Statistics is used in researches of almost all disciplines. In fact,
there is hardly any field where statistical methods can not be applied, whether it may be
human population or agriculture, business, economics, planning, education, health,
industry, sociology, management, biometry, physics, chemistry, astronomy, meteorology,
environment, insurance, accounting, auditing, medicine, psychology etc.
Limitation of Statistics:
The drawbacks of the statistics are:
(i) Statistics is not suited to the study of qualitative phenomenon.
(ii) Statistics does not study individuals.
(iii) Statistical laws are not exact.
(iv) Statistics is liable to misused.
Page 1 of 7
,Types of Statistics:
Statistics deals with both statistical data and statistical methods. Statistical methods are
again divided into two branches like
(i) Descriptive Statistics and
(ii) Inductive Statistics
Descriptive Statistics:
Descriptive Statistics deals with collection, tabulation, presentation and analysis of data
without considering the theory of probability. The study of frequency distribution is an
aspect of tabulation. The analytical aspects deal with the measures of central tendency,
measures of dispersion, skewness and kurtosis. The shape of the frequency curve is
studied by skewness and kurtosis. All the above measures are used for univariate, bi-
variate and multivariate data. The study of correlation, regression and association of
attributes are included in the bi-variate descriptive statistics.
Inductive Statistics:
Statistics is based on inductive logic. Inductive Statistics is concerned with making
estimates, predictions and generalizations, or reaching decisions about population based
on sample observations. The method of taking decision is known as statistical inference.
The inference is made by sampling, sampling distribution, estimation of parameter and
test regarding any hypothesis on parameter.
Statistical data:
Any measurement of one or more characteristics recorded (as a result of observation,
interview and so on) either from population or sample units are called data. Data are the
raw, disorganized facts and figures collected from any field of inquiry.
For example, the heights of 14 randomly selected persons from a group of N = 100
persons are as follows: 152, 160, 158, 155, 150, 152, 151, 150, 153, 154, 153, 154, 151,
155. This information on height of people constitutes a data.
Types of data
Statistical data depending upon the sources are of two types, they are:
(i) Primary data
(ii) Secondary Data
Primary Data:
The data, which are collected from the main sources by basic investigation or direct
observation of the experimental units, are called primary data.
Page 2 of 7
,Secondary data:
The data that are collected from indirect sources such as from any institution or
organization, publication, report, journal etc. is called secondary data.
Collected data are stored in two fashions, they are:
(i) Raw data
(ii) Classified data
Raw data:
The data which are collected from sampling units and stored or recorded without any
systematic fashion are known as raw data.
For example: The number of road accident in 5 selected days in high ways in a year: 12,
10. 4, 12, 5
Classified data:
The primary data which are presented in a systematic fashion in rows or columns or even
in ordered way are known as classified data.
For example, the following data represent the number of some selected private
universities according to their number of students:
C.I. of number of Students Number of Universities
<500 5
500-1000 15
1000-1500 4
1500-2000 3
2000+ 2
Continuous Data:
A set of data is said to be continuous if the observations belonging to it may take on any
value within a finite or infinite interval. For example height, weight, temperature, the
amount of sugar in an orange, the time required to run a mile.
Measurement of Data:
Data are also be classified as the followings:
Categorical Data:
A set of data is said to be categorical if the values or observations belonging to it can be
sorted according to category. For example, people have the characteristic of 'gender' with
categories 'male' and 'female'.
Page 3 of 7
,Nominal Data:
A set of data is said to be nominal if the observations belonging to it can be assigned a
code in the form of a number where the numbers are simply labels. One can count but not
order or measure nominal data. For example, in a data set males could be coded as 0,
females as 1; marital status of an individual could be coded as Y if married, N if single
Ordinal Data:
A set of data is said to be ordinal if the observations belonging to it can be ranked (put in
order) or have a rating scale attached. One can count and order, but not measure, ordinal
data. For example, suppose a group of people were asked to taste varieties of biscuit and
classify each biscuit on a rating scale of 1 to 5, representing strongly dislike, dislike,
neutral, like, strongly like. A rating of 5 indicates more enjoyment than a rating of 4, for
example, so such data are ordinal.
Interval data:
An interval scale is a scale of measurement where the distance between any two adjacent
units of measurement (or 'intervals') is the same but the zero point is arbitrary. Scores on
an interval scale can be added and subtracted but cannot be meaningfully multiplied or
divided. For example, the time interval between the starts of years 1981 and 1982 is the
same as that between 1983 and 1984, namely 365 days. The zero point, year 1 AD, is
arbitrary; time did not begin then. Other examples of interval scales include the heights of
tides, and the measurement of longitude.
Ratio data:
Ratio variable is one, which can take numeric values that are actual as well as absolute.
The zero value on this scale is absolutely zero. The variable height, weight, family size
etc. are examples of ratio variable
Sources of Statistical data:
Statistical data may be collected in a variety of ways. These sources may broadly be
categorized as primary source and secondary source. Primary data come mainly from
direct field operations, which may either be a census or a specially designed survey. On
the other hand, secondary data are usually procured from already published or
unpublished documents rather than undertaking first-hand field investigations. So the
primary data collected by an agency or organization, constitute the secondary data in the
hands of other agencies. Bangladesh Bureau of Statistics (BBS), for example, conducts
occasional surveys on various aspects, such as health, migration, marriage and morbidity.
Such data in their hands are regarded as primary data. They are compiling, analyzing and
preparing periodic reports on the issues. If these data are used by some other interested
groups to serve their own purpose, the BBs data become secondary in nature to them.
Page 4 of 7
,Population
An aggregate of all individuals or items under investigation defined on some common
characteristics is called a population.
For example, first year honours students in statistics (session: 2007-2008) of SUST
constitute a population. Here, the common characteristics are:
(i) Students of SUST
(ii) Students of first year honours students in statistics and
(iii) Students of the session 2007-2008
Or, An aggregate of all individuals or items under investigation according to some pre-
determined objective and are available in a specified area at a specified time period.
For example, if the objective is to estimate the per capita salary of female employees
working in different garments industries in Bangladesh, then all female employees in all
industries of Bangladesh during a particular time period constitute the population.
Types of Population:
A population can be classified in different types which is shown by the following
diagram:
Population
Finite Population Infinite Population
Finite Existent Finite Non-existent Infinite Existent Infinite Non-existent
Finite Population:
A population consisting of a finite number of individuals or items is called a finite
population. For example, first year honours students in statistics (session: 2007-2008) of
SUST constitute a finite population.
Infinite Population:
A population consisting of an infinite number of individuals or items is called an infinite
population. For example, if we toss a coin for an infinite number of times and write down
the upturned face of the coin then the sequence of Head (H) and Tail (T) (like
HHHTTHT-----) will constitute an infinite population.
Page 5 of 7
, Sample
A small but representative part with finite number individuals or items of a population
which is under investigation is called a sample.
For example, a group of students, representing the first year first semester honours
students of Shahjalal University of Science and Technology is called a sample.
Random Sample:
If each individual or item in the population from which a sample has been drawn or
selected, has an equal chance of being included in the sample, then the sample is called a
random sample.
For example, If we have a complete list of 100 students and if we select a sample of 20
students from these 100 students completely at random, then each of the students has an
equal chance of being included in the sample. Therefore, the sample 20 students is a
random sample.
Variable:
A variable is a characteristic whose value can vary from person to person, object to object
or from phenomenon to phenomenon.
For example, (i) Sex is variable which is composed of two categories, male and female
and it varies from one to another, (ii) Age is a variable which may vary from person to
person and may assume values 10 years, 15 years 20 years and so on.
Types of variable:
There are two types of variables, they are
(i) Qualitative variable: A qualitative variable is one for which numerical
measurement is not possible, such as hair colour, religion, race, sex etc.
(ii) Quantitative variable: A quantitative variable is one for which the resulting
observations are numeric and thus possesses a natural ordering. Example: Age,
Height, Family size etc.
Quantitative variable can also be classified as
(i) Discrete variable: When the variable can assume only the isolated values, the
variable is called discrete variable. Example: - the number of children in a family.
(ii) Continuous variable: A variable is said to be continuous if it assumes any value
within a certain range. Example: - Age, Height, Temperature etc.
Page 6 of 7
