BUSINESS CALCULATION AND STATISTICS STUDY NOTES
Chapter 1 INTRODUCTION TO STATISTICS
Introduction
The word “statistics” appears to have been derived from the Latin word “Status”. Statistics was
simple the collection of numerical data, by the kinds on different aspects useful to the state.
Today statistics is the scientific study of handling quantitative information. It embodies a
methodology of collection, classification description and interpretation of data obtained through
the conduct of surveys and experiments.
Population
The total group under discussion or the group to which results will be generalized is called
population. For example collection of height measurements of all college students is called
population.
Sample
A part of the population selected in the belief that it will represent all the characteristics of the
population is called a sample. For example a sample of 10 students is selected from a population of
100 students in order to analyse the average height of the students.
Meaning of Statistics
Now a days the word “Statistics” is used in two senses i.e.
Singular Senses
In its singular sense, the word statistics means the science of statistics which deals with statistical
methods.
Plural Senses
The word statistics, when used in plural senses means numerical facts collected in any field of
study by using a statistical method.
Definition Of Statistics
Statistic is the numerical statement of facts capable of analysis and interpretation, and science of
statistics is the study of their principles and methods applied in collecting, presenting, analysis
and interpretation the numerical data in any field of inquiry. OR
Science of facts and figures is called statistics.
Scope of Statistics
Statistics is the branch of mathematics that deals with data. Statistics uses data, collected through
systematically method of data collection and the theories are employed to arrive at the
conclusion.
MAIN BRANCHES OF STATISTICS / DIVISION OF STATISTICS
The science of statistics may be classified into following two main branches.
1. Statistical Methods
In case of statistical inquiry the last 1st step is the collection of data. Most of the data are complex
and confused. So for a clear picture of this data, we reduced the complexity and confusion of this
data, which is done by statistical method. Statistical method includes all the rules of procedure
and techniques which are used in the collection, classification, tabulation, comparison and
interpretation of data. Simply statistical data simplifies the complex of numerical data.
2. Applied Statistics
It deals with the application of statistical method to some specific problem; applied statistics has
two types.
PREPARED BY MR ANTONY AMBIA Page 1
,a. Descriptive Applied Statistics
In descriptive applied statistics it is applied to these data which relates to the present or past
information for e.g. census in Pakistan for achieving certain conclusion.
b. Scientific Applied Statistics
We apply general rules on the quantitative data which is useful for forecasting and for this
purpose we use scientific applied statistics.
Limitation of Statistics
1. Statistical has a handicap in dealing with qualitative observation or values.
2. Statistical results are applied only on the average
3. Statistics does not study qualitative phenomena
4. Statistical deals with fact which can be numerically expressed for e.g. love, hate, beauty,
poverty health cannot be measured.
5. Sufficient care need be exercised in the collection, analysis and interpretation of data otherwise
statistical results may be false.
Use or Functions of Statistics
1. Statistical simplifies the complicated data
2. Statistical test the law of other sciences
3. Statistics help a lot in policy making purposes
4. Statistics and Forecasting
5. Statistics and Administration
6. Statistics helps in proper and efficient playing of a statistical inquiry in any field of study
Relationship of Statistics with other Sciences
Now a days statistics and statistical data, methods being applied increasing in agriculture,
Economics, Biology, Business, Physics, Chemistry, Astronomy, Medicine, Administration,
Education, Mathematics, Meteorology and Physical science.
1. Statistics and Administration
Statistics plays an important role in the field of administration and management in providing
measure of performance of the employees. Statistical data are widely used in taking all
administration decision. For example the authorities want of rise the pay scales of employees in
view of an increase in the cost of living. Statistical methods will be used to calculate the rise in
cost of living.
2. Statistics and Agriculture
Agriculture Statistics cover a wide field. These include Statistics of land utilization, production of
crop, price and wages in agriculture etc. Agriculture is greatly benefited by the statistical
methods.
3. Statistics and Medicine
Statistics plays an important role in the field of medicine, to test the effectiveness of different
types of medicines. Vital Statistics may be defined as the science. This deals with the application
of numerical methods to vital fact. It is a part of the broader field of demography. Demography is
a statistical study of all phases of human life relating to vital facts such as births, deaths, age,
marriages, religions, social affairs, education and sanitation. Vital statistics is a part of demography
and comprises of vital data.
4. Statistics and Mathematics
All statistical methods have their foundations in mathematics. No calculating work can be done
without the help of mathematics. Therefore, mathematics is applied widely in statistics. The
branch of statistics is called mathematical statistic. Both these subjects are so interrelated.
PREPARED BY MR ANTONY AMBIA Page 2
,5. Statistics and Physical Sciences
Physical science greatly depending upon science of statistics in analysis and testing their
significance for drawing result. Statistical methods are used in physical science like physics,
chemistry, Geology etc.
6. Statistics and Economics
Important phenomena in all branches of economics can be described, compared with the helps of
statistics. Statistics of production described wealth of nation and compare it year after showing
there by the effect of changing economics policies and other factors on the level of production.
7. Statistics Helps in Forecasting
Through estimating the variables that exit in the fast forecasting about in times to come, can
easily be done. Statistics helps in forecasting future events. Use of some statistical techniques like
extrapolation and time series analysis helps in saying some thing the future courses of events.
Statistics plays an important role in filed of astronomy, transportation, communication publics,
health, teaching methods, engineering psychology, meteorology wealth forecasting.
Statistics and Business
Statistics plays in important role in business. It helps the business men to plan production
according to the tastes of the customers; the quality of the products can also be checked by using
statistical methods
Characteristic of Statistics
Statistics have the following characteristics.
1. Statistics are aggregates of facts
Statistics are a number of facts.
A single fact even it numerically expressed, cannot called statistics.
A single death, an accident etc, does not constitute statistics but on the other hand a number of
deaths, accidents are statistics.
2. Statistics are affected by many causes
Statistics are aggregates of such facts only as grow out of variety of circumstances – their size,
shape at any particular moments is the result of the action and interaction of forces.
3. Statistics are numerically expressed
In statistics, we study quantitative expressions and not qualitative like old, young, good, bad etc.
4. Statistics are estimates to a reasonable standard
What standard of accuracy is to be regarded as reasonable will depends upon the aims and objects
of inquiry and what so ever the standard of accuracy is once adopted it must be uniformly
maintained throughout the inquiry.
5. Statistics are collected in a systematic manner
Statistics collected in a haphazard manner can not be accurate.
Statistics Inquiry
The inquiry about any problem which has done with the help of statistical principles and methods
is called statistical inquiry.
Steps in Statistical Inquiry
Requiring collection of data, the following steps are involved in statistical inquiry.
1. Planning inquiry.
2. Collection of data.
3. Editing the collected data.
4. Tabulating the data.
PREPARED BY MR ANTONY AMBIA Page 3
, 5. Analyzing the data by calculated statistical measures.
Planning of Statistics Inquiry
Following are the factors of planning of statistical inquiry.
1. Object and Scope of Inquiry
2. Nature and Type of Inquiry
i. Primary or Secondary
ii. Census or Samples
iii. Open and Secret
iv. Direct or Indirect
v. Regular or Adhoc
vi. Initial or Receptive
vii. Official, Semi Official or Non Official
3. Statistical Unit
The unit of measurements which are applied in the collected of data is called statistical unit. For
e.g. if we collect the rice crop according to per acre then it will be a statistical unit, for wheat crop
there are two types of statistical unit.
i. Physical Unit
ii. Arbitrary Units
Advantages of statistical Units
i. If fulfills the object of inquiry stable.
ii. Stable.
iii. Homogeneous.
iv. In obvious words.
4. Degree of Accuracy
This decision about the nature of inquiry and purpose of investigation is called degree of accuracy.
VARIABLE
A measurable quantity which can vary (differ) from one individual to another or one object to
another object is called variable. For e.g. height of students, weight of children. It is denoted by
the letters of alphabet e.g. x, y, z etc.
Type of Variable
There are many type of variable.
1. Continuous Variable
A variable which can take set of values (fractional) b/w two limits and has continuous integer
numbers is called continuous variable. Or
A variable which can assume any value within a given range is called a continuous variable. For
e.g. age of persons, speed of car, temperature at a place, income of a person, height of a plant, a life
time of a T.V tube etc.
2. Discrete Variable
A variable which can assume only some specific values within a given range is called discrete
variable. For e.g. Number of students in a class, Number of houses in a street, number of children
in a family etc. it can’t occur in decimal.
3. Quantitative Variable
A characteristic which varies only in magnitude from one individual to another is called
quantitative variable. It can measurable. Or A characteristics expressed by mean of quantitative
terms is known as quantitative variable. For e.g. number of deaths in a country per year, prices
temperature readings, heights, weights etc.
4. Qualitative Variable
PREPARED BY MR ANTONY AMBIA Page 4
Chapter 1 INTRODUCTION TO STATISTICS
Introduction
The word “statistics” appears to have been derived from the Latin word “Status”. Statistics was
simple the collection of numerical data, by the kinds on different aspects useful to the state.
Today statistics is the scientific study of handling quantitative information. It embodies a
methodology of collection, classification description and interpretation of data obtained through
the conduct of surveys and experiments.
Population
The total group under discussion or the group to which results will be generalized is called
population. For example collection of height measurements of all college students is called
population.
Sample
A part of the population selected in the belief that it will represent all the characteristics of the
population is called a sample. For example a sample of 10 students is selected from a population of
100 students in order to analyse the average height of the students.
Meaning of Statistics
Now a days the word “Statistics” is used in two senses i.e.
Singular Senses
In its singular sense, the word statistics means the science of statistics which deals with statistical
methods.
Plural Senses
The word statistics, when used in plural senses means numerical facts collected in any field of
study by using a statistical method.
Definition Of Statistics
Statistic is the numerical statement of facts capable of analysis and interpretation, and science of
statistics is the study of their principles and methods applied in collecting, presenting, analysis
and interpretation the numerical data in any field of inquiry. OR
Science of facts and figures is called statistics.
Scope of Statistics
Statistics is the branch of mathematics that deals with data. Statistics uses data, collected through
systematically method of data collection and the theories are employed to arrive at the
conclusion.
MAIN BRANCHES OF STATISTICS / DIVISION OF STATISTICS
The science of statistics may be classified into following two main branches.
1. Statistical Methods
In case of statistical inquiry the last 1st step is the collection of data. Most of the data are complex
and confused. So for a clear picture of this data, we reduced the complexity and confusion of this
data, which is done by statistical method. Statistical method includes all the rules of procedure
and techniques which are used in the collection, classification, tabulation, comparison and
interpretation of data. Simply statistical data simplifies the complex of numerical data.
2. Applied Statistics
It deals with the application of statistical method to some specific problem; applied statistics has
two types.
PREPARED BY MR ANTONY AMBIA Page 1
,a. Descriptive Applied Statistics
In descriptive applied statistics it is applied to these data which relates to the present or past
information for e.g. census in Pakistan for achieving certain conclusion.
b. Scientific Applied Statistics
We apply general rules on the quantitative data which is useful for forecasting and for this
purpose we use scientific applied statistics.
Limitation of Statistics
1. Statistical has a handicap in dealing with qualitative observation or values.
2. Statistical results are applied only on the average
3. Statistics does not study qualitative phenomena
4. Statistical deals with fact which can be numerically expressed for e.g. love, hate, beauty,
poverty health cannot be measured.
5. Sufficient care need be exercised in the collection, analysis and interpretation of data otherwise
statistical results may be false.
Use or Functions of Statistics
1. Statistical simplifies the complicated data
2. Statistical test the law of other sciences
3. Statistics help a lot in policy making purposes
4. Statistics and Forecasting
5. Statistics and Administration
6. Statistics helps in proper and efficient playing of a statistical inquiry in any field of study
Relationship of Statistics with other Sciences
Now a days statistics and statistical data, methods being applied increasing in agriculture,
Economics, Biology, Business, Physics, Chemistry, Astronomy, Medicine, Administration,
Education, Mathematics, Meteorology and Physical science.
1. Statistics and Administration
Statistics plays an important role in the field of administration and management in providing
measure of performance of the employees. Statistical data are widely used in taking all
administration decision. For example the authorities want of rise the pay scales of employees in
view of an increase in the cost of living. Statistical methods will be used to calculate the rise in
cost of living.
2. Statistics and Agriculture
Agriculture Statistics cover a wide field. These include Statistics of land utilization, production of
crop, price and wages in agriculture etc. Agriculture is greatly benefited by the statistical
methods.
3. Statistics and Medicine
Statistics plays an important role in the field of medicine, to test the effectiveness of different
types of medicines. Vital Statistics may be defined as the science. This deals with the application
of numerical methods to vital fact. It is a part of the broader field of demography. Demography is
a statistical study of all phases of human life relating to vital facts such as births, deaths, age,
marriages, religions, social affairs, education and sanitation. Vital statistics is a part of demography
and comprises of vital data.
4. Statistics and Mathematics
All statistical methods have their foundations in mathematics. No calculating work can be done
without the help of mathematics. Therefore, mathematics is applied widely in statistics. The
branch of statistics is called mathematical statistic. Both these subjects are so interrelated.
PREPARED BY MR ANTONY AMBIA Page 2
,5. Statistics and Physical Sciences
Physical science greatly depending upon science of statistics in analysis and testing their
significance for drawing result. Statistical methods are used in physical science like physics,
chemistry, Geology etc.
6. Statistics and Economics
Important phenomena in all branches of economics can be described, compared with the helps of
statistics. Statistics of production described wealth of nation and compare it year after showing
there by the effect of changing economics policies and other factors on the level of production.
7. Statistics Helps in Forecasting
Through estimating the variables that exit in the fast forecasting about in times to come, can
easily be done. Statistics helps in forecasting future events. Use of some statistical techniques like
extrapolation and time series analysis helps in saying some thing the future courses of events.
Statistics plays an important role in filed of astronomy, transportation, communication publics,
health, teaching methods, engineering psychology, meteorology wealth forecasting.
Statistics and Business
Statistics plays in important role in business. It helps the business men to plan production
according to the tastes of the customers; the quality of the products can also be checked by using
statistical methods
Characteristic of Statistics
Statistics have the following characteristics.
1. Statistics are aggregates of facts
Statistics are a number of facts.
A single fact even it numerically expressed, cannot called statistics.
A single death, an accident etc, does not constitute statistics but on the other hand a number of
deaths, accidents are statistics.
2. Statistics are affected by many causes
Statistics are aggregates of such facts only as grow out of variety of circumstances – their size,
shape at any particular moments is the result of the action and interaction of forces.
3. Statistics are numerically expressed
In statistics, we study quantitative expressions and not qualitative like old, young, good, bad etc.
4. Statistics are estimates to a reasonable standard
What standard of accuracy is to be regarded as reasonable will depends upon the aims and objects
of inquiry and what so ever the standard of accuracy is once adopted it must be uniformly
maintained throughout the inquiry.
5. Statistics are collected in a systematic manner
Statistics collected in a haphazard manner can not be accurate.
Statistics Inquiry
The inquiry about any problem which has done with the help of statistical principles and methods
is called statistical inquiry.
Steps in Statistical Inquiry
Requiring collection of data, the following steps are involved in statistical inquiry.
1. Planning inquiry.
2. Collection of data.
3. Editing the collected data.
4. Tabulating the data.
PREPARED BY MR ANTONY AMBIA Page 3
, 5. Analyzing the data by calculated statistical measures.
Planning of Statistics Inquiry
Following are the factors of planning of statistical inquiry.
1. Object and Scope of Inquiry
2. Nature and Type of Inquiry
i. Primary or Secondary
ii. Census or Samples
iii. Open and Secret
iv. Direct or Indirect
v. Regular or Adhoc
vi. Initial or Receptive
vii. Official, Semi Official or Non Official
3. Statistical Unit
The unit of measurements which are applied in the collected of data is called statistical unit. For
e.g. if we collect the rice crop according to per acre then it will be a statistical unit, for wheat crop
there are two types of statistical unit.
i. Physical Unit
ii. Arbitrary Units
Advantages of statistical Units
i. If fulfills the object of inquiry stable.
ii. Stable.
iii. Homogeneous.
iv. In obvious words.
4. Degree of Accuracy
This decision about the nature of inquiry and purpose of investigation is called degree of accuracy.
VARIABLE
A measurable quantity which can vary (differ) from one individual to another or one object to
another object is called variable. For e.g. height of students, weight of children. It is denoted by
the letters of alphabet e.g. x, y, z etc.
Type of Variable
There are many type of variable.
1. Continuous Variable
A variable which can take set of values (fractional) b/w two limits and has continuous integer
numbers is called continuous variable. Or
A variable which can assume any value within a given range is called a continuous variable. For
e.g. age of persons, speed of car, temperature at a place, income of a person, height of a plant, a life
time of a T.V tube etc.
2. Discrete Variable
A variable which can assume only some specific values within a given range is called discrete
variable. For e.g. Number of students in a class, Number of houses in a street, number of children
in a family etc. it can’t occur in decimal.
3. Quantitative Variable
A characteristic which varies only in magnitude from one individual to another is called
quantitative variable. It can measurable. Or A characteristics expressed by mean of quantitative
terms is known as quantitative variable. For e.g. number of deaths in a country per year, prices
temperature readings, heights, weights etc.
4. Qualitative Variable
PREPARED BY MR ANTONY AMBIA Page 4
