Simple Definition of Business Mathematics And Advantages of Business Mathematics

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        Business mathematics may be define different mathematical formulas or mathematical steps which are taken for development in business . Large number of business theories which is used to solve business problems are included in business mathematics .

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Explanation of Definition of Business Mathematics 

How to Formulate the Problem as A Linear Programming Problem

It is very necessary to formulate the given business problem as a linear programming problem  because after this , we can calculate the solution of LPP . In other words if we want to know the quantity of our business

How to Calculate the Value of Annuity ?

There are many types of annuities which will decide how to calculate the value of annuity but if we have to use formula , then there are two formulae which are most used for calculating value of annuity .

How to Calculate the Value of Any Number Whose Power is Negative ?

In annuity related problems , you have seen that , you have to calculate the value of number whose power is negative . For solving this , we can take the help of logarithm . We can take one example for telling you its

Types of Annuities

In the business world , no one pay advance to purchase  commodities or assets  , most of customers pay some advance amount and other amount is payment on fixed installment and these installment have given on the basis which of type annuity , you have selected . So this article describes the

Do the Transpose of Matrix in Google Docs

We have already told you that transpose of matrix means changing of row into column . Now you can do this transpose in Google docs also . For this you have to apply following steps .

What are Singular and Non Singular Matrices?

Definition of Singular Matrix

Singular matrix is square matrix whose determinant is equal to Zero .

What is Rank of Matrix? What are Conditions for Finding The Rank of Matrix?

Definition of Rank of Matrix

" Rank of Matrix is the order of that square matrix whose determinant is not zero. If determinant is "

How to Calculate the Value of X, Y & Z with the Help of Cramer's Rule

To solve linear equation with the help of Cramer's Rule and calculate the value of X, Y and Z are very easy. It is used in solution of Matrix and Determinant problems. First of all we convert the linear equation into

Definition of Co-factor in Matrix and Determinant Topics

Co- factor is very important in the topics of matrix and determinant because , with this , we can calculate adjoint and inverse of matrix . So , understand the definition of co-factor

What is Minor ?

Definition of Minor

Minor of any element of the determinant is the submatrix , if we leave element's row and column .

How to Calculate the Value of Determinant with The Help of Its Properties

If you have read Properties of Determinant in Business Mathematics , then you can calculate the value of determinant with the help of its properties . There is no hard and fast rule for applying properties on

One Example of Solution of Determinant Problem

In following example , you have given the value of matrix in two brackets and you have to calculate the value of determinant , just simple multiply each co-factor of first row to first row's elements and sum the results .

How to Calculate the Value of Determinant ?

Calculating the value of determinant is very easy  and it is very important topic in Matrix and Determinant lesson of Business Mathematics . Just understand its main steps

How to Multiply Two Matrices

There are two easy steps for multiplying two matrices with each other .  First steps tells you the main condition which you have to check yourself and second step will tell you how practical we can multiply two matrices .

Method of Moving Averages

While applying this method the given values are grouped containing 3,4,5........... items and their averages are taken . The averages are written in the middle of the period of the moving average . The totals are taken for overlapping periods . For example in a five year moving average the total of first five items will be written against the third value .

Then the total of next five items leaving the first one will written against the third value . Then the total of next five items leaving the first one will written against the next item . This process will be continued till all the groups , each containing five items , are summed up and averages are taken . The set of averages of these total will determine the trend values .


This process of taking means , smooths the curve and reduces the fluctuations in the data . It simplifies the analysis and removes the periodicity . Variations of the period of moving average is equal to the period of the cycle . As such if there is regularity in the occurrences of business cycle ,the moving average will form a straight lines .

when the values are plotted on a graph , otherwise it will be a set of straight lines . The period of moving averages have to be determined with due consideration to the periodicity of cycle .In case the period of moving averages and the period of the cycle are not same then the trend values will display a cycle having the same period as the cycle in the data .

But the amplitude will be less as compared to that data. The period of moving average is taken a little greater than the period of the cycle if the cycles in the data are uniform duration .If the period of moving average is even then some extra precautions have to be taken while computing the trend values . Let us suppose that the period of moving average is four years .

As usual the over lapping totals will be taken in groups each containing four items . First total will be written in between the second and the third item . Next total will be between third and fourth items . This will continue till all the groups are totalled and written properly at the corresponding positions .

The averages of these totals will fail to determine trend values because these will not be against the given values and such will be non comparable with the given values . To overcome this discrepancy the averages are grouped in pairs and again written in the middle of each pair . The averages of these pairs will be the trend values . This technique is known as centering the averages . Moving averages of all even periods are processed by the centering method .

How to investigate importance of Variance with F -test

F- Test is important tool for investigating the importance of variance with F - Test . We can explain it with simple example

Suppose , There is the sample of 8 Variables , and total of Variance from mean is 94.5 . Another sample of 10 variables total of variance from mean is 101.7 . Investigate whether its variance are important or not ?

Solution :

Ho : Q1 's power two = Q2 's power two
n1 = 8
Sigma ( X1 - mean 1 ) power 2 = 94.5
n2 = 10

Sigma ( X2 - mean 2 ) power 2 = 101.7

S1's power 2 = 94.5/8-1 = 13.5 ; S2's power 2 = 101.7 / 10-1 = 11.3

F = S1power 2/S2's power 2 = 13.5 / 11.5 = 1.195

Decision :
F's calculated value is less than F's table value , so variance is not so important . Our assumption is true .

Simple Definition of Variance Analysis

According to Prof. R.A. Fisher ," Variance analysis is to know whether variance between two sample is important or not . For this we do one important sample test , that is called F- Test .
In other words , " Analysis of variance is the separation of the variance ascribable to the group of causes from the variance ascribable to other group ."

Understand F - Test more easy way

Prof. R.A. Fisher used the word variance first time in 1920 for the statistical analysis of data . This variance is used for calculating variation . Prof. R.A. Fisher developed a new technique for analysis the variance and study the features of two and more variables variation . If we have to investigate chi - square variates , then we should use F -Test . In other words , it is sample test for analysis chi square variation .

Its formula is given below :-

Simplified - What is sampling in Statistics ?

Sampling is that technique of statistical analysis in which we choose few items from large group of data and we take decision about whole group on these few items of sample .
Sampling is cheapest method of statistical analysis and within we short time we can get required information . Sampling data can easily used for calculating mean , median , mode , standard deviation and other advance tool of statistics for taking decision about whole population .

Data collection and its method

Data is very useful source of information for business and its collection process is done by business statistics . In business statistics different type of data are collected according to the need of business and organisation .
This term is also used for any decision taking process in which first we collect the data and after this we analysis this data and take decisions. There are large number of objectives for collecting data . From a small publisher to large scale multinational companies all collect data for achieving their targets and objectives .

If a company want to know whether public accepts or rejects his products , then that company must collect data relating to reaction of public on new launched product . So , it is very necessary to adopt different method for collecting of data . Data can be collect with following method

Methods from data type point of view

1. Primary method

under this method , company collects fresh data from population and after this these data analyze and take different decisions . Primary data may collect with one of following way

a ) Personal interview

Researcher goes to respondents personally and takes interview . In interview , he asks different question and its answer is written on paper by him and this becomes primary data .

b) Questionnaire method

Under this way , researcher sends questionnaire to respondents and respondents reply to researcher and after this it is processed for taking decisions .

2nd method - Secondary data

All data are called secondary data , if it is collected by someone else in past and it is only used by researchers . Suppose , if I have collected primary data and published in this blog relating to business and researcher only uses my collected data for his own purpose , then this will be secondary data . These data can be collected by online journals , blogs , websites , printed magzines , newspapers and TV etc.

Method of data collection from time element point of view

a) Census

If researcher has time for collecting data , then if he collects data from each respondent , then this is called census .

Sample

b) If researcher has no time for collecting all data , then if he collects only small representatives of all respondents , then this is called sample .
you can also watch following PowerPoint presentation for deep understanding of data collection methods .

methods of data collection

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What is data processing ?

Data processing is scientific technique of business statistics in which raw data is converted into useful information. In other words , classification ,tabulation and analysis of data for changing raw data into important information data is called data processing .
These days , data processing work is done by computer's important software ms excel or Google docs ( for online data processing ) . Data processing is very important for business development .


Business collects large number of data from direct and indirect sources and after this it is processed under different classification and then it becomes information . On these information , further statistical tool like average , standard deviation or correlation are applied and try to reach conclusion .

What are the main data type used in business statistics ?

Statistics is the science of collection and analysis of data . If you do not know about data , you never learn this science . So first of all you should know data and its main type .

Data

Data means any fact , thing which we may count but logically we can explain these facts .


Data Type

1. Qualitative data

Qualitative data includes honesty , poor , cleverness , sharpness etc . These are actually quality of human being but these can also explain in qualitative data .

2. Quantitative data

Quantitative data includes figure and numerical data which can compare with each other and analysis them and it is so easy for use that we can take some decision on these quantitative data because quantitative data is more useful in statistics than qualitative data .

Population optimization

Demographers have invented various terms to understand, reconcile and rethink the population explosion in India. That a country touching the one billion mark and giving a tough competition to china in terms of population growth is by now a very well known fact. But what matters is the difference between optimization of this population by China through various policies and methodologies while we are still fighting our best to stabilize our population explosion.

The 1991 census showed an increased of 160 million in the past decade with birth rate declining, nevertheless its place and distribution being slow and uneven and that too with signification regional and state variations. In the beginning it was population seemed to be militating against the objective itself. Then it was family welfare and population stabilization. This has certainly been a more successful venture.

Even since the national family, planning programme was launched in the 50s, the mortality has fallen by nearly two thirds fertility has gone down by about two fifth with life expectancy at birth almost doubling. Mortality and fertility were on even keel for many years stabilizing the growth rate of population around 2% per year in 1991. Serious efforts towards preventive family welfare programme through various methods, the country could achieve 60 % of its goal of replacement fertility with an average declining of 50% in the birth rate.
Notwithstanding the stabilization of population growth at two percentage during the intervening decades as well as the reduction rate in re productivity among women, the most powerful segment , namely young adults in the age group of 10 to 24 has an in built structure which fuels population growth . Almost 25% of the population falls in theirs age group. That means educating optimizing and channeling the enormous energy in this group holds the key for optimizing population growth. The word optimizing has a qualitative dimension compared to control or stabilization when used in the context of population. While control has a negative connotation, stabilization hinges upon futuristic idealization. However, optimization works at the ground reality encompassing the existing population at a specific reference time frame and the projected future growth rate, there by culminating towards a strategy for balancing the two.

Among the various options available to target the young adults orienting, guiding, counseling and nurturing them towards proper career both for education and job opportunities can contribute substantially for diverting their energy and hidden power towards creative and gainful opportunities in the job market. Additionally recreating the power of youth toward development activities involving overall welfare of the country and the people could act as a boost to this approach

Mathematics : the way of bright career

Mathematics is the very base of human civilization. From cutting vegetables to arranging books on the shelves, from tailoring cloth to motion of planets mathematics applies almost every where. From the wonders of the taj mahal, Egyptian pyramids and the learning tower of Pisa to the making of atomic bombs and space crafts including missions to heavenly bodies like planets ,each of these can be unraveled using mathematics .In fact, everything we do in our daily life is governed by mathematics .


Mathematics might make you sweat. But mathematicians do not agree. In fact, they claim that mathematics can be real fun. We practice mathematics without realizing that we are using the same intricate algebraic formulae and complicated geometrical theorems, which used to sent shivers down our spine when we studied them in childhood. Maths may be broadly defined as the scientific study of quantities, including their relationship, operations and measurements expressed by numbers and symbols .It is a tool subject like languages. Its knowledge is essential for understanding of various other subjects .Mathematics has two branches, pure and applied. Pure mathematics is concerned with concepts and ideas that do not necessarily have any immediate practical application .Applied mathematics is concerned with the use of mathematical theories and principles as tools to solve problems in any fields of physics , chemistry , biology , social sciences , earth sciences , business and industry . Work in applied mathematics requires a theoretical background, which enables the mathematician to understand the physical dimensions and technicalities of problems. The study of pure and applied mathematics is interdependent. Mathematics has various major branches ranging from algebra to trigonometry.

With application in a wide variety of occupations like actuarial science, economics, and financial analysis and in meteorology and oceanography, one can not just manage without mathematics. The mathematicians work in operations research, numerical analysis, information and data processing. They work in the field of aviation, in aerodynamics, applied physics, robotics, market research, population studies and commercial surveys and in industrial research and development. A combined degree in mathematics and computer science is suited for jobs in data processing and other allied fields.

Mathematics offers scope for teachers at the school and college level. Reputed teachers may find suitable job opportunities in coaching centers that prepare students for admission to various professional courses. Furthermore, there are always new areas which command the attention of society. Candidate who pass 10+2 with maths are not only eligible for admission to courses relating to engineering and technology , architecture , pharmacy , but also become eligible for seeking admission to bachelor of computer application , bachelor of financial and investment analysis and B.Com. hons. courses. in some universities economics is offered at graduation level only to those who have studied maths at +2 level .


Maths may be offered as a paper in various competitive examinations conducted by the union public service commission, state service commissions. Bsc. and msc. Courses in mathematics are offered by most universities. The BITS Pilani and IIT offer five year integrated courses in mathematics to school leavers . Various universities offer M.A. / M.Sc. in maths through distance learning system . Some of them are Alagappa university, karakudi -6300003 , Annamalai university , Mahatma Gandhi univ. Madurai


The specialised courses in mathematics are available in the following institute , Channai mathematical institute ,92 N chetty road , T Nagar , Channai - 600017, The institute of mathematical sciences , Taramani , Channai -600113 . Mehta research institute of mathematical sciences, Taramani, Channai.

Shortcomings of population statistics in India

In spite of serious efforts by Govt. and various other agencies the population statistics in the country have remained an issue of controversy from various quarters . Some of the short comings are discussed as under :

1. Geographical coverage :

There have generally been found a change in political area from one census to another . Before independence Burma , Pakistan, Bangle- Desh were very much a part of Indian population census . In 1951 princely states were included due to their merger with Indian Union .In this census Jammu and Kashmir although an integral part of the country was not counted for the purpose of population counting .It was only in 1961 census when Jammu and Kashmir although an integral part of the country was not counted for the purpose of population counting .It was only in 1961 census when Jammu and Kashmir was included in the process of population census . In addition to it because of a vast geographical area of the country most of the distant regions are not accessible. An attempt was made to cover such areas in 1961. Under these circumstances the population figures are not totally compared from one period to the other .

2. Definition of Age :

In different censuses the age was defined quite differently .By the year 1921 age was counted as per the year completed .From 1931 age was recorded as the age to the nearest birthday. It was further changed in 1951 and age to the nearest birthday. Since then same process is adopted . In addition to this illustration in this regards . In the past , age of the child was always expressed as in multiples of 5. Even for the marriage purposes the actual age was concealed . Old persons even at for the marriage purposes the actual age was concealed . Old persons even at this progressive world are not aware about their actual age.It looks quite surprising the most of the old persons do not know their actual date of birth even .They have generally been seen coinciding their date of birth with some incident such as war , famine , earth quake etc. Ladies too hide their age to themselves younger to their actual age .

3. Biased information :

At so many occasions it is experienced that the information is given and recorded by the recording personnel's with prejudiced mind . The information regarding insanity , dumbness , deafness is generally concealed .

Significance of Population statistics

1. Useful for research purposes :

The population census are very useful for research . The distribution of population among urban and rural areas, the sex ratio , density of population etc. are important for research of problems.

2. Utility in planning :

Population census provide basic material for formulae of economic and social planning of the country . It determines per capita income and standard of living of the community .

3. Utility in administration and policy :

Population statistics provides the information on demographic and economic features of the population which helps in establishing administrative structure.

4. Utility for business and industry :

The occupational classification of population helps to find out whether in a particular area there is majority of agriculturalists , labourers or businessmen etc. It helps business man in estimating demand for goods in different areas .

5. Utility in transport :

It helps to make transport system more efficient and effective . Population census provide an estimated demand for transport facilities in a region .

6. Utility in education :

Population census provide information regarding literacy ratio i n the country which helps in determining the educational structure of an economy .

7. Utility to electoral rolls

Census data is also useful in determining the electoral rolls .

Type of Correlation

1. Perfect Correlation

When the two variables vary in such a manner that their ratio is always constant , the correlation is said to be perfect .

Consider two variables as diameter and circumference of a circle . We know that circumference is always a fixed number times of diameter . When diameter varies , the circumference also varies and the ratio of variation is always the same . In this case , correlation is perfect .

Perfect correlation is of two types :

(i) Perfect positive correlation

(ii) Perfect negative correlation

When the value of two variables move in the same direction to that an increase in the value of one variable also , and a decrease in the value of one variable is associated with the proportional decrease in the value of other variable also , correlation is said to be positive , if on the other hands , the values of two variables move in different directions , so that with an increase in the value of one variable the value of the other variable , decreases proportionally , correlation is said to be negative .

2. No Correlation

If the change in one variable do not result in change in other , then the two variables are said to be uncorrelated . In this case , there is zero correlation between them.

Coefficient of Correlation

We know that covariance is a measure which indicates by its value the existence of a statistical relationship between two quantitative variables , and indicating by its sign of the nature of the relationship , that is , whether the values of the two variables move in general in the same or opposite directions .
The value of the covariance depends upon the units in which x and y are measured to get rid of this difficulty .

Introduction Of Distribution

We know that two terms " unit of observation and variable of observation are frequency used in frequency distribution. Each recorded or observed value of a variable of observation is associated with a particular person , place , object etc. and that term unit of observation is used to describe what the values of a variable of observation are attached to . Thus , when we are discussing data about examination results , the units of observation are students and the variable of observation is total marks obtained each recorded value of the variable denotes the total marks obtained by a particular student who has appeared in that examination
If there are more than one variable of observation for which values are being observed for each unit of observation , then we say that distribution is multivariate . But we are concerned with two distributions given below :

1. Univariate distribution

A distribution in which there is only variable , is called a univariate distribution. For example , the marks obtained by students of a class form a univariate distribution.

2. Bivariate distribution

A distribution which involves two varriables is called a bivariate distribution . For example , the heights and weights of the students of a class in a school form a bivariate distribution.

In the bivariate distribution of two variables age and sex , one variable age is quantitative variable whereas second variable sex is a qualitative variable. We can have bivariate distributions in which both variables are qualitative or both are quantitative.

Further , if the two variables are denoted by x and y with possible values x1 , x2 ,x3 ......... x n and y1 , y 2 ,y 3 ,.......... yn respectively , the raw data would be represented by ordered pairs like ( x1, x2 ) ,(y1, y2) and so on , there being one ordered pair of value of the variables for each unit of observation. There are mn possible ordered pairs of values (xi ,yi ) , though not every one these m pairs may be observed in any particular situation.

Now we discuss two particular distributions.

• Marginal distribution
• Conditional distribution

Types of Vector

1. Null Vector or Zero Vector

If the initial and terminal points of a vector coincide , then it is called a zero vector clearly its length is zero and it can have any direction .
Note : A null vector has no definite direction.
Unit Vector : A vector whose length is unity is called a unity vector . The unit vector in the
2. direction of vector .
Note 1. Any vector is equal to its modulus multiplied by a unit vector in that direction.
3. Proper Vector
Any non zero vector is called a proper vector .
4. Like and unlike vectors
Vectors having the same direction are called like vectors and vectors having the opposite directions are called unlike vectors .
5. Collinear vectors
Vectors which have the same or parallel support , are called collinear vectors .
6. Coplanar vectors
Vectors which lie in the same plane or parallel to same plane are called coplanar vectors.
7. Co initial vectors
Vectors having the same starting point are called co-initial vectors.
8. Reciprocal Vectors
Two vectors are said to be reciprocal vectors when they have the same direction and product of their lengths is one.
9. Equal vectors
Two vectors are said to be equal if they have

1. the same magnitude
2. the same sense
3. the same or parallel support

10. Localised vector

A vector whose initial point is fixed is called a localised vector.

Example force is a localised vector.

11. Free vector

A vector whose initial point is not fixed is called a free vector .

Operation on vectors

As each vector is either a row vector or column vector , therefore operations on vector are performed in the same way as the operations on matrices .
Geometrical concept of Vectors
Scalar A physical quantity which has magnitude but no direction is called a scalar .
For example mass , volume , temperature are scalars .
Vectors . A physical quantity has magnitude as well as direction is called vector .
For example velocity , acceleration , momentum , force are vectors.

Vectors

An order set of n numbers is called an n vector or a vector of order n . X which is an order set of n number x1, x2 ,x3 ...... , xn can be written in two forms.
The vector x in the first form is known as row vector and vector x in the second form is known as column vector .
The numbers x1, x2 ,x3 ...... , xn are called the components of the vector X .

Random Experiments

The term experiment used in physical science like chemistry and physics is totally different from the statistical experiment . The term experiment used in statistics is in much wider sense . The tossing of a fair die , drawing a card from pack of cards are the operations which are statistically known as trials or experiments . Firstly each trial has a number of possible outcomes which are known , even before the operation is performed and secondly it is definite that one of the outcomes already known to us will occur . While throwing a die we know in advance that any one of the six numbers 1,2,3,4,5,6 corresponding to six faces will come up , but which of these six faces will come up , when thrown cannot be known in advance . It can be determined only when the operation is performed . Such operations when take place without any prejudice or bias are known as random experiments or trials .

Definition of business mathematics

Business mathematics is the branch of mathematics which is helpful for businessmen . Every businessmen is in tension about how to solve different business problems . In these problems we can include , interest calculation , hire rates , salary calculation , tax calculation , Public provident fund calculation , Foreign exchange calculation and more over what is the quantity he should produce etc. Business mathematics is not only helpful for businessmen but also it is helpful for general public because , if they learn it , they can deal with businessmen with better way. Business mathematics is easier than general mathematics . It can learn businessmen very easily . At Graduation and post graduation level , it is the main subject of commerce . Its certain theories are so famous and very useful for businessmen .
You should know that Google search engine also calculate Page rank on the basis of Probability theory . AdSense payment is calculate with page impression , Click through rate (CTR ) and Cost per mile basis . That are the simple example of practical use of mathematics . But if we look every where in different business , we see only business mathematics . Business's all part like Man , money machine and material depends on business mathematics . There are following feature of business mathematics :-

1. It is totally related to business and solution of business problem .
2. It is main branch of general mathematics .
3. Statistics also include in it .
4. Its main feature is also that variety of formulae are in this mathematics , so businessmen have higher option to choose any one best formula for solve their business problem .