Business Statistics Hand Written Notes

Business Statistics Hand Written Notes

Business Statistics Hand Written Notes:- B.BA or Bachelor of commercial enterprise administration is an undergraduate enterprise control route. The length of Bachelor of commercial enterprise management is 3-4 years, divided into several semesters. The path can be pursued either as a full-Time Graduate course or element-Time Graduate path i.e. through Correspondence or Distance schooling depending upon one’s choice. B.BA is regularly referred as B.B.A. (preferred) or B.B.A. bypass course. it’s far fashionable inside the sense that it is not challenge unique, and you’ll be able to pick numerous mixtures of topics, apart from 1-2 obligatory topics. these mixtures range from institute to institute. Bachelor’s diploma programs in commercial enterprise management are also recognized with the aid of various names in exclusive institutes; B.B.S. (Bachelor of enterprise research), B.M.S. (Bachelor of control studies) and so on. are guides which are greater or much less the same element. B.B.A direction is designed to offer fundamental know-how approximately control training and to teach the students in communique billies correctly which inculcate entrepreneurship talents. the scholars are prepared to explor Business Statistics Notes possibilities being newly created in control profession. enterprise management study method entails schooling via practical revel in within the shape of case studies, projects, displays, industrial visits, and interplay with specialists from the enterprise.



The purpose of this paper is to inculcate and analytical ability among the students. 



INTRODUCTORY : Meaning, Scope, Importance and Limitations of Statistics. 


STATICALLY INVESTIGATION: Planning of statistical investigation, census and sampling methods Collection of Collection of Primary and Secondary data, Statistical errors and approximation, classification and Tabulation of data, Frequency distribution. 


DIAGRAMMATIC AND GRAPHIC PRESENTATION: One Dimensional. Two dimensional Diagrams Histogram, Historigram, Frequency polygon. Frequency curve and give curves. Graphs on Natural and semi- Logarithmic scales Graphic location of mode Median and quartiles. 


STATISTICAL AVERAGE: Arithmetic, geometric and Harmonic means, Mode Median, Qualities and percentiles, Simple and weighted averages. Uses and Limitations of different averages. 


DISPERSION AND SKEW NESS: Range Quartile deviation mean, Deviation and their coefficients, Standards deviation coefficient of variation , Skew ness and its coefficients. 


CORRELATION: Kari person’s coefficient of correlation, Probable Error and interpretation of coefficient of correlation Rank Difference Method and Concurrent Deviation method. 


ANALYSIS OF TIME SERIES: Component of time Series, calculation of Secular Trend-Moving Average method and method of Least squares. 


INDEX NUMBERS: Utility of index numbers. Problems in the construction of index numbers, simple and weighted index number, Base shifting fishers ideal index number and tests of Reversibility.. 


INDIAN STATISTIC: Census Price, Agriculture and industrial statistics. 

Suggested Readings 1. D.N. Elhance, Fundamentals of Statistics. 2 S.P. Singh, Hiper PAGITTI 3. K.N. Nagar, Hifi HGT||  R.P. Hooda, Statistics for business and Economics.

Hand Written Notes Paid : Download

Structure of Business Statistics

  • Introduction
  • Meaning and Definitions of Statistics
  • Types of Data and Data Sources
  • Types of Statistics
  • Scope of Statistics
  • Importance of Statistics in Business
  • Limitations of statistics
  • Summary
  • Self-Test Questions
  • Suggested Readings

Introduction (Business Statistics Hand Written Notes)

For a layman, ‘facts’manner numerical information expressed in quantitativeterms. This information might also relate to gadgets, subjects, activities, phenomena, or regions of area. As a count number of fact, data have no limits as to their reference, coverage, and scope. at the macro level, those are records on gross countrywide product and shares of agriculture, manufacturing, and offerings in GDP (Gross domestic Product).

at the micro degree, character firms, howsoever small or large, produce vast facts on their operations. the yearly reports of corporations incorporate sort of facts on income, manufacturing, expenditure, inventories, capital employed, and other sports. these facts are regularly field statistics, amassed through employing medical survey techniques. unless regularly updated, such information are the made from a one-time effort and have constrained use past the state of affairs which can have called for their collection. A pupil is aware of data more in detail as a topic of take a look at like economics, arithmetic, chemistry, physics, and others. it’s far a subject, which scientifically deals with records, and is regularly described as the technological know-how of records. In managing data as information, facts has advanced suitable methods of collecting, offering, summarizing, and analysing information, and for that reason includes a body of these methods.

That Means And Defination Of information

inside the starting, it could be mentioned that the word ‘statistics’ is used instead apparently in senses plural and singular. in the plural experience, it refers to a set of figures or records. inside the singular feel, information refers back to the complete body of tools that are used to collect statistics, organise and interpret them and, sooner or later, to draw conclusions from them. It have to be cited that both the aspects of statistics are vital if the quantitative records are to serve their motive. If facts, as a subject, is insufficient and consists of terrible method, we could not understand the proper manner to extract from the statistics the facts they comprise. in addition, if our facts are defective or that they’re inadequate or misguided, we couldn’t reach the right conclusions despite the fact that our concern is properly advanced.

A.L. Bowley has defined information as: (i) information is the technological know-how of counting, (ii) statistics may also rightly be referred to as the technological know-how of averages, and (iii) information is the science of size of social organism seemed as an entire in all its mani-

Festations. Boddington defined as: statistics is the technological know-how of estimates and chances. further, W.I. King has defined statistics in a wider context, the science of information is the approach of judging collective, herbal or social phenomena from the outcomes received through the evaluation or enumeration or series of estimates.

Seligman explored that statistics is a technological know-how that offers with the methods of accumulating, classifying, supplying, comparing and deciphering numerical information accrued to throw a few mild on any sphere of enquiry. Spiegal defines statistics highlighting its position in choice-making especially beneath uncertainty, as follows: statistics is worried with scientific method for accumulating, setting up, summa rising, providing and analyzing data as well as drawing valid conclusions and making affordable choices on the basis of such evaluation. in keeping with Prof. Horace Secrist, facts is the mixture of records, affected to a marked volume through multiplicity of reasons, numerically expressed, enumerated or anticipated consistent with reasonable requirements of accuracy, amassed in a systematic way for a pre-determined cause, and placed on the subject of each other.


Statistical data are the basic raw material of statistics. Data may relate to an activity of our interest, a phenomenon, or a problem situation under study. They derive as a result of the process of measuring, counting and/or observing. Statistical data, therefore, refer to those aspects of a problem situation that can be measured, quantified, counted, or classified. Any object subject phenomenon, or activity that generates data through this process is termed as a variable. In other words, a variable is one that shows a degree of variability when successive measurements are recorded. In statistics, data are classified into two broad categories: quantitative data and qualitative data. This classification is based on the kind of characteristics that are measured.
Quantitative data are those that can be quantified in definite units of measurement. These refer to characteristics whose successive measurements yield quantifiable observations. Depending on the nature of the variable observed for measurement, quantitative data can be further categorized as continuous and discrete data.

Obviously, a variable may be a continuous variable or a discrete variable.

(i) Continuous data represent the numerical values of a continuous variable:-  A continuous variable is the one that can assume any value between any two points on a line segment, thus representing an interval of values. The values are quite precise and close to each other, yet distinguishably different. All characteristics such as weight, length, height, thickness, velocity, temperature, tensile strength, etc., represent continuous variables. Thus, the data recorded on these and similar other characteristics are called continuous data. It may be noted that a continuous variable assumes the finest unit of measurement. Finest in the sense that it enables measurements to the maximum degree of precision.
(ii) Discrete data are the values assumed by a discrete variable:- A discrete variable is the one whose outcomes are measured in fixed numbers. Such data are essentially count data. These are derived from a process of counting, such as the number of items possessing or not possessing a certain characteristic. The number of customers visiting a departmental store everyday, the incoming flights at an airport, and the defective items in a consignment received for sale, are all examples of discrete data.
(iii) Qualitative data refer to qualitative characteristics of a subject or an object :- A characteristic is qualitative in nature when its observations are defined and noted in terms of the presence or absence of a certain attribute in discrete numbers. These data are further classified as nominal and rank data.
(iv) Nominal data are the outcome of classification into two or more categories of items or units comprising a sample or a population according to some quality characteristic. Classification of students according to sex (as males and (females), of workers according to skill (as skilled, semi-skilled, and unskilled), and of employees according to the level of education (as matriculates, undergraduates, and post-graduates), all result into nominal data. Given any such basis of classification, it is always possible to assign each item to a particular class and make a summation of items belonging to each class. The count data so obtained are called nominal data.
(v) Rank data, on the other hand, are the result of assigning ranks to specify order in terms of the integers 1,2,3, …, n. Ranks may be assigned according to the level of performance in a test. a contest, a competition, an interview, or a show. The candidates appearing in an interview, for example, may be assigned ranks in integers ranging from I to n, depending on their performance in the interview. Ranks so assigned can be viewed as the continuous values of a variable involving performance as the quality characteristic.
Data sources could be seen as of two types, viz., secondary and primary. The two can be defined as under:
(vi) Secondary data: They already exist in some form: published or unpublished – in an identifiable secondary source. They are, generally, available from published source(s), though not necessarily in the form actually required.
(vii) Primary data: Those data which do not already exist in any form, and thus have to be collected for the first time from the primary source(s). By their very nature, these data require fresh and first-time collection covering the whole population or a sample drawn from it.

Assessments of Sekewness Business Statistics Hand Written Notes

a good way to confirm whether or not a distribution is skewed or now not the subsequent checks can be applied. Skewness is present if:
1. The values of mean, median and mode do not coincide.

2. when the information are plotted on a graph they do no longer give the normal bell- shaped shape i.e. whilst cut along a vertical line via the centre the 2 halves are not same.
3. The sum of the superb deviations from the median is not identical to the sum of the terrible deviations.
4. Quartiles are not equidistant from the median.

5. Frequencies are not similarly dispensed at factors of equal deviation from the mode.
on the contrary, when skewness is absent, i.e. in case of a symmetrical distribution, the following situations are glad:
1. The values of mean, median and mode coincide.

2. statistics whilst plotted on a graph supply the normal bell-fashioned shape.

3. Sum of the nice deviations from the median is identical to the sum of the bad deviations.

4. Quartiles are equidistant from the median.

5. Frequencies are similarly disbursed at factors of identical deviations from the mode.


There are four measures of skewness, every divided into absolute and relative measures. The relative degree is referred to as the coefficient of skewness and is more regularly used than absolutely the measure of skewness. further, while a assessment among two or extra distributions is involved, it’s miles the relative measure of skewness, which is used. The measures of skewness are: (i) Karl Pearson’s degree, (ii) Bowley’s degree, (iii) Kelly’s degree, and (iv) moment’s degree. those measures are mentioned in brief underneath:

MEASURES OF SKEWNESS Business Statistics Hand Written Notes

There are four measures of skewness, each divided into absolute and relative measures. The relative degree is known as the coefficient of skewness and is extra regularly used than the absolute degree of skewness. further, when a contrast between or greater distributions is concerned, it’s far the relative degree of skewness, that’s used. The measures of skewness are: (i) Karl Pearson’s degree, (ii) Bowley’s degree, (iii) Kelly’s degree, and (iv) moment’s measure. these measures are discussed in short under:

Example 3.12: From the following data, calculate the measure of skewness using the mean, median and standard deviation:


X 10 – 20 20 – 30 30 – 40 40 – 50 50-60 60 – 70 70 – 80
f 18 30 40 55 38 20 16




MVx dx F fdx 2


10 – 20 15 -3 18 -54 162 18
20 – 30 25 -2 30 -60 120 48
30 – 40 35 -1 40 -40 40 88
40-50 45=a 0 55 0 0 143
50 – 60 55 1 38 38 38 181
60 – 70 65 2 20 40 80 201
70 – 80 75 3 16 48 144 217
Total 217 -28 584

a = Assumed mean = 45, cf = Cumulative frequency, dx = Deviation from assumed mean, and i = 10


Skewness            =          3 (Mean – Median)

=          3 (43.71 – 43.82)

=          3 x -0.011

=          -0.33


BBA Organisation Behaviour Question Paper 2018-2020

Regression Analysis



In business, several times it will become vital to have a few forecast in order that the management can take a decision concerning a product or a specific course of action. if you want to make a forecast, one has to ascertain some relationship among or extra variables relevant to a particular scenario. for example, a company is fascinated to recognise how a long way the call for for tv units will increase within the next 5 years, retaining in thoughts the growth of populace in a sure town. here, it actually assumes that the boom in populace will result in an increased demand for tv sets. thus, to decide the nature and quantity of dating among those variables turns into crucial for the employer.
Inside the preceding lesson, we studied in a few intensity linear correlation between variables. right here we’ve got a comparable issue, the affiliation among variables, except that we increase it further in two respects. First, we discover ways to build statistical models of relationships between the variables to have a higher expertise of their functions. 2d, we expand the models to bear in mind their use in forecasting.
For this motive, we need to use the method – regression evaluation – which paperwork the challenge-be counted of this lesson.

what is Regression

In 1889, Sir Francis Galton, a cousin of Charles Darwin posted a paper on heredity, “natural Inheritance”. He suggested his discovery that sizes of seeds of candy pea flora appeared to “revert” or “regress”, to the mean size in successive generations. He also suggested consequences of a study of the relationship between heights of fathers and heights of their sons. A instantly line became fit to the information pairs: height of dad versus peak of son. here, too, he found a “regression to mediocrity” The heights of the sons represented a motion away from their

fathers, towards the common top. We credit score Sir Galton with the concept of statistical regression.
at the same time as most programs of regression analysis can also have little to do with the “regression to the imply” found by means of Galton, the term “regression” remains. It now refers to the statistical approach of modeling the connection among or more variables. In wellknown sense, regression evaluation manner the estimation or prediction of the unknown price of one variable from the regarded cost(s) of the opposite variable(s). it’s miles one of the maximum vital and widely used statistical techniques in nearly all sciences – natural, social or physical.
In this lesson we are able to focus best on simple regression –linear regression concerning simplest two variables: a based variable and an independent variable. Regression analysis for studying greater than variables at a time is referred to as multiple regressions.

Unbiased and dependent Variables

simple regression includes handiest two variables; one variable is anticipated by means of another variable. The variable to be expected is referred to as the based variable. The predictor is known as the independent variable, or explanatory variable. for instance, whilst we are trying to predict the call for for tv sets on the basis of population growth, we’re using the call for for television sets because the structured variable and the populace growth as the unbiased or predictor variable.
The choice, as to which variable is which once in a while, causes problems. often the selection is apparent, as in case of demand for tv sets and populace increase because it would make no sense to indicate that populace increase can be depending on television call for! The population growth must be the independent variable and the television call for the structured variable.

If we’re uncertain, right here are some factors that might be of use:

  • if we’ve manage over one of the variables then this is the impartial. as an example, a manufacturer can determine how much to spend on advertising and expect his income to be structured upon how a lot he spends.
  • it there may be any lapse of time among the two variables being measured, then the latter ought to depend on the previous, it can’t be the other way spherical.
  • if we need to predict the values of one variable from your knowledge of the alternative variable, the variable to be anticipated should be dependent on the known one.

Linar Regression Notes Business Statistics Hand Written Notes

The challenge of bringing out linear courting consists of growing methods of fitting a straight line, or a regression line as is frequently known as, to the data on two variables.

The road of Regression is the graphical or courting representation of the exceptional estimate of 1 variable for any given cost of the opposite variable. The nomenclature of the road depends on the impartial and established variables. If X and Y are variables of which courting is to be indicated, a line that gives great estimate of Y for any fee of X, it’s far referred to as Regression line of Y on X. If the structured variable modifications to X, then exceptional estimate of X with the aid of any cost of Y is called Regression line of X on Y.

Now imagine this experiment is repeated two hundred times, we may additionally anticipate ‘no head’ and ‘3 heads’ will each arise 25 times; ‘one head’ and ‘two heads’ each will arise 75 times. considering that these outcomes are what we count on on the idea of principle, the resultant distribution is referred to as a theoretical or expected distribution.

However, whilst the experiment is honestly executed 200 instances, the effects, which we can also absolutely attain, will generally differ from the theoretically anticipated consequences. it’s miles quite possible that in actual experiment ‘no head’ and ‘three heads’ may additionally occur 20 and 28 instances respectively and ‘one head’ and ‘ heads’ might also occur sixty six and 86 times respectively. The distribution so obtained via real test is known as the empirical or located distribution.

In exercise, but, assessing the opportunity of each feasible value of a random variable through real experiment can be tough, even impossible, especially while the probabilities are very small. however we may be able to discover what form of random variable the one at hand is by using inspecting the causes that make it random. understanding the type, we can regularly approximate the random variable to a trendy one for which convenient formulae are to be had.

The right identity of experiments with certain regarded methods in possibility concept can help us in writing down the chance distribution feature. such tactics are the Bernoulli system and the Poisson system. the usual discrete chance distributions that are consequent to these processes are the Binomial and the Poisson distribution. we will now check out the conditions that symbolize these procedures, and examine the same old distributions related to the approaches. this may enable us to perceive situations for which those distributions apply.

allow us to first have a look at the Bernoulli random variable, named so in honor of the mathematician Jakob Bernoulli (1654-1705). it’s far the building block for other random variables and the ensuing distributions we can have a look at on this lesson.

The surveys are involved with the attributes of sure entities, inclusive of enterprise corporations, human beings, etc. The attributes that are the object of the take a look at are referred to as traits and the devices owning them are called the elementary gadgets.

The combination of primary gadgets to which the conclusions of the take a look at observe is named as populace| universe, and the units that form the premise of the sampling method are known as sampling devices. The sampling unit can be an standard unit.

The sample is described as an aggregate of sampling gadgets without a doubt chosen in obtaining a consultant subset from which inferences approximately the population are drawn. The body— a list or directory, defines all of the sampling units within the universe to be protected. This body is both constructed for the purpose of a particular survey or might also encompass formerly available description of the populace; the latter is the commonly used method. for instance, cellphone listing can be used as a frame for conducting opinion surveys in a city or locality.

just so, sampling effects mirror the characteristics of the population, it’s far necessary that the sample selected for have a look at should be


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