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CHAPTER 1

INTRODUCTION:

The techniques discussed in this section are classical statistical methods asopposed to EDA techniques. EDA and classical techniques are not mutuallyexclusive and can be used in a complementary fashion. For example, theanalysis can start with some simple graphical techniques such as the 4-plotfollowed by the classical confirmatory methods discussed herein to providemore rigorous statements about the conclusions. If the classical methodsyield different conclusions than the graphical analysis, then some effortshould be invested to explain why. Often this is an indication that some of the assumptions of the classical techniques are violated categories:

1. Interval estimation2. Hypothesis tests

1. Interval Estimates

It is common in statistics to estimate a parameter from a sample of data. Thevalue of the parameter using all of the possible data, not just the sample data,is called the population parameter or true value of the parameter. Anestimate of the true parameter value is made using the sample data. This is

called a point estimate or a sample estimate.For example, the most commonly used measure of location is the mean. The

population, or true, mean is the sum of all the members of the given population divided by the number of members in the population. As it istypically impractical to measure every member of the population, a randomsample is drawn from the population. The sample mean is calculated bysumming the values in the sample and dividing by the number of values inthe sample. This sample mean is then used as the point estimate of the

population mean.

Interval estimates expand on point estimates by incorporating the uncertaintyof the point estimate. In the example for the mean above, different samplesfrom the same population will generate different values for the sample mean.An interval estimate quantifies this uncertainty in the sample estimate bycomputing lower and upper values of an interval which will, with a givenlevel of confidence (i.e., probability), contain the population parameter.



2. Hypothesis Tests

Hypothesis tests also address the uncertainty of the sample estimate.However, instead of providing an interval, a hypothesis test attempts torefute a specific claim about a population parameter based on the sampledata. For example, the hypothesis might be one of the following:• the population mean is equal to 10• the population standard deviation is equal to 5• the means from two populations are equal• the standard deviations from 5 populations are equalTo reject a hypothesis is to conclude that it is false. However, to accept ahypothesis does not mean that it is true, only that we do not have evidence to

believe otherwise. Thus hypothesis tests are usually stated in terms of both a

condition that is doubted (null hypothesis) and a condition that is believed(alternative hypothesis).A common format for a hypothesis test is:H0: A statement of the null hypothesis, e.g., two population means are equal.Ha: A statement of the alternative hypothesis, e.g., two population means arenot equal.

Test Statistic: The test statistic is based on the specific hypothesis test.Significance Level: The significance level, , defines the sensitivity of the

test. A value of = 0.05 means that we inadvertently reject the null hypothesis5% of the time when it is in fact true. This is also called the type I error. Thechoice of is somewhat arbitrary, although in practice values of 0.1, 0.05, and0.01 are commonly used.The probability of rejecting the null hypothesis when it is in fact false iscalled the power of the test and is denoted by 1 - . Its complement, the

probability of accepting the null hypothesis when the alternative hypothesisis, in fact, true (type II error), is called and can only be computed for aspecific alternative hypothesis.

Critical Region:

The critical region encompasses those values of the test statistic that lead toa rejection of the null hypothesis. Based on the distribution of the test



statistic and the significance level, a cut-off value for the test statistic iscomputed. Values either above or below or both (depending on the directionof the test) this cut-off define the critical region.

Quantitative analysis is now extended & several aliases of businessoperation & responsibilities probably the most effective approach tohandling of some types of decision problems. A significant benefit of attaining some degree of proficiency with quantitative methods is exhibitedin the way problems are formulated. A problem has to well defined before itcan be formulated in a well structure framework for solution.

The 2 different divisions of quantitative techniques are:-

1) Business statistics

2) 2) Operative Researches

BUSINESS STATISTICS

Statistical data & statistical method are of immense helping the proper understanding of the economic problem & in the formulations of economic

policies as well as evaluating of their effect for example in order to check the overgrowing population, if emphasis has been placed on family planning

methods one can ascertain statistically the efficiency of such methods inattaining the desired goals.

OPERATION RESEARCH

It is the application of scientific methods, technique & tools to problemsinvolving the operation of system. So as to provide these in control of operation & optimum solution to the problem.The modus of operandi of each are:-



1. Formulate the problem2. Analyze the data & collection of data3. Analyze the dataa. central tendencyi) meanii) medianiii) mode

b. Dispersioni) Standard deviationii) Mean deviationiii) Skew ness

CORRELATION, REGRESSION ANALYSIS ETC.Testing

Hypothesis be it data & accurate to what extentInterpret the result



SCOPE OF QUANTATIVE TECHNJQUES:

In ancient times the scope of statistics was limited but now a days thescope of statistics is so vast and ever expanding that it is difficult todefine it. Statistics is a tool of all sciences indispensable to research andintelligent judgment and has become a recognized discipline in its ownright. The scope of statistics stretches over all those branches of humanknowledge in which a grasp of the significance of large numbers islooked for. The scope of statistics iswide,the limiting factor being itsaccountability to studies of quantitative character alone. However, thescope of statistics may be discussed under three main headings.

1. Division of statistics

2. Importance of statistics

3.Application of statistics in various disciplines

OBJECTIVES OF QUANTITATIVE TECHNIQUES:

1. It simplifies complexity.

2. Statistics presents facts in a definite and precise form.

3. Statistics provides comparison.

4. Statistics studies the relationship between different facts.

5. Statistics helps in formulation of policies and measures their effects.6. It formulates and tests hypothesis.



CHAPTER-2

• USES OF PICTORIAL DIAGRAMS

We can use various diagrams, charts and graphs to interpret theavailable data.

The different types of diagrams used are:

• CIRCLE GRAPH



A circle graph is a graph in the form of a circle that is divided in sectors,

with each sector representing of a set of data.

Here is the circle graph showing the total expenditure on education including

the tuitions fees, transportation, books, board and room.

POLYGON GRAPH

To represent discrete series by polygons, the values of the variableand the corresponding frequencies are plotted as points with the help

of rectangular co-ordinates.

The graph below shows the minimum hourly wages of the federal

employees.



A graph that uses points connected by lines to show howsomething changes in value (as time goes by, or as

something else happens).



Visual presentation of data using icons, pictures, symbols,etc., in place of or in addition to common graph elements(bars, lines, points). Pictographs use relative sizesor repetitions of the same icon, picture, or symbol to show

comparison. Also called pictogram, pictorial chart, pictorialgraph, or picture graph.

It consists of a set of continuous rectangles one over each class intervalhaving their areas proportional to the class frequencies.

The class interval is taken on the x axis and the class frequencies on the y

axis.

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OBJECTIVES OF THE STUDIES

The objectives of the study is to find out:

1. Uses of quantitative techniques in day to day business activities.

2. To analyses a business situation using tools of quantitative techniques.

3. To study the definitive terms of quantitative techniques.



Graph showing the total monthly expenses of a family on different

things like food, rent, education, recreation, miscellaneous and

savings.



• BAR GRAPHS

The bar graph is a graphical representation of discretefrequency distribution. In its construction the differentvalues of the variables are taken as points on the x axisand at each of these points a perpendicular line isdrawn to represent the corresponding frequencies.

A graph consisting of parallel, usually vertical bars orrectangles with lengths proportional to the frequency with



which specified quantities occur in a set of data. Also calledbar chart .

CONCLUSION:

We can conclude from the above data that the quantitative techniques can be used to collect, analyze and interpreting numerical facts and takingdecisions on the basis of the quantitative data.

“Statistics is a science and an art which deals with collection,

classification, tabulation, presentation, establishment of relationship,interpretation of data in connection with social, economics, natural

and other problems so that the predetermined aims can be achieved”



CHAPTER-3

USES OF PICTORIAL DIAGRAMS TO ANALYZE REAL LIFEBUSINESS SITUATIONS

A survey by Morgan Stanley shows that India is likely to receive $80 billion of foreign direct investment (FDI) over the next 12-24 months.India has received FDI of $48 billion over the past two years. Thisevidence lends conviction to the company's forecast of $70 billion of FDIover the coming two years. The survey says that global companies see a

big opportunity in India's growing market, though they consider

infrastructure to be a bottleneck. India still doesn't appear to rank highlyas a FDI destination. At the sector level, metals and mining, technologyand auto are likely to gain market share in the total FDI inflows. Telecomhas been the biggest recipient of FDI over time.

CONTENTS



• OBJECTIVES OF THE STUDY

• CHAPTER-1 : INTRODUCTION

• CHAPTER-2: USES OF PICTORIAL DIAGRAM

• CHAPTER-3: USES OF PICTORIAL DIAGRAMS TOANALYSES A BUSINESS SITUATION

• CONCLUSION



The following data shows the power generation by major energy sourcesthe thermal, hydro, nuclear and Bhutan import.

It also gives information regarding the sector wise generation share andthe fuel wise generation share in the country.

POWER GENERATION BY MAJOR ENERGY SOURCES

NUCLEAR 4

HYDRO 25

THERMAL 70

BHUTAN IMPORT 1.3

SECTOR WISE GENERATION SHARE

CENTRAL 42

PRIVATE 42

STATE 16



PROJECT WORK

ON

QUANTITATIVE TECHNIQUES

FOR THE REQUIREMENT OF THE

AWARD OF PGDM

SUBMITTED TO: SUBMITTED BY:

RUPALI MAM ASEEM SINGH CHAUHAN

PGDM SEM 1

ASIAN BUSINESS SCHOOL

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