QUANTATIVE TECHNIQUE IN MANGEMENT.docx COMLETED

QUANTATIVE TECHNIQUE IN MANGEMENT (COMPLETE PACKAGE) Assignement (A) 1-: Quantitative analysis requires the representation of the problem using a mathematicalmodel. Mathematical modeling is a critical part of the quantitative approach to decision making.Quantitative factors can be measured in terms of money or quantitative units. Examples areincremental revenue, added cost, and initial outlay. Qualitative factors in decision making are the factors relevant to a decision that are difficult tomeasure in terms of money. Qualitative factors may include: (1) effect on employee morale,schedule and other internal elements; (2) relationship with and commitments to suppliers;(3) effect on present and future customers; and (4) long-term future effect on profitability. Insome decision-making situations, qualitative aspects are more important than immediatefinancial benefit from a decision.Different Statistical Techniques Measures of Central Tendency:   For proper understanding of quantitative data, they shouldbe classified and converted into a frequency distribution. This type of condensation of datareduces their  bulk and gives a clear picture of their structure. If you want to know any specificcharacteristics, of the given data or if frequency distribution of one set of data to be comparedwith another, then it is necessary that the frequency distribution itself must be summarized andcondensed in such a manner that it must help us to make useful inferences about the data andalso provide yardstick for comparing different sets of data. Measures of Dispersion: Measures of dispersion would tell you the number of values, whichare substantially different from the mean, median or mode. The commonly used measures ofdispersion are range, mean deviation and standard deviation. Correlation: Correlation coefficient measures the degree to which the change in one variable(the dependent variable) is associated with change in the other variable (Independent one). Forexample, as a marketing manager, you would like to know if there is any relation between theamounts of money you spend on advertising and the sales you achieve. Here, sales are thedependent variable and advertising budget is the independent variable. Correlation coefficient, inthis case, would tell you the extent of relationship between these two variables, whether therelationship is directly proportional (i.e. increase or decrease in advertising is associated withincrease or decrease in sales) or it is an inverse relationship (i.e. increasing advertising isassociated with decrease in sales and vice-versa) or there is no relationship between the twovariables. Regression Analysis: Regression analysis includes any techniques for modeling and analyzingseveral variables, when the focus is on the relationship between a dependent variable and one ormore independent variables. Using this technique you can predict the dependent variables on the basis of the independent variables. In 1970, NCAER (National Council of Applied andEconomic Research) predicted the annual stock of scooters using a regression model in which  real personal disposable income and relative weighted price index of scooters were used asindependent variable. Time Series Analysis: With time series analysis, you can isolate and measure the separateeffects of these forces on the variables. Examples of these changes can be seen, if you startmeasuring increase in cost of living, increase of population over a period of time, growth ofagricultural food production in India over the last fifteen years, seasonal requirement of items,impact of floods, strikes, and wars so on. Index Numbers: An index number is an economic data figure reflecting price or quantitycompared with a standard or base value. The base usually equals 100 and the index number isusually expressed as 100 times the ratio to the base value. For example, if a commodity coststwiceas much in 1970 as it did in 1960, its index number would be 200 relative to 1960. Indexnumbers are used especially to compare business activity, the cost of living, and employment.They enable economists to reduce unwieldy business data into easily understood terms. Sampling and Statistical Inference: In many cases due to shortage of time, cost or nonavailability of data, only limited part or section of the universe (or population) is examinedto (a) get information about the universe as clearly and precisely as possible, and (b)determine the reliability of the estimates. This small part or section selected from theuniverse is called the sample, and the process of selections such a section (or past) is calledsampling.  Example: Site selection process (quantitative and qualitative factors)  While quantitative factors have been and will continue to be very important in the site selection process, qualitative factors are also critical in order to ensure that the company makes the bestdecision. What are the most important quantitative and qualitative factors evaluated by siteselection advisors and companies when making a decision regarding the location of a new orexpanded operation? The list will vary depending on type of facility (i.e. manufacturing,logistics, research & technology, office), but most factors apply to all forms of projects. Below isa summary of the most important quantitative and qualitative factors considered by companies.Quantitative Factors 1.Property Tax Rates  2.Corporate Income Tax Rates  3.Sales Tax Rates  4.Real Estate Costs  5.Utility Rates  6.Average Wage/Salary Levels  7.Construction Costs  8.Worker’s Compensation Rates  9.Unemployment Compensation Rates  10.Personal Income Tax Rates  11.Industry Sector Labor Pool Size  12.Infrastructure Development Costs  13.Education Achievement Levels  14.Crime Statistics  15.Frequency of Natural Disasters  16.Cost of Living Index  17.Number of Commercial Flights to Key Markets  18.Proximity to Major Key Geographic Markets  19.Unionization Rate/Right to Work versusNon-Right to Work State 20.Population of Geographic Area Qualitative Factors1.Level of Collaboration with Government, Educational and Utility Officials  2.Sports, Recreational and Cultural Amenities  3.Confidence in Ability of All Parties to Meet Company’s Deadlines  4.Political Stability of Location  5.Climate  6.Availability of Quality Healthcare  7.Chemistry of Project Team with Local and State Officials  8.Perception of Quality of Professional Services Firms to Meet the Company’s Needs  9.Predictability ofLong-term Operational Costs 10.Ability to Complete Real Estate Due Diligence Process Quickly  Another important part of the site selection evaluation process relates to the weighting of the keyquantitative and qualitative factors. Depending on the type of project, factors will be weighteddifferently. As an example, for a new manufacturing facility project, issues such as utility rates,real estate costs, property tax rates, collaboration with governmental entities, and average hourlywage rates may be weighted more heavily. By contract, for a new office facility factors such asreal estate costs, number of commercial flights, crime statistics, climate and industry sector labor pool size may be more important.Every project is unique and must be evaluated based upon its own individual set ofcircumstances 2-A sample is a group of units selected from a larger group (the population). By studying thesample, one hopes to draw valid conclusions about the larger group.A sample is generally selected for study because the population is too large to study in itsentirety. The sample should be representative of the general population. This is often bestachieved by random sampling. Also, before collecting the sample, it is important that onecarefully and completely defines the population, including a description of the members to beincluded.A common problem in business statistical decision-making arises when we need informationabout a collection called a population but find that the cost of obtaining the information is prohibitive. For instance, suppose we need to know the average shelf life of current inventory. Ifthe inventory is large, the cost of checking records for each item might be high enough to cancelthe benefit of having the information. On the other hand, a hunch about theaverage shelf life might not be good enough for decision-making  purposes. This means we mustarrive at a compromise that involves selecting a small number of items and calculating anaverage shelf life as an estimate of the average shelf life of all items in inventory. This is a   compromise, since the measurements for a sample from the inventory will produce only anestimate of the value we want, but at substantial savings. What we would like to know is how"good" the estimate is and how much more will it cost to make it "better". Information of thistype is intimately related to sampling techniques . Cluster sampling can be used whenever the population is homogeneous but can be partitioned.In many applications the partitioning is a result of physical distance. For instance, in theinsurance industry, there are small" clusters" of employees in field offices scattered about thecountry. In such a case, a random sampling of employee work habits might not required travel tomany of the" clusters" or field offices in order to get the data. Totally sampling each one of asmall number of clusters chosen at random can eliminate much of the cost associated with thedata requirements of management 3-Regression analysis is a powerful technique for studying relationship between dependent variables (i.e., output, performance measure) and independent variables (i.e., inputs, factors, decision variables). Summarizing relationships among the variables by the most appropriate equation (i.e., modeling) allows us to predict or identify the most influential factors and study their impacts on the output for any changes in their current values. Unlike the deterministic decision-making process, such as linear optimization by solving systems of equations, Parametric systems of equations and in decision making under pure uncertainty, the variables are often more numerous and more difficult to measure and control. However, the steps are the same. They are: 1.Simplification 2.Building a decision model 3.Testing the model 4.Using the model to find the solution: ØIt is a simplified representation of the actual situation ØIt need not be complete or exact in all respects ØIt concentrates on the most essential relationships and ignores the less essential ones. ØIt is more easily understood than the empirical (i.e., observed) situation, and hence permits the problem to be solved more readily with minimum time and effort. 5. It can be used again and again for similar problems or can be modified. Fortunately the probabilistic and statistical methods for analysis and decision making under uncertainty are more numerous and powerful today than ever before. The computer makes possible many practical applications. A few examples of business applications are the following: ØAn auditor can use random sampling techniques to audit the accounts receivable for clients. ØA plant manager can use statistical quality control techniques to assure the quality of his production with a minimum of testing or inspection. ØA financial analyst may use regression and correlation to help understand the relationship of a financial ratio to a set of other variables in business. ØA market researcher may use test of significace to accept or reject the hypotheses about a group of buyers to which the firm wishes to sell a particular product. ØA sales manager may use statistical techniques to forecast sales for the coming year. Case study Please read the case study given below and answer questions given at the end.Kushal Arora, a second year MBA student, is doing a study of companies going public for thefirst time. He is curious to see whether or not there is a significant relationship between the sizesof the offering (in crores of rupees) and the price per share after the issue. The data are given below: Size (in 108 3968.40 5110.40 4.40crore ofrupees)Price ( in 12 1319 126.50 4rupees) QuestionYou are required to calculate the coefficient of correlation for the above data set and commentwhat conclusion Kushal should draw from the sample.  Answer:N X Y XY X 2  Y 2  1 12 108 1296 144 116642 13 39 507 169 15213 19 68.4 1299.6 361 4678.564 12 51 612 144 26015 6.5 10.4 67.6 42.25 108.166 4 4.4 17.6 16 19.36TOTALS 66.5 281.2 3799.8 876.25 20592.086(3799.8) - (66.5)(281.2) r=[6(876.25) - (66.5)2[]6(20592.08) - (281.2)2 = 0.67 Conclusion: There is a positive correlation for the above set of data  ASSIGNMENT C Ques 1 : b Ques 11 : b Ques 21 : b Ques 31 : cQues 2 : a Ques 12 : a Ques 22 : c Ques 32 : aQues 3 : c Ques 13 : Ques 23 : b Ques 33 : dQues 4 : a Ques 14 : b Ques 24 : d Ques 34 : bQues 5 : a Ques 15 : a Ques 25 : c Ques 35 : cQues 6 : d Ques 16 : b Ques 26 : c Ques 36 : aQues 7 : a Ques 17 : b Ques 27 : b Ques 37 : aQues 8 : c Ques 18 : a Ques 28 : c Ques 38 : dQues 9 : d Ques 19 : b Ques 29 : b Ques 39 : bQues 10 : d Ques 20 : c Ques 30 : a Ques 40