QT

Quantitative Methods

rishabIntroduction to Quantitative MethodWhy should I care to study this subject?

What is your view on this?What are we dealing with? QM in BusinessQM helps managers to Identify, Collect, Interpret, Analyze, and Manipulating Data

Why?Because managers need answers.Why managers need answers?Because managers have to take decisions.Why managers need to take decisions?TO REMAIN IN THE BUSINESS

Some more questions about QMDo managers really need QM to take decisions?Do managers use mathematics while thinking about a problem and finding the solution and then take the decision?Yes or NoMost of the problems require quick solutions and many a times a manager has to take a shot based on intuition.

How does QM help managers to take quick decisions?By mastering the skill of quick decision making How does one master this skill? Use QM.

Some applications of quantitative methodsMarketing Electronic point-of-sale scanners at retail checkout counters are used to collectdata for a variety of marketing research applications.Production A variety of statistical quality control charts are used to monitorthe output of a production process.FinanceFinancial advisors use price-earning ratios and dividend yields to guide their investment recommendations.

Syllabus Scales of Measurement: Nominal, Ordinal, Interval, and Ratio Scale

Probability: Fundamentals, Addition Theorem, Multiplication Theorem, Bayes Theorem, Random Variable

Probability Distributions: Binomial, Poisson and Normal Distribution

Sampling and Sampling Distributions: Population, Sample, Types of Sampling, Sampling Distributions, Standard Errors, Sampling from Normal and Non-normal Population, Central Limit Theorem, Finite Population ParametersSyllabus Estimation: Point and Interval Estimation, Confidence Intervals, Interval estimates of Mean and Proportion from Large Samples, Interval Estimation using t-distribution, Sample size for estimating means and proportionsHypothesis: Null, Alternate Hypothesis, Steps of Formulating HypothesesTesting of Hypotheses: Basic Concepts, Type I and Type II Errors, One Tailed and Two Tailed Tests, One Sample Tests, Hypothesis Testing of Means when Population Standard Derivation is Known and when Unknown, Hypothesis Testing of Proportions for Large Samples. Two Sample Tests for Equality of Means for Large and Small Samples, Equality of Means for Dependent Samples, Difference between Proportions for Large Samples. CoverageChi-Square: Chi Square Test of Independence. and Goodness of fit. Analysis of Variance (One Way ANOVA): Test for Equality of Means. Inference about a population variance and about two population variances. Bivariate analysis: Bivariate correlation and regression, Coefficient of determination, assumptions in the regression model, tests of significance for the correlation and regression coefficients.

SyllabusTime Series Analysis: Components of Time Series, Trend Analysis- Moving Average, Fitting linear and second degree trends, Seasonal Variation (Computing using Ratio to Trend Method), Cyclical Variation. Irregular Variation, Problems Involving All Four Components of Time Series. Decision Trees: Decision Tree Analysis-Expected value under risk, under perfect information, and under sample information. Linear Programming, Transportation and Assignment problems: Formulating Linear Programming Problems, Graphical approach, Formulation of Transportation and Assignment problems, Solutions using Excel solver and other software.

Case Studies ICICI Banks Get up to 100% Cash Back offerReal FoodsSolnyx Pharmaceuticals: The Atoxeril Clinical TrialCare HygieneHindustan FoodsRoja SilksRam PublishersAlexander Machine CompanyBest FibreLakshmi Engines

Text Books 1.Louise Swift and Sally Piff (2010), Quantitative Methods for business, management and finance, 3rd Edition, Palgrave Macmillan.2.Anderson, Sweeney and Williams (2011), Statistics for Business and Economics, 9th Edition, Cengage Learning3.Levine, Stephan, Krehbiel and Berenson (2010), Statistics for Managers, 5th Edition, PHI

Scales of MeasurementNominal ScaleOrdinal ScaleInterval ScaleRatio ScaleNominal ScaleTagOrdinal ScaleRank

Interval ScaleDifferenceRatio ScaleProportionTrue Zero Scales of Measurement

Introduction to ProbabilityExperiments, Counting Rules, and Assigning ProbabilityEvents and their probabilitiesBasic Relationships of ProbabilityConditional ProbabilityBayes TheoremProbability : Measure of Chance of Favorable Occurrence 01.5Increasing Likelihood of OccurrenceProbability:The eventis veryunlikelyto occur.The occurrenceof the event is just as likely asit is unlikely.The eventis almostcertainto occur.An Experiment and its Sample SpaceAn experiment is any process that generates well-defined outcomesThe sample space for an experiment is the set of all experimental outcomesAn experimental outcome is also called a sample pointAssigning Probability Classical MethodRelative Frequency MethodSubjective MethodClassical Method If an experiment has n possible outcomes, this method would assign a probability of 1/n to each outcome.Experiment: Rolling a dieSample Space: S = {1, 2, 3, 4, 5, 6}Probabilities: Each sample point has a 1/6 chance of occurringExampleRelative Frequency MethodEach probability assignment is given bydividing the frequency (number of days) bythe total frequency (total number of days).4/40ProbabilityNumber ofPolishers RentedNumberof Days01234 4 61810 240 .10 .15 .45 .25 .051.00Subjective Method When economic conditions and a companys circumstances change rapidly it might be inappropriate to assign probabilities based solely on historical data. We can use any data available as well as our experience and intuition, but ultimately a probability value should express our degree of belief that the experimental outcome will occur. The best probability estimates often are obtained by combining the estimates from the classical or relative frequency approach with the subjective estimate.Event and their Probabilities An event is a collection of sample points. The probability of any event is equal to the sum of the probabilities of the sample points in the event. If we can identify all the sample points of an experiment and assign a probability to each, we can compute the probability of an event.Some Basic Probability RelationshipsThere are some basic probability relationships thatcan be used to compute the probability of an eventwithout knowledge of all the sample point probabilities. Complement of an Event Intersection of Two Events Mutually Exclusive EventsUnion of Two EventsCompliment of an Event The complement of A is denoted by Ac. The complement of event A is defined to be the event consisting of all sample points that are not in A.Event AAcSampleSpace SVennDiagramUnion of Two Event The union of events A and B is denoted by A B The union of events A and B is the event containing all sample points that are in A or B or both.SampleSpace SEvent AEvent BIntersection of Two Events The intersection of events A and B is denoted by A The intersection of events A and B is the set of all sample points that are in both A and B.SampleSpace SEvent AEvent BIntersection of A and BAddition Law The addition law provides a way to compute the probability of event A, or B, or both A and B occurring. The law is written as:

P(A B) = P(A) + P(B) - P(A BMutually Exclusive Events Two events are said to be mutually exclusive if the events have no sample points in common. Two events are mutually exclusive if, when one event occurs, the other cannot occur.SampleSpace SEvent AEvent B