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Session 1

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Session 1

  1. 1. Quantitative Methods – I Outline of today’s class [QM 105] • General introduction • What is statistics? Class-I: • Introductory examples /problems Course rules and framework • Application to other management Course Overview disciplines Case: Price of flats in Bangalore • Case: Price of flats in Bangalore Data Summarization and Presentation • Data presentation and summarization methods Rules and General Guidelines General Information • Punctuality – Attendance --- code of conduct • Come prepared with the case(s) assigned in the session • Office Location: C 2nd Floor • Phone(ext) 3150 • Bring calculator, text book to class everyday • E-mail shubho@iimb.ernet.in • Question-answers, discussions and CP • Tutors: to be announced • Difficulty level and frame of mind • Moodle will be used for providing/collecting – All lecture presentations (?) • Course objective: different aspects of learning and relative – Announcement importance – Question-banks – Concepts – (Computer) Assignment – Reading material • Register yourself at moodle http://moodle.iimb.ernet.in/ – Key required for registering : Do not share course key with anybody else – Problem solving – Do not allow anybody unauthorized use of your account – Use of software – Upload your picture along with registration How to use – Create discussion group Text-book Question bank What is STATISTICS? Where will you use Statistics? Finance, Marketing DATA PopulationOperations Management,Organization Behaviour Personal Life probability Directly Arrangement or Presentation INFERENCE as a Supervisor Summarization 1
  2. 2. Some Applications in Statistical application in Finance and Accounting Managerial Function • Finance & accounting • Insurance – companies have to estimate how much it is likely to pay to cover a ‘risk’. • Operations management • Investment mgmt -- relationship between • Marketing risk and return • Human resource management – Market model (Regression) • Economics • Portfolio diversification • Information systems • Managerial accounting – prepare budget – Forecast sales, cost Some Applications in Operations Management Price of flats in Bangalore What does the figures convey? 21.32 9.75 32.96 75.27 70.71 108.47 24.72 22.48 65.10 11.36• Product design -- analyze survey result to determine what 15.60 17.01 16.18 12.40 14.60 14.98 17.21 19.62 30.20 20.23 20.87 20.16 79.36 25.32 23.36 17.98 131.33 54.19 81.92 16.05 customers want, feasibility study 102.42 7.46 41.72 55.79 125.85 25.34 17.83 46.53 19.98 49.70 8.53 13.76 18.02 20.28 26.41 27.72 20.94 156.89 6.72 15.04• Facility location in a stochastic world 13.44 86.32 9.73 16.07 49.70 39.38 54.58 43.66 9.04 11.10 47.23 35.09 12.78 22.35 30.12 42.36 30.29 13.08 122.47 40.03• Inventory management 28.72 52.66 54.03 16.29 12.95 65.95 10.37 7.79 47.89 45.18 158.30 86.05 76.94 29.67 27.15 38.97 26.56 11.66 6.55 52.59• Queuing (probability/stochastic process) 38.68 44.44 32.16 11.92 73.00 21.13 13.84 14.05 19.23 18.86 17.83 53.49 40.87 16.66 77.01 6.62 42.11 24.70 28.03 16.06• Project management – PERT/CPM (probability 17.46 53.48 51.54 39.06 47.13 99.93 34.57 43.43 119.37 20.72 62.21 30.41 67.54 24.07 14.52 64.12 17.02 41.55 41.95 21.04 Distribution) 19.05 9.09 133.53 17.23 29.04 22.47 161.98 73.81 54.85 78.70 31.50 41.82 22.20 10.20 74.69 21.51 9.53 49.96 50.77 38.18• Quality control (statistical testing) 37.45 16.14 48.35 41.27 64.07 2.95 39.29 87.68 6.83 28.11 80.09 104.64 32.81 30.44 119.53 26.20 16.03 56.03 26.89 62.26 38.38 86.72 24.60 12.56 7.91 3.48 29.44 34.44 26.72 31.82 33.33 88.31 29.02 11.09 8.91 31.60 58.02 8.10 16.64 41.21 22.79 20.59 23.78 19.07 14.26 45.41 28.41 74.49 33.43 28.38 Forming Class-Intervals • How many intervals? • Equal or unequal width? • Gaps? • Open or close ended? Sturges Formula for no. of class intervals 1 + 3.3log(n) 2
  3. 3. Diagrammatic Representation of Data• Bar diagram (of various kinds) Pie Chart• Pie diagram• Frequency Polygon Data Types (different scale)• Histogram Ratio scale Interval scale• Ogive Ordinal data• Stem and leaf Nominal data• Box-plot Bar Chart Frequency Polygon and Ogive Fig. 1-11 Airline Operating Expenses and Revenues Relative Frequency Polygon Ogive 12 Average Revenues 10 Average Expenses 0.3 1.0 8 0.2 0.5 6 0.1 4 0.0 0.0 0 10 20 30 40 50 0 10 20 30 40 50 2 Sales Sales 0 American Continental Delta Northwest Southwest United USAir •Join the points (class-mark, rel. freq.) to form a polygon; A i r li n e •Can plot frequency or relative frequency density as well. Summary Statistics Features of good diagrammatic conversation within a company dealing with electronics and electrical engineering representation of data • GM: How is demand for contactors and ACBs (Air circuit breakers) in your region Ravi? • Must be self-explanatory • RM: We are doing fine in both, Mr. Kasyap. • Clear labels stating variables • GM: Dont you feel like giving some numbers so that we are in the same page in terms of what we are talking about? • Drawn to scale --- indicate unit • RM: For contactors, the demand is about 25K per month --- well, • Simple and pleasant to look at and useful you know, some months its more and in some its slightly less. But mostly its very close to this figure. Its lot more difficult for me to say about ACB demand as it varies a lot. • GM. But surely you agree that we need to be lot more informative, specially in the case of ACBs, for us to do any kind of planning. • RM: Sir, then, I would say about 30 in a month. (He actually implies 3000 in this case) 3
  4. 4. Frequently Used symbols Chart Summarization Population Sample Characteristic Rest (skewness, kurtursis etc) Mean µ XFrequency distribution Standard deviation σ S Central Tendency Proportion π p Dispersion Size N n Mean Measures of Central tendency • Did you hear about the statistician who had • Objective his head in an oven and his feet in a bucket • MEAN, MEDIAN and MODE of ice? When asked how he felt, he replied, “On the average I feel just fine.” • Computation from grouped or ungrouped data • Relative advantages and disadvantages • Did you know that the great majority of (effect of outliers) people have more than the average number of legs? • Other measures liked truncated or winsorized meanData from 2011 state election winners Source: www.adrindia.org www.myneta.info Inference from Data? Aggregate AvgSl. No. of MLAs wealth (Rs. wealth (Rs • Are WB politicians more honest?No. State analyzed cr) cr) 1 Assam 126 209 1.66 2 West Bengal 294 200 0.68 3 Tamil Nadu 234 932 3.98 4 Kerala 140 199 1.42 5 Pondicherry 30 138 4.59 Total 824 1,678 2.04 4
  5. 5. Computation of summary statistics Computation of mean/median/mode from grouped data: from grouped data Price of flats in Bangalore Mean→ use class mark price range (lakh) frequency n +1 <=10 17 −F 10 to 20 46 Median (m)=Lm + 2 × wm , where Lm , f m , wm are the lower boundary, fm 20 to 30 40 frequency and width of the class containing the median. F denotes the sum 30 to 50 47 of the frequencies of all the classes prior to the median. 50 to 75 25 75 to 100 13 100 to 135 9 d1 Mode (M )=LM + × wM , where d1 = f M − f −1 , d 2 = f M − f1 > 135 3 d1 + d 2 5

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