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 Population
Operations Management,
Organization Behaviour Personal Life
probability
Directly Arrangement
or Presentation INFERENCE
as a Supervisor Summarization
1

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)
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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 ACB's (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: Don't 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 it's more and in some it's slightly less. But
mostly it's very close to this figure. It's 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 ACB's, 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)
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4. Frequently Used symbols Chart
Summarization
Population Sample
Characteristic
Rest (skewness, kurtursis etc)
Mean µ X
Frequency 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 mean
Data from 2011 state election winners
Source: www.adrindia.org www.myneta.info Inference from Data?
Aggregate Avg
Sl. 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
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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
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