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QUANTITIVE METHODS OF BUSINESS
NARSEE MONJEE COLLEGE OF COMMERCE AND
ECONOMICS
CLASS: F.Y.B.M.S
DIV: B
DATE OF SUBMISSION: 8/9/2008
NAME OF STUDENTS:
NAMES ROLL NUMBERS
VISHAL GALA 69
YASMIN KHAN 77
NIVEDITA NATHAN 86
NIRALI SHAH 100
ESHA SINGH 107
RESHMA LALA 115
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ACKNOWLEDGEMENT
We would like to put forward our deep gratitude towards our
QMB professor Mrs. Kinjal for giving us such a topic that helped
us to grasp the topic better. It also helped us to understand its
practical applications.
This entire process gave us beyond text book knowledge and
hence was an enriching process. It helped us know how a group
co-ordinates while making a project.
Lastly we would like to acknowledge the authors and editors of
various newspapers, books and websites which we used for our
reference work.
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INDEX
1. Introduction of project2. Collection of data
Names of 50 financial companies with their approximate sharecapital and market capitalization
3. Application of dataa)Introduction to statistics and presentation data
Numerical representation of data Graphical representation of data
b)Measures of central tendency Mean Median
o Quartileo Decileso Percentile
Modec)Measures of dispersion
Range and coefficient of range
Inter quartile range Quartile deviation and coefficient of quartile deviation Mean deviation and coefficient of mean deviation Variance and standard deviation Combined mean and combined standard deviation
d)Correlation Spearmans rank correlation coefficient
Karl Pearsons coefficient of correlatione)Regression
4.Bibliography
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INTRODUCTION
Statistics is defined as the science of collecting data, classifying it in
similar groups measuring the data quantitatively with different
parameters, analyzing the measures and estimating the future to
facilitate in proper long term or short term planning.
Statistics is very useful in business. It is the core of business activity.
Survey of the market, measuring the production, comparison of
different products, analysis of the previous data, quality control,
estimation for the future, planning the policies, taking decisions in
situations involving uncertainty, are those aspects where statistics plays
a very important role
In this project, we have collected the share capital and market
capitalizations of 50 various companies.
SHARE CAPITAL:
Share capital is the fund raised by a company through the issuance of
common or preferential shares to individuals/ institutions/ investors for
the growth and expansion aspect of the company.
MARKET CAPITALIZATION:
It is a measurement corporate or economy size equal to the share price
times the economy of shares outstanding of a public company.
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1.INTRODUCTION TO STATISTICS ANDPRESENTATION OF DATA
The data given below is a list of 50 financial companies having their share capital
and market capitalization values. From this data, we have prepared;
1)Frequency distribution table for each.2)Cumulative Frequency distribution table3)Relative Frequency distribution table4)Percentage Frequency distribution table5)Bivariate Frequency distribution table6)Marginal Frequency distribution table7)Conditional Frequency distribution table
From the Frequency distribution table prepared for each; share capital and
market capitalization, we have also found;
i. The upper limits and the lower limits of the class intervalsii. Highest and the lowest values for the dataiii. Class mark or each intervalsiv. Class width
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SR. NO NAME OF COMPANY SHARE CAPITAL.(IN CRS)
MARKETCAPITALIZATION.
(IN 100 CRS)
1 Bank of India 526 153
2 State Bank of India 631 966
3 HDFC Bank 354 544
4 HDFC 284 714
5 Reliance Capital 246 348
6 ICICI Bank 1463 8117 Indiabulls Financial Services 384 79
8 IFCI 1068 38
9 Yes Bank 280 41
10 IDBI Bank 725 67
11 Bajaj Auto Finance 37 5
12 Punjab National Bank 315 158
13 Bank of Baroda 366 104
14 Kotak Mahindra Bank 345 220
15 Axis Bank 358 264
16 Allahabad Bank 447 29
17 Federal Bank 171 3818 Oriental Bank of Commerce 251 43
19 Vijaya Bank 434 17
20 UCO Bank 799 30
21 Dena Bank 287 14
22 Motilal Oswal Financial services 14 15
23 Karnataka Bank 121 17
24 Bank of Rajasthan 134 12
25 Geojit Financial Services 21 10
26 Union Bank of India 505 76
27 Central Bank of India 1204 26
28 Centurion Bank of Punjab 157 79
29 Canara Bank 410 89
30 Development Credit Bank 174 10
31 IDFC 1294 133
32 Shriram Transport Finance 203 69
33 Edelweiss Capital 38 47
34 India Infolines 57 46
35 Power Finance Corporation 1148 166
36 Bank Of Maharashtra 431 15
37 City Union Bank 32 10
38 Corporation Bank 143 41
39 Future Capital Holdings 63 23
40 Ing Vysya Bank 102 2441 Karrur Vysya Bank 54 18
42 JM Financial 30 39
43 IL&FS Investsmart 70 12
44 Prime Securities 12 1
45 Syndicate Bank 522 31
46 Sundaram Finance 28 17
47 Religare Enterprise 64 29
48 J&K Bank 48 25
49 Bajaj Finserv 72 77
50 Bajaj Holdings 101 46
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SHARE CAPITAL1. FREQUENCY DISTRIBUTION TABLE FOR SHARE CAPITAL.
CLASS
INTERVALS
TALLY MARKS FREQUENCY CLASS MARK
0 300 29 150
300 600 13 450
600 900 3 750900 1200 2 1050
1200 1500 3 1350
TOTAL 50
LOWER LIMITS: 0, 300, 600, 900, 1200 UPPER LIMITS: 300, 600, 900, 1200, 1500 CLASS WIDTH =Upper Limit Lower Limit
=300 0
=300
LOWEST VALUE: 12 HIGHEST VALUE: 1463 CLASS MARK:
2. CUMULATIVE FREQUENCY DISTRIBUTION TABLE FOR SHARECAPITAL.
CLASS
INTERVALS
FREQUENCY LESS THAN CUMULATIVE
FREQUENCY
GREATER THAN
CUMULATIVE FREQUENCY
0 300 29 29 50
300
600 13 42 21600 900 3 45 8
900 1200 2 47 5
1200 1500 3 50 3
TOTAL 50
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3. RELATIVE AND PERCENTAGE FREQUENCY DISTRIBUTION TABLEFOR SHARE CAPITAL.
CLASS
INTERVALS
FREQUENCY RELATIVE
FREQUENCY
PERCENTAGE
FREQUENCY
0 300 29 0.58 58%
300 600 13 0.26 26%
600 900 3 0.06 6%
900 1200 2 0.04 4%
1200 1500 3 0.06 6%
TOTAL 50
RELATIVE FREQUENCY =
PERCENTAGE FREQUENCY = MARKET CAPITALIZATION
1. FREQUENCY DISTRIBUTION TABLE FOR SHARE CAPITAL.CLASS
INTERVALS
TALLY MARKS FREQUENCY CLAS
MARK
0
200 43 100200 400 3 300
400 600 1 500600 800 1 700
800 1000 2 900
TOTAL 50
LOWER LIMITS: 0, 200, 400, 600, 800 UPPER LIMITS: 200, 400, 600, 800, 1000 CLASS WIDTH =Upper Limit Lower Limit
=200 0 =200
LOWEST VALUE: 1 HIGHEST VALUE: 966 CLASS MARK:
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2. CUMULATIVE FREQUENCY DISTRIBUTION TABLE FOR SHARECAPITAL.
CLASS
INTERVALS
FREQUENCY LESS THAN CUMULATIVE
FREQUENCY
GREATER THAN
CUMULATIVE FREQUENCY
0 200 43 43 50
200 400 3 46 7
400 600 1 47 4
600 800 1 48 3
800 1000 2 50 2
TOTAL 50
3. RELATIVE AND PERCENTAGE FREQUENCY DISTRIBUTIONTABLE FOR SHARE CAPITAL.
CLASS
INTERVALS
FREQUENCY RELATIVE
FREQUENCY
PERCENTAGE
FREQUENCY
0 200 43 0.86 86
200 400 3 0.06 6
400 600 1 0.02 2
600 800 1 0.02 2
800 1000 2 0.04 4
TOTAL 50
RELATIVE FREQUENCY =
PERCENTAGE FREQUENCY =
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BIVARIATE FREQUENCY DISTRIBUTION TABLE
SHARE
CAPITAL
MARKET
CAPITALIZATION0300 300600 600900 9001200 12001500 TOTAL
0200
27
11
2
2
2
44
200400
1
1
0
0
0
2
400600
0
1
0
0
0
1
600800
1
0
0
0
0 1
8001000
0
0
1
0
1
2
TOTAL29 13 3 2 3
50
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MARGINAL FREQUENCY DISTRIBUTION TABLE
MARGINAL FREQUENCYFOR SHARE CAPITAL
FREQUENCY MARGINAL FREQUENCY FORMARKET CAPITALIZATION
FREQUENCY
0 300 29 0 200 44
300 600 13 200 400 2
600 900 3 400 600 1
900 1200 2 600 800 1
1200 1500 3 800 1000 2
TOTAL 50 TOTAL 50
CONDITIONAL FREQUENCY DISTRIBUTION TABLE:
a.Considering share capital whose market capitalization isless than 400 crs.
b.Considering market capitalization whose share capital ismore than 900 crs.
CONDITIONAL FREQUENCY
FOR SHARE CAPITAL
FREQUENCY CONDITIONAL FREQUENCY FOR
MARKET CAPITALIZATION
FREQUENCY
0 300 28 0 200 4
300 600 12 200 400 0
600 900 2 400 600 0
900 1200 2 600 800 0
1200 1500 2 800 1000 1
TOTAL 46 TOTAL 5
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PRESENTING THE ABOVE DATA IN THE FORM OF:1)Histogram2)Frequency curve3)Frequency polygon4)Ogive curves1)HISTOGRAM:Histogram is a graph on a frequency distribution table where adjacent rectangles are
drawn to represent the data.
While drawing the histogram, the class intervals are taken on the x-axis and the
frequencies are taken on the y-axis.
HISTOGRAM FOR SHARE CAPITAL:
CLASS INTERVALS FREQUENCY
0 300 29
300 600 13
600 900 3
900 1200 2
1200 1500 3
TOTAL 50
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2)FREQUENCY CURVE:Points which are plotted on a graph where class marks are on x-axis and frequencies
are on y-axis and joined by a smooth curve, it forms a frequency curve.
FREQUENCY CURVE FOR SHARE CAPITAL:
CLASS INTERVALS FREQUENCY CLASS MARK
0 300 29 150
300 600 13 450
600 900 3 750
900 1200 2 1050
1200 1500 3 1350
TOTAL 50
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3)FREQUENCY POLYGONPoints plotted on a graph where class marks are on x-axis and frequencies are on y-axisare joined by a straight lines, it forms a frequency polygon.
FREQUENCY POLYGON FOR MARKET CAPITALTZATION:
CLASS INTERVALS FREQUENCY CLASS MARK
0 200 43 100
200 400 3 300
400
600 1 500
600 800 1 700
800 1000 2 900
TOTAL 50
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4)OGIVE CURVESFrequency curves in which class limits are plotted instead of class marks and
cumulative frequencies are plotted instead of individual frequencies, are called ogive
curves.
For less than ogive curve, upper class limit is taken and for more than ogive curve,
lower class limit is taken.
OGIVE CURVES FOR MARKET CAPITALIZATION:
CLASSINTERVALS
FREQUENCY LESS THAN CUMULATIVEFREQUENCY
GREATER THANCUMULATIVE FREQUENCY
0 200 43 43 50
200 400 3 46 7
400 600 1 47 4
600 800 1 48 3
800 1000 2 50 2
TOTAL 50
The median for ogive curves is:
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2. MEASURES OF CENTRAL TENDENCYMEAN:Mean is the average of a data. It is the ratio of the total values by the number
of values.
ARITHMETIC MEAN FOR SHARE CAPITAL:
CLASS INTERVALS FREQUENCY
(f)
CLASS MARK
(x)
fx
0 300 29 150 4350
300 600 13 450 5850
600 900 3 750 2250
900 1200 2 1050 2100
1200 1500 3 1350 4050
TOTAL N = 50 18600
N = 50, fx = 18600
=
=
= 372Ans: MEAN = 372
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ARITHMETIC MEAN FOR MARKET CAPITALIZATION:
CLASS INTERVALS FREQUENCY(f) CLASS MARK(x) fx
0 200 43 100 4300
200 400 3 300 900
400 600 1 500 500
600 800 1 700 700
800 1000 2 900 1800
TOTAL N = 50 8200
N = 50, fx = 8200
=
= = 164Ans: MEAN = 164
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2)m =
=
= 12.5 Class interval = 0 300
Q1 = = =
= 129.31
Ans: Q1 = 129.31
3)m =
=
= 37.5 Class interval = 300 600
Q3 =
= =
= 300 + 196.15
= 496.15
Ans: Q3 = 496.15
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(DECILES)
4TH
DECILE: m = =
= 20
D4 = = =
= 206.90
Ans: D4 = 206.90
(PERCENTILES)
30TH
PERCENTILE: m = = = 15
P30 =
= = = 155.17
Ans: P30 = 155.17
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MEDIAN (Q2) OF MARKET CAPITALIZATION:(QUARTILES)
CLASS INTERVALS FREQUENCY LESS THAN CUMULATIVE
FREQUENCY
0 200 43 43
200 400 3 46
400 600 1 47
600 800 1 48
800 1000 2 50
TOTAL 50
1)m =
=
= 25 CLASS INTERVAL: 0 - 200
Median (Q2) = = =
= 116.28
Ans: Q2 = 116.28
2)m = = = 12.5 CLASS INTERVAL: 0 - 200
Q1 =
= =
= 58.14
Ans: Q1 = 58.14
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3)m = = = 37.5 CLASS INTERVAL: 0 - 200Q3 =
= = 174.28
Ans: Q3 = 174.28
(DECILES)
4TH
DECILE: m = = = 20D4 =
= = 93.02
Ans: D4 = 93.02
(PERCENTILES)
30TH
PERCENTILE: m = =
= 15
P30 =
= = 69.77
Ans: P30 = 69.77
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MODEThe most frequently occurring value of the data is known as mode.
MODE FOR SHARE CAPITAL:Here, the maximum frequency is 29, corresponding to the class interval 0 300The modal class is 0 300L1= 0, L2 = 300, f= 29, f0= 0, f2 = 13
Mode (z) = =
= = = 193.33
Ans: mode for share capital = 193.33
MODE FOR MARKET CAPITALIZATION:Here, the maximum frequency is 43, corresponding to the class interval 0 200
The modal class is 0 200L1= 0, L2 = 200, f= 43, f0= 0, f2 = 3
Mode (z) = =
= = = 103.61
Ans: mode for share capital = 103.61
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3. MEASURES OF DISPERSIONSHARE CAPITAL
CLASS INTERVALS FREQUENCY
0 300 29
300 600 13
600 900 3
900 1200 2
1200 1500 3
TOTAL 50
1.RANGE AND CO-EFFICIENT FOR RANGE OR SHARE CAPITAL:Range = Upper limit of highest class interval Lowest limit of lowest class interval
= 1500 0
= 1500
Co-efficient of Range =
=
= 1
2.INTER QUARTILE RANGE FOR SHARE CAPITAL:Given: Q1 = 129.31 Q3 = 496.15
Inter quartile range = Q3 Q1
= 496.15 - 129.31
= 366.84
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3.QUARTILE DEVIATION AND CO-EFFICIENT OF QUARTILE DEVIATION:Quartile deviation =
=
=
= 183.42
Co-efficient of quartile deviation =
=
=
= 0.59
4.MEAN DEVIATION AND COEFFICIENT OF MEAN DEVIATION:C.I FREQUENCY
(F)C.F CLASS
MARK (X)
X M FX M0 300 29 29 150 108.27 3149.98
300 600 13 42 450 191.38 2487.94
600 900 3 45 750 491.38 1474.14
900 1200 2 47 1050 791.38 1582.761200 1500 3 50 1350 1091.38 3274.14
TOTAL 50 11968.96
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m = n/4 = 50/2 = 25
Q2 = = = = 258.62
Mean deviation =
=
= 239.38
Coefficient of mean deviation =
=
= 0.93
5.VARIANCE AND STANDARD DEVIATION:
C.I FREQUENCY (F) CLASS MARK (x) fx fx2
0 300 29 150 4350 652500
300 600 13 450 5850 2632500
600 900 3 750 2250 1687500
900 1200 2 1050 2100 2205000
1200 1500 3 1350 4050 5467500
TOTAL 50 18600 12645000
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= =
= 372
S.D ( =
=
= =
= 338.40
Variance ( = = 114516
Co-efficient of variation =
=
=
= 90.97
MARKET CAPITALIZATION
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CLASS INTERVALS FREQUENCY
0 200 43
200 400 3
400 600 1
600 800 1800 1000 2
TOTAL 50
1.RANGE AND CO-EFFICIENT OF RANGE FOR SHARE CAPITAL:Range = Upper limit of highest class interval Lowest limit of lowest class interval
= 1000 0= 1000
Co-efficient of Range =
=
= 1
2.INTER QUARTILE RANGE FOR SHARE CAPITAL:Given: Q1 = 58.14, Q3 = 174.42
Inter quartile range = Q3 Q1
= 174.42 - 58.14
= 116.28
3.QUARTILE DEVIATION AND CO-EFFICIENT OF QUARTILE DEVIATION:
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Quartile deviation =
=
=
= 58.14
Co-efficient of quartile deviation =
=
= = 0.5
4.MEAN DEVIATION AND COEFFICIENT OF MEAN DEVIATION:
C.I FREQUENCY(F)
C.F CLASS
MARK (X)
X M FX M0 200 43 43 100 16.28 700.04
200 400 3 46 300 183.72 551.16
400 600 1 47 500 383.72 383.72
600 800 1 48 700 583.72 583.72
800 1000 2 50 900 783.72 1567.44
TOTAL 50 3786.08
m = n/4 = 50/2 = 25
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Q2 = = =
= 116.28
Mean deviation =
=
= 75.72
Coefficient of mean deviation =
=
= 0.65
5.VARIANCE AND STANDARD DEVIATION:
C.I FREQUENCY (F) CLASS MARK (x) fx fx2
0 200 43 100 4300 430000
200 400 3 300 900 270000
400 600 1 500 500 250000
600 800 1 700 700 490000
800 1000 2 900 1800 1620000
TOTAL 50 3060000
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= =
= 164
S.D ( =
=
=
= = 185.21
Variance ( = = 185.21
Co-efficient of variation =
=
= = 112.93
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COMBINED MEAN AND COMBINED S.D:SHARE CAPITAL MARKET CAPITALIZATION
OBSERVATIONS (n) 50 (n1 ) 50 (n2)
MEAN () 372 (1) 164 (2)S.D () 338.40 () 185.21 ()
Combined mean (12) =
=
=
= 268
d1 = (1 2) = 372 268 = 104
d2 = (1 12) = 164 268 = 104
Combined S.D = ( )
=
=
= = 291.63
4. CORRELATION
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SPEARMANS RANK CORRELATION COEFFICIENT:SHARE CAPITAL
(I)
MARKET
CAPITALIZATION
(II)
RANK I RANK II D (R1-R2) D2
54 18 6 7 -1 1
30 39 8 3 5 25
70 12 4 9 -5 25
12 1 10 10 0 0
522 31 1 4 -3 9
28 17 9 8 1 1
64 29 5 5 0 0
48 25 7 6 1 1
72 77 3 1 2 4
101 46 2 2 0 0
Total 66
R = 1
= 1
= 1 0.4
= 0.6
KARL PEARSONS CO-EFFICIENT OF CORRELATION:
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SHARE
CAPITAL
(x)
MARKET
CAPITALIZATION
(y)
(x ) (y) (x )(y) (x )2 (y)
5 10 0 0 0 0 0
3 9 2 1 2 4 1
7 12 2 2 4 4 4
10 15 5 5 25 25 25
5 8 0 2 0 0 4
2 7 3 3 9 9 9
6 12 1 2 2 1 4
4 8 1 2 2 1 4
7 14 2 4 8 4 16
1 5 4 5 20 16 25
50 100 72 64 97
Note: The values considered for share capital and market capitalization are the
approximate values considered as single units in 100 and 1000 crs respectively
= =
= 5
=
= = 10
r =
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=
=
=
=
= 0.91869
0.92
5. REGRESSIONSHARE CAPITAL
(X)
MARKET
CAPITALIZATION
(Y)
X2
Y2
XY
102 24
10404 576 2448
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54 18
2916 324 972
30 39
900 1521 1170
70 12
4900 144 840
12 1144 1 12
522 31
272484 961 16182
28 17
784 289 476
64 29
4096 625 1856
48 25
2304 841 1200
72 77
5184 5929 5544
101 46
10201 2116 4647
314317 13327 35346
Regression equation for line y on x and x on y:
byx =
=
bxy =
= 0.82
(y) = byx (x )Y 29 = 0.016 (x 100.27)
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Y 29 = 0.016x 1.644472
Y = 0.016x + 27.355
Regression equation of y on x: Y = 0.016x + 27.355
(x ) = bxy(y)X 100.273 = 0.82(y 29)
X 100.273 = 0.82y 23.78
Regression equation of x on y: x = 0.82y + 76.49
Relation between byx and bxy:r =
= 0.116254359 0.12
BIBLIOGRAPHY
BooksText Books
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Mandar Bhanushe A. V. Deshpande
Reference Books Statistics for management Levin and Rubins Statistics for business and economics Anderson and
Sweng
Web sites Moneycontrol.com Myiris.com
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