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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:


(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


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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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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