Statistical Analysis On Stock Prices

Wednesday, July 23, 2008   

BUSINESS  STATISTICS I  (BA‐205)   

A REPORT ON ANALYSIS OF SHARE STOCK  PRICES OF FIVE COMPANIES 

 

A Report On-

Analysis of Share Prices Of

Five Companies Prepared for-

Tania Afroze Assistant Professor Business Administration Discipline Khulna University

Prepared byName Abdur Rakib Akon

ID 070305

Md Masrul Mollah

070314

Md Nazmul Huda

070323

Ahmed Ibtehaj

070324

SM Mazharul Islam

070351

Date of Submission: July 23, 2008

BBA Program Business Administration Discipline Khulna University

Letter of Transmittal

July 23, 2008

Tania Afroze Assistant Professor Business Administration Discipline Khulna University

Dear Madam,

Here is the report on ‘Analysis of Share Prices Of Five Companies’. This is for you asked to make a report on any topic on June 17. As you will see, the statistical calculations we have used a variety of methods and that resulted some conclusions about all the prices. These calculations are made by the formulas and techniques we’ve learned through our course of ‘Business Statistics I’. As a student of BA discipline we enjoyed to prepare this report. We tried our best to make this report best to present. Therefore we hope that our report will fulfill your requirements about share prices of the five companies we’ve observed. Any short comings or mistakes are absolutely our fault and we will be always available at any time to interpret any portion of the report.

Sincerely yours,

Abdur Rakib Akon (070305)

Md Masrul Mollah (070314)

Md Nazmul Huda (070323)

Ahmed Ibtehaj (070324)

SM Mazharul Islam (070351) 2nd Year, 1st Term BBA Program Business Administration Discipline Khulna University

Acknowledgement First we would like to thank the Almighty Allah for completing the report successfully. And it was also a great pleasure to us to make this report. We wish to express thank to all who helped me a lot during the making of the report. We would like to express my gratitude and regards to our honorable course teacher and instructor Mrs. Tania Afroze, Assistant Professor, Business Administration Discipline, Khulna University. It was very difficult to make such a report of statistical analysis without group work. We are so glad that we have made it to complete this assignment. We have chosen these five companies – Social Investment Bank Ltd., Lanka Bangla Finance Ltd., BD Autocars Ltd., Jamuna Oil Ltd., and Square Pharmaceuticals Ltd. We have collected the prices of the shares from the ‘Daily Prothom-Alo’. Finally we want to thank all who helped us to prepare this report. And again thank you also to assign us such type of job.

V

Table of Contents

Contents

Page No.

Letter of Transmittal Acknowledgement

III V

Summary of the report

01

Part 1: Introduction Origin of the report Purpose of the report Scopes of the report Limitations of making the report Hard to find Inaccuracy Time Limit & Exam Time Methodology Sources of collecting data Method of preparing the report

01-05 03 03 03 04 04 04 04 04 04 05

Part 2: Statistical Analysis Business Statistics Chapter 2: Collection of Data Category of data: Secondary data Business Statistics Chapter 3: Presentation of Data Type of data class: Geographical classified data Frequency Distribution Tabulation of Data Type of Table Diagrams Business Statistics Chapter 4: Measures of Central Tendency Arithmetic Mean Direct Method Short-cut method Combined arithmetic mean Median Quartiles, Deciles, Percentiles Mode Geometric Mean Harmonic Mean Business Statistics Chapter 5: Measures of Variation Range Inerquartile range or Quartile deviation

06-37 07 07 07 07 07 07 08 08 11 11 12 13 14 15 15 16 16 17 19 19 19

Average deviation Standard deviation Combined Standard Deviation Coefficient of variation Business Statistics Chapter 7: Correlation Analysis Scatter Diagram Karl Pearson’s coefficient of correlation Actual mean method Assumed mean method Probable error of coefficient correlation Rank correlation coefficient Business Statistics Chapter 6: Correlation Analysis Regression equation Regression equation using arithmetic mean Part 3: Statistical Analysis Conclusion Appendix

20 22 24 25 26 26 30 30 31 32 33 34 34 36 38-39 39 40

Summary of the Report Share market is like flowing river. Every time the prices of the shares are changing. We have prepared a report which shows the statistical analysis of the share prices of five selected companies of first seven working days of May and June. The prices list is given belowDate

Social Lanka Bangla BD Autocars Jamuna Oil Investment Finance Ltd. Ltd. Ltd. Bank Ltd. 30 April 2008 341.00 115.60 202.25 265.50 01 June 2008 361.75 175.60 190.00 210.00 04 May 2008 338.00 121.90 203.00 263.30 02 June 2008 357.25 181.10 191.00 206.90 05 May 2008 335.75 127.10 196.50 264.40 03 June 2008 369.00 182.20 190.00 204.30 06 May 2008 336.00 131.80 199.75 263.20 04 June 2008 431.00 191.10 191.50 201.30 07 May 2008 334.00 135.10 196.00 261.00 05 June 2008 414.00 210.90 190.00 204.90 08 May 2008 335.25 137.30 203.75 260.60 08 June 2008 414.50 205.20 187.75 201.50 11 May 2008 330.00 136.70 207.50 256.60 10 June 2008 399.25 195.30 181.25 221.80 HolidaysMay 2008 - 01 (May Day), 02 (Friday), 03 (Saturday), 09 (Friday), 10 (Saturday) June 2008 - 06 (Friday), 07 (Saturday), 09 (Budget Day)

Square Pharmaceuticals Ltd. 4552.25 5397.25 4649.00 5295.50 4679.50 5293.25 4660.50 5292.25 4657.25 5273.75 4660.50 5247.50 4733.25 5164.75

Page | 1  

Chapter 1 

Introduction             

   

 

Origin of the Report Mrs. Tania Afroze, the honorable course instructor of ‘Business Statistics I’, assigned us to prepare a report on June 17, 2008 about ‘Statistical Analysis on Five Companies of May and June’ according to the rules we have learned through the course. So this is the report as the result of that action. The date of submission of this report is July 23, 2008.

Purpose of the Report We are very much passionate to obtain educational background through practical work besides the theoretical studies. We do not want to study only with the classroom materials; I want to gather some practical knowledge so that it will help me in achieving my personal objectives. The purposes of our report are•

To make a clear concept through making a relationship between my report writing theoretical knowledge and my practices.

•

To gather knowledge about ‘Stock Exchange’.

•

To know something about how share market goes on and how a price change can have effect on some other variables.

Scopes of the Report We have collected data from newspaper. We got the needed information from the ‘Daily Prothom-Alo’. But for the excess of holidays we have included a price of April 30. As the report is calculation based we have used the secondary source to collect data. We got no internal data to prepare this report but the secondary data we have collected was sufficient enough to make it done. And we have used our text book ‘Business Statistics – Gupta and Gupta’ as a guide to prepare this report.

Page | 3  

Limitations of making the Report We are lucky that we have completed the report successfully within this short time but we had to face some problems in collecting the data and in making the report. We tried our best to overcome the difficulties; Allah knows how much we could do. There were basically 3problems.

Hard to Find It was so tough to collect the newspaper cutting of May and June. But it we were so lucky that we got those in collection.

Inaccuracy The data we have collected was not so accurate. We have got the rates of the last of those working days. But if we could manage to have the average rate of those days it would be better for us.

Time Limit & Exam Time It needs more time to well prepare this kind of report; but we had to prepare it within a very short time. On the other hand now it took much time during preparatory leave for our term final examination. We were so busy with my study. In this busyness we had to give time for this report. This made us so confusing about the report.

Methodology Sources of collecting data Primary Sources No primary sources found. Secondary Sources The ‘Daily Prothom-Alo’ (Share prices page)

Page | 4  

Method of preparing the report To prepare this report we have collected the data we needed and made the calculations we have learned through our ‘Business Statistics I’. And finally we are submitting this report today.

Page | 5  

Chapter 2 

Statistical Analysis             

 

Business Statistics Chapter

2: Collection of Data

Category of Data: Secondary Data We didn’t get any internal source of data. We have collected data from newspaper. So we have collected data from ‘Secondary Source’.

Business Statistics Chapter

3: Presentation of Data

Type of Data Class: Geographical Classified Data Our collected data is in a chronological order. So it can be defined as a ‘Chronological Classified Data’. So this will be a ‘Geographical Classification’ of data type.

Frequency Distribution Our collected data can’t be distributed in fixed frequency.

Tabulation of Data

June

May

Month

Table 2.1: Prices of Shares (in tk.) Date

Social Investment Bank Ltd.

30 April 2008 04 May 2008 05 May 2008 06 May 2008 07 May 2008 08 May 2008 11 May 2008 01 June 2008 02 June 2008 03 June 2008 04 June 2008 05 June 2008 08 June 2008 10 June 2008

341.00 338.00 335.75 336.00 334.00 335.25 330.00 361.75 357.25 369.00 431.00 414.00 414.50 399.25

Lanka Bangla Finance Ltd. 115.60 121.90 127.10 131.80 135.10 137.30 136.70 175.60 181.10 182.20 191.10 210.90 205.20 195.30

BD Autocars Ltd.

Jamuna Oil Ltd.

Square Pharmaceuticals Ltd.

202.25 203.00 196.50 199.75 196.00 203.75 207.50 190.00 191.00 190.00 191.50 190.00 187.75 181.25

265.50 263.30 264.40 263.20 261.00 260.60 256.60 210.00 206.90 204.30 201.30 204.90 201.50 221.80

4552.25 4649.00 4679.50 4660.50 4657.25 4660.50 4733.25 5397.25 5295.50 5293.25 5292.25 5273.75 5247.50 5164.75

Page | 7

N.B.: May 2008 - 01 (May Day), 02 (Friday), 03 (Saturday), 09 (Friday), 10 (Saturday), June 2008 - 06 (Friday), 07 (Saturday), 09 (Budget Day) were holidays.

Type of Table The table we have presented is a ‘Simple Table’.

Diagrams The diagrams of the rates of the shares are given below N.B.: Here we calculated the prices by first seven working days.

Page | 8

Page | 9

Page | 10

As the data is not distributed in frequency we have only made ‘Bar Diagrams’. It is not possible to draw ‘Histogram’, ‘Frequency Polygon’, or ‘Cumulative Frequency Curves or Ogives’.

Business Statistics Chapter

4: Measures of Central Tendency

To calculate ‘Central Tendency’ of the prices of shares we got our data is not ‘Grouped Data’; this is ‘Ungrouped Data’. So, we followed only rules of ‘Ungrouped Data’ for this chapter.

Arithmetic Mean We have calculated the ‘Arithmetic Mean’ in two approaches -

Page | 11

1. Direct Method 2. Indirect Method

Direct Method N

Formula:

X + X 2 + ... + X N X = 1 = N

∑X i =1

1

N

If the subscripts are dropped, the formula becomes: X =

∑X N

Here, X = Average X = Observation N = Number of Observations

Average of the Prices of Social Investment Bank Ltd. of May: N

∑X

1 X 1 + X 2 + ... + X N i =1 = X = N N 341.00 + 338.00 + 335.75 + 336.00 + 334.00 + 335.25 + 330.00 X = 7 X = 335.71

Averages: Prices of May Social Investment Bank Ltd.

= 335.71

Lanka Bangla Finance Ltd.

= 129.36

BD Autocars

= 201.25

Jamuna Oil

= 262.09

Square Pharmaceuticals Ltd.

= 4656.04

Prices of June Social Investment Bank Ltd.

= 392.3929

Lanka Bangla Finance Ltd.

= 191.6286

Page | 12

BD Autocars

= 188.7857

Jamuna Oil

= 207.2429

Square Pharmaceuticals Ltd.

= 5280.6071

Short-cut Method

Formula:

X = A+

∑d N

Here, X = Average d = ( X − A) [Here, A = Assumed Mean] N = Number of Observations

Average of the prices of Social Investment Bank Ltd. of June: We take, Assumed Mean, A = 400

Calculation of Average Price d X ( Tk. ) ( X − 400) 361.75 -38.25 357.25 -42.75 369.00 -31.00 431.00 +31.00 414.00 +14.00 414.50 +14.50 399.25 -00.75

∑ d = -53.25

X = A+

∑d

N − 53.25 X = 400 + 7 X = 392 .3929

Averages: Averages of May

Page | 13

Social Investment Bank Ltd.

= 335.71

Lanka Bangla Finance Ltd.

= 129.36

BD Autocars

= 201.25

Jamuna Oil

= 262.09

Square Pharmaceuticals Ltd.

= 4656.04

Averages of June Social Investment Bank Ltd.

= 392.3929

Lanka Bangla Finance Ltd.

= 191.6286

BD Autocars

= 188.7857

Jamuna Oil

= 207.2429

Square Pharmaceuticals Ltd.

= 5280.6071

Combined Arithmetic Mean X 12 =

Formula:

N1 X 1 + N 2 X 2 N1 + N 2

Here, X 12 = Combined mean of the two groups. X 1 = Arithmetic mean of the first group. X 2 = Arithmetic mean of the second group. N1 = Number of the observations in the first group. N 2 = Number of the observations of the second group.

Combined Average of May and June Prices of Social Investment Bank Ltd.: N1 X 1 + N 2 X 2 N1 + N 2 7 × 335.71 + 7 × 392.3929 = 7+7 = 364.0515

X 12 = X 12

X 12

Averages: Social Investment Bank Ltd.

= 364.0515

Page | 14

Lanka Bangla Finance Ltd.

= 160.4943

BD Autocars

= 195.0179

Jamuna Oil

= 234.6665

Square Pharmaceuticals Ltd.

= 4968.3236

Median

Formula:

N +1 th observation 2 7 +1 = Size of th observation 2 = Size of 4th observation

Median = Size of

Medians: Medians of May Social Investment Bank Ltd.

= 336.00

Lanka Bangla Finance Ltd.

= 131.80

BD Autocars

= 199.75

Jamuna Oil

= 263.20

Square Pharmaceuticals Ltd.

= 4660.50

Medians of June Social Investment Bank Ltd.

= 431.00

Lanka Bangla Finance Ltd.

= 191.10

BD Autocars

= 191.50

Jamuna Oil

= 201.30

Square Pharmaceuticals Ltd.

= 5292.25

Quartiles, Deciles, Percentiles etc. As our data is ungrouped, we didn’t get any formula to calculate Quartiles, Deciles, or Percentiles.

Page | 15

Mode Modes: Modes of May Social Investment Bank Ltd.

= No mode

Lanka Bangla Finance Ltd.

= No mode

BD Autocars

= No mode

Jamuna Oil

= No mode

Square Pharmaceuticals Ltd.

= No mode

Modes of June Social Investment Bank Ltd.

= No mode

Lanka Bangla Finance Ltd.

= No mode

BD Autocars

= 190.00

Jamuna Oil

= No mode

Square Pharmaceuticals Ltd.

= No mode

Mode is calculated by determining the value repeated most.

Geometric Mean:

Formula: Here,

G.M . = anti log

∑ log X N

G.M . = Geometric Mean X = Observations N = Number of Observation

Geometric Mean of Prices Lanka Bangla Finance Ltd. of May: Log List of Prices Price, X log X 115.60 121.90 127.10

2.0630 2.0860 2.1041 Page | 16

131.80 135.10 137.30 136.70

2.1199 2.1307 2.1377 2.1358 ∑ log X = 14.7771

14.771 7 G.M . = anti log 2.110 G.M . = 129.1269 G.M . = anti log

Geometric Means: Geometric Means of May Social Investment Bank Ltd.

= 335.6996

Lanka Bangla Finance Ltd.

= 129.1269

BD Autocars

= 201.2139

Jamuna Oil

= 262.0711

Square Pharmaceuticals Ltd.

= 4655.7677

Geometric Means of June Social Investment Bank Ltd.

= 391.4397

Lanka Bangla Finance Ltd.

= 191.2499

BD Autocars

= 188.7570

Jamuna Oil

= 207.1415

Square Pharmaceuticals Ltd.

= 5280.2190

Harmonic Mean

Formula:

Here,

H .M . =

N ⎛1⎞ ∑ ⎜⎝ X ⎟⎠

H .M . = Harmonic Mean X = Observations N = Number of Observation Page | 17

Harmonic Mean of Prices of Lanka Bangla Finance Ltd. of June: 1 list X

X, Price 175.6 181.1 182.2 191.1 210.9 205.2 195.3

1 X 0.0057 0.0055 0.0055 0.0052 0.0047 0.0049 0.0051 ⎛1⎞ ∑ ⎜⎝ X ⎟⎠ = 0.0367

N ⎛1⎞ ∑ ⎜⎝ X ⎟⎠ 7 H .M . = 0.0367 H .M . = 190.8755

H .M . =

Harmonic Means:

Harmonic Means of May Social Investment Bank Ltd.

= 335.6849

Lanka Bangla Finance Ltd.

= 128.8907

BD Autocars

= 201.1778

Jamuna Oil

= 262.0565

Square Pharmaceuticals Ltd.

= 4655.4982

Harmonic Means of June Social Investment Bank Ltd.

= 390.4852

Lanka Bangla Finance Ltd.

= 190.8755

BD Autocars

= 188.7277

Jamuna Oil

= 207.0430

Square Pharmaceuticals Ltd.

= 5279.8308

Page | 18

Business Statistics Chapter

5: Measures of Variation

Range Range = L − S L = Largest Value S = Smallest Value

Formula:

Range of the prices of BD Autocars Ltd. of May:

Range = 207.50 – 196.00 = 11.50 Ranges:

Ranges of May Social Investment Bank Ltd.

= 11.00

Lanka Bangla Finance Ltd.

= 21.70

BD Autocars

= 11.50

Jamuna Oil

= 8.90

Square Pharmaceuticals Ltd.

= 181.00

Ranges of June Social Investment Bank Ltd.

= 73.75

Lanka Bangla Finance Ltd.

= 35.30

BD Autocars

= 10.25

Jamuna Oil

= 20.50

Square Pharmaceuticals Ltd.

= 232.50

Inerquartile Range or Quartile Deviation Inerquartile Range or Quartile Deviation can’t be determined by ‘Ungrouped Data’.

Page | 19

Average Deviation

Formula:

A.D.( Med .) =

∑ | X − Med . | N

Coefficient of A.D.( Med .) =

A.D. Median

Here,

A.D. = Average Deviation X = Observation Med. = Median N = Number of Observations Average Deviation of the Prices of BD Autocars Ltd. of June:

Here, Median = 191.50 Average Deviation Chart | X − Med . | X, Price 190 1.5 191 0.5 190 1.5 191.5 0 190 1.5 187.75 3.75 181.25 10.25 ∑ | X − Med. |= 19 A.D.( Med .) = A.D.( Med .) A.D.( Med .)

∑ | X − Med . |

N 19 = 7 = 2.7142

Average Deviations:

Average Deviations of May Social Investment Bank Ltd.

= 2.2900

Lanka Bangla Finance Ltd.

= 6.3571

BD Autocars

= 3.5000

Page | 20

Jamuna Oil

= 2.1429

Square Pharmaceuticals Ltd.

= 30.6786

Average Deviations of June Social Investment Bank Ltd.

= 38.6071

Lanka Bangla Finance Ltd.

= 10.6571

BD Autocars

= 2.7143

Jamuna Oil

= 5.9429

Square Pharmaceuticals Ltd.

= 42.8571

Coefficient of Average Deviation of the Prices of Jamuna Oil Ltd. of May:

Here, A.D. = 2.1429 Median = 263.20 2.1429 263.20 = 0.0081

∴ Coefficient of A.D.( Med .) =

Coefficients of Average Deviations:

Coefficients of Average Deviations of May Social Investment Bank Ltd.

= 0.0068

Lanka Bangla Finance Ltd.

= 0.0482

BD Autocars

= 0.0175

Jamuna Oil

= 0.0081

Square Pharmaceuticals Ltd.

= 0.0066

Coefficients of Average Deviations of June Social Investment Bank Ltd.

= 0.0896

Lanka Bangla Finance Ltd.

= 0.0558

BD Autocars

= 0.0142

Jamuna Oil

= 0.0295

Square Pharmaceuticals Ltd.

= 0.0081

Page | 21

Standard Deviation

Formula:

Here,

σ=

∑(X − X ) N

2

; (Deviation taken from Actual Mean)

σ = Standard Deviation

X = Observation X = Average N = Number of Observations

σ=

Here,

∑d

2

N

⎛ ∑d ⎞ ⎟ ; (Deviation taken from Assumed Mean) −⎜ ⎜ N ⎟ ⎝ ⎠ 2

σ = Standard Deviation

d= X−A A = Assumed Mean N = Number of Observations

Standard deviation taken from Actual Mean of the Prices of Jamuna Oil Ltd. of June:

Here, Average = 207.2429 Standard Deviation Chart X, ( X − X )2 Prices 210 7.6018 206.9 0.1176 204.3 8.6604 201.3 35.3176 204.9 5.4890 201.5 32.9804 221.8 211.9104 ∑ ( X − X ) 2 = 302.0771

302.0771 7 σ = 6.5692

∴σ =

Standard Deviations:

Page | 22

Standard Deviations of May Social Investment Bank Ltd.

= 3.1408

Lanka Bangla Finance Ltd.

= 7.6150

BD Autocars

= 3.8126

Jamuna Oil

= 2.7570

Square Pharmaceuticals Ltd.

= 49.8210

Standard Deviations of June Social Investment Bank Ltd.

= 27.2943

Lanka Bangla Finance Ltd.

= 12.1066

BD Autocars

= 3.2635

Jamuna Oil

= 6.5692

Square Pharmaceuticals Ltd.

= 64.0233

Standard deviation taken from Assumed Mean of the Prices of Square Pharmaceuticals Ltd. of May:

Take, Assumed Mean = 4660.50 Assumed Mean Chart X, Prices 4552.25 4649.00 4679.50 4660.50 4657.25 4660.50 4733.25

17514.4375 ⎛ − 31.25 ⎞ −⎜ ⎟ 7 ⎝ 7 ⎠ σ = 49.9760

d, X−A -108.25 -11.50 19.00 0.00 -3.25 0.00 72.75 ∑ d = −31.25

d2

11718.0625 132.25 361 0 10.5625 0 5292.5625 ∑ d 2 = 17514.4375

2

∴σ =

Standard Deviations

Standard Deviations of May Page | 23

Social Investment Bank Ltd.

= 3.1408

Lanka Bangla Finance Ltd.

= 7.6150

BD Autocars

= 3.8126

Jamuna Oil

= 2.7570

Square Pharmaceuticals Ltd.

= 49.9760

Standard Deviations of June Social Investment Bank Ltd.

= 27.2943

Lanka Bangla Finance Ltd.

= 12.1066

BD Autocars

= 3.2635

Jamuna Oil

= 6.5692

Square Pharmaceuticals Ltd.

= 64.0233

Combined Standard Deviation

Formula:

σ 12 =

N 1σ 1 + N 2σ 2 + N 1 d1 + N 2 d 2 N1 + N 2 2

2

2

2

Here,

N1 = Number of observations of the first group N 2 = Number of observations of the second group σ 1 = Standard Deviation of the first group σ 2 = Standard Deviation of the second group d1 = | X 1 − X 12| | d 2 = | X 2 − X 12| | X 1 = Average of the first group X 2 = Average of second group X 12 = Combined Average of the two groups Combined Standard Deviation of the Prices of Square Pharmaceuticals Ltd.:

Here,

N1 = 7 N2 = 7 σ 1 = 49.8210 Page | 24

σ 2 = 64.0233 X 12 = 5292.25 X 1 = 4656.04 X 2 = 5280.6071 d1 = 312.2836 d 2 = 312.2835

σ 12 =

N 1σ 1 + N 2σ 2 + N 1 d1 + N 2 d 2 N1 + N 2 2

2

2

2

7 × 49.8210 2 + 7 × 64.0233 2 + 7 × 312.2836 2 + 7 × 312.2835 2 7+7 = 317.5084

σ 12 = σ 12

Combined Standard Deviations

Social Investment Bank Ltd.

= 34.3607

Lanka Bangla Finance Ltd.

= 32.7357

BD Autocars

= 7.1717

Jamuna Oil

= 27.8677

Square Pharmaceuticals Ltd.

= 317.5084

Coefficient of Variation

Formula: Here,

C.V . =

σ X

× 100

C.V . = Coefficient of Variation = Standard Deviation X = Arithmetic Mean of the observations

σ

Coefficient of Variation of the prices of Square Pharmaceuticals Ltd. of June:

Here,

σ X

= 64.0233 = 5280.6071 64.0233 × 100 5280.6071 = 1.2124

∴ C.V . =

Page | 25

Coefficients of Variations

Coefficients of Variations of May Social Investment Bank Ltd.

= 0.9356

Lanka Bangla Finance Ltd.

= 5.8868

BD Autocars

= 1.8945

Jamuna Oil

= 1.0519

Square Pharmaceuticals Ltd.

= 1.0700

Coefficients of Variations of June Social Investment Bank Ltd.

= 6.9559

Lanka Bangla Finance Ltd.

= 6.3177

BD Autocars

= 1.7287

Jamuna Oil

= 3.1698

Square Pharmaceuticals Ltd.

= 1.2124

Combined Coefficients of Variations (Combined Standard Deviation×100/Combined Arithmetic Mean) Social Investment Bank Ltd.

= 9.4384

Lanka Bangla Finance Ltd.

= 20.3968

BD Autocars

= 3.6764

Jamuna Oil

= 11.8754

Square Pharmaceuticals Ltd.

= 6.3907

Business Statistics Chapter

7: Correlation Analysis

Scatter Diagram Here the scatter diagrams of the share prices are drawn.

Page | 26

 

 

Page | 27

 

 

 

Page | 28

 

 

 

Page | 29

Karl Pearson’s Coefficient of Correlation Actual Mean Method

Formula:

r=

∑ ( X − X )(Y − Y ) ∑ ( X − X ) ∑ (Y − Y ) 2

2

The above formula can be written as: r=

∑ xy ∑x ∑y 2

2

Where, x = ( X − X ) and y = (Y − Y )

Here,

X = Observation from the first group X = Arithmetic Mean of the first group Y = Observation from the second group Y = Arithmetic Mean of the second group

Calculation of Correlation Coefficient of the prices of Social Investment Bank Ltd. (of May and June)

Take X as the prices of May and take Y as the prices of June.

Page | 30

Working Day 1 2 3 4 5 6 7

May Prices, X 341.0000 338.0000 335.7500 336.0000 334.0000 335.2500 330.0000

∑X =

2350.0000

r=

r=

( X − X ), x

x2

+5.2900 +2.2900 +0.0400 +0.2900 -1.7100 -0.4600 -5.7100

27.9841 5.2441 0.0016 0.0841 2.9241 0.2116 32.6041

∑x =

∑x

0.0300

69.0537

∑ xy ∑x ∑y 2

2

June Prices, Y 361.7500 357.2500 369.0000 431.0000 414.0000 414.5000 399.2500

=

∑Y =

2746.7500

(Y − Y ), y

y2

xy

-30.6429 -35.1429 -23.3929 +38.6071 +21.6071 +22.1071 +6.8571

938.9873 1235.0234 547.2278 1490.5082 466.8668 488.7239 47.0198

-162.1009 -80.4772 -0.9357 +11.1961 -36.9481 -10.1693 -39.1540

∑y=

-0.0003

∑y

=

∑ xy =

5214.3571

-318.5893

2

2

− 318.5893

69.0537 × 5214.3571 r = −0.5309 Correlation Coefficients between May and June Prices:

Social Investment Bank Ltd.

= -0.5309

Lanka Bangla Finance Ltd.

= 0.8746

BD Autocars

= -0.6982

Jamuna Oil

= -0.5775

Square Pharmaceuticals Ltd.

= -0.9390

Assumed Mean Method

Formula:

r=

N ∑ dxd y − ∑ dx ∑ d y

N ∑ d x − (∑ d x ) 2

2

N ∑ d y − (∑ d y ) 2

2

Here,

r N dx X Ax dy Y Ay

= Correlation Coefficient = Number of Observations = X − Ax = Observation of the first group = Assumed Mean of the first group = Y − Ay = Observation of the second group = Assumed Mean of the second group

Page | 31

Calculation of Correlation Coefficient of the prices of Lanka Bangla Finance Ltd. (of May and June):

Take X as the prices of May and take Y as the prices of June.

Worki ng Day 1 2 3 4 5 6 7

( X − 131.80) dx

May Prices,

X 115.60 121.90 127.10 131.80 135.10 137.30 136.70

-16.20 -9.90 -4.70 0 +3.30 +5.50 +4.90

∑X =

∑d

x

∑d

=

∴r =

Y

262.44 98.01 22.09 0 10.89 30.25 24.01

-17.10

905.50

dx

June Prices,

2

2 x

175.60 181.10 182.20 191.10 210.90 205.20 195.30

=

447.69

∑Y = 1341.40

(Y − 191.10), dy -15.50 -10.00 -8.90 0 +19.80 +14.10 +4.20

∑d

y

=

3.70

dy

2

dxd y

240.25 100.00 79.21 0 392.04 198.81 17.64

∑d

2 y

-3982.05 -990.00 -372.287 0 +1293.732 +1093.455 +86.436

=

1027.95

∑d

x

dy =

-2780.714

(7 × −2780.714) − (−17.10 × 3.70)

(7 × 447.69) − (−17.10}2 (7 × 1027.95) − (3.70) 2 ∴ r = −4.2949 Correlation Coefficients between May and June Prices:

Social Investment Bank Ltd.

= 44.9742

Lanka Bangla Finance Ltd.

= -4.2949

BD Autocars

= 10.2148

Jamuna Oil

= -20.2547

Square Pharmaceuticals Ltd.

= -0.5551

Probable Error of Coefficient of Correlation

Formula:

P.E.r = 0.6745

1− r2 N

Here, P.E.r = Probable error of Coefficient of Correlation r = Correlation Coefficient N = Number of observations

Probable Error of Coefficient of Correlation of the prices of May and June of BD Autocars Ltd.:

Page | 32

P.E.r = 0.6745 ×

1 − (10.2148) 2 7

P.E.r = −26.3457

Probable Errors of Correlation Coefficients of the share prices of May and June:

Social Investment Bank Ltd.

= -515.4008

Lanka Bangla Finance Ltd.

= -4.4477

BD Autocars

= -26.3457

Jamuna Oil

= -104.3337

Square Pharmaceuticals Ltd.

= 0.1764

Rank Correlation Coefficient

Formula:

R = 1−

6∑ D 2

N ( N 2 − 1)

or1 −

6∑ D 2

N3 − N

Here,

R D R1 R2 N

= Rank Correlation Coefficient = R1 − R2 = Rank of observation of the first group = Rank of observation of the second group = Number of Observations

Rank Correlation Coefficient of the prices of BD Autocars Ltd. of May and June:

Take, R1 as the Prices of May and R2 as the Prices of June Working Days 1 2 3 4 5 6 7 N = 10

May Prices 202.25 203.00 196.50 199.75 196.00 203.75 207.50

Rank for May Prices, R1 4 5 2 3 1 6 7

June Prices 190.00 191.00 190.00 191.50 190.00 187.75 181.25

Rank for June Prices, R2 1 4 2 5 3 7 6

( R1 − R2 ) 2 ,

D2

∑D

9 1 0 4 4 1 1 2

= 20

Page | 33

∴ R = 1−

6∑ D 2

N3 − N 20 ∴ R = 1− 3 7 −7 ∴ R = 0.6429 Rank Correlation Coefficients: Social Investment Bank Ltd.

= -0.5000

Lanka Bangla Finance Ltd.

= 0.8929

BD Autocars

= 0.6429

Jamuna Oil

= 0.0000

Square Pharmaceuticals Ltd.

= -0.7500

Business Statistics Chapter

8: Regression Analysis

Regression Equation Formula: Regression Equation of X on Y: X = a + bY To determine the values of a and b the following two normal equations are to be solved simultaneously: ∑ X = Na + b∑ Y

∑ XY = a∑ Y + b∑ Y

2

Regression Equation of Y on X: Y = a + bX To determine the values of a and b the following two normal equations are to be solved simultaneously: ∑ Y = Na + b∑ X

∑ XY = a∑ X + b∑ X

2

Regression Equation of the prices of Jamuna Oil Ltd.: May Prices, X 265.50

X2 70490.25

June Prices, Y 210.00

Y2 44100.00

XY 55755.00

Page | 34

263.30 264.40 263.20 261.00 260.60 256.60

∑ X = 1834.60 ∑ X

69326.89 69907.36 69274.24 68121.00 67912.36 65843.56 2

= 480875.66

206.90 204.30 201.30 204.90 201.50 221.80

∑ Y = 1450.70 ∑ Y

42807.61 41738.49 40521.69 41984.01 40602.25 49195.24 2

=300949.29

54476.77 54016.92 52982.16 53478.90 52510.90 56913.88 ∑ XY =

380134.53

From this, using the formula, we can say that1834.60 = 7a + 1450.70b 380134.53 = 1450.70a + 300949.29b From these equations, we geta = 312.3160 b = -0.2424 Then the regression equation of the prices of May on the prices of June of Jamuna Oil Ltd. is – X = 312.3160 – 0.2424Y Regression equations:

Price of May on Price of June Social Investment Bank Ltd. →

X = 359.6885 – 0.0611Y

Lanka Bangla Finance Ltd. →

X = 23.9350 + 0.5504Y

BD Autocars Ltd. →

X = 355.2364 – 0.8157Y

Jamuna Oil Ltd. →

X = 312.3160 – 0.2424Y

Square Pharmaceuticals Ltd. →

X = 8514.7970 – 0.7307Y

Price of June on Price of May Social Investment Bank Ltd. →

Y = 1941.1260 – 4.6132X

Lanka Bangla Finance Ltd. →

Y = 11.7540 + 1.3905X

BD Autocars Ltd. →

Y = 309.0680 – 0.5977X

Jamuna Oil Ltd. →

Y = 567.8763 – 1.3760X

Square Pharmaceuticals Ltd. →

Y = 10898.4480 – 1.2066X

Page | 35

Regression Equation using Arithmetic Mean Y − Y = b yx ( X − X )

Formula:

X − X = bxy (Y − Y )

Here,

X Y X Y

= Observation of the first group = Observation of the second group = Arithmetic Mean of the first group = Arithmetic Mean of the second group ∑ xy and b = ∑ xy b yx = xy ∑ x2 ∑ y2 = X−X = Y −Y

x y

Regression Equation of the prices of Square Pharmaceuticals Ltd.: Working Day

May Prices, X

x=X−X

x2

June Prices, Y

y = Y −Y

y2

xy

1 2 3 4 5 6 7 Total

4552.25 4649.00 4679.50 4660.50 4657.25 4660.50 4733.25 32592.25

-103.7860 -7.0357 23.4643 4.4643 1.2143 4.4643 77.2143 0.0000

10771.4745 49.5013 550.5727 19.9298 1.4745 19.9298 5962.0459 17374.9300

5397.25 5295.50 5293.25 5292.25 5273.75 5247.50 5164.75 36964.25

5397.25 5295.50 5293.25 5292.75 5273.75 5247.50 5164.75 0.0000

13605.56 221.7972 159.8418 135.5561 47.0204 1096.0830 28688.7300 28688.73

-12105.900 -104.7820 296.6556 51.9770 -8.3265 -147.8000 -8945.8300 -20963.96

Here,

X = 32592.25 and Y = 5280.6071 − 20963.96 17374.9300 b yx = 1.2066

b yx =

Then the equation of the price of June on price of May of Square Pharmaceuticals Ltd. is(Y − 32592.25) = 1.2066( X − 5280.6071) Y = 10898.4480 – 1.2066X Or, Regression equations:

Price of May on Price of June Social Investment Bank Ltd. →

X = 359.6885 – 0.0611Y

Page | 36

Lanka Bangla Finance Ltd. →

X = 23.9350 + 0.5504Y

BD Autocars Ltd. →

X = 355.2364 – 0.8157Y

Jamuna Oil Ltd. →

X = 312.3160 – 0.2424Y

Square Pharmaceuticals Ltd. →

X = 8514.7970 – 0.7307Y

Price of June on Price of May Social Investment Bank Ltd. →

Y = 1941.1260 – 4.6132X

Lanka Bangla Finance Ltd. →

Y = 11.7540 + 1.3905X

BD Autocars Ltd. →

Y = 309.0680 – 0.5977X

Jamuna Oil Ltd. →

Y = 567.8763 – 1.3760X

Square Pharmaceuticals Ltd. →

Y = 10898.4480 – 1.2066X

Page | 37

Chapter 3 

Report Ending       

Conclusion It was really a tough job to complete this report without any error. But our group work made this possible to make this without any error. We are thanking again to the Almighty, you who gave us such an assignment and those who helped us and made this report more beautiful and complete in information.

Page | 39  

Appendix               

 

 

We have collected our all the data from newspaper. We have attached the copies of the paper with this report.