Business Statistics 25 Sept
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BUSINESS STATISTICS AFTERSCHO☺OL – DEVELOPING CHANGE MAKERS CENTRE FOR SOCIAL ENTREPRENEURSHIP PGPSE PROGRAMME – World’ Most Comprehensive programme in social entrepreneurship & spiritual entrepreneurship OPEN FOR ALL FREE FOR ALL
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
BUSINESS STATISTICS Dr. T.K. Jain.
AFTERSCHO☺OL Centre for social entrepreneurship Bikaner M: 9414430763 [email protected] www.afterschool.tk, www.afterschoool.tk www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
THERE ARE 2 GROUPS WITH AVERAGE OF 50 AND 60 AND GROUP SIZE OF 30 AND 20. WHAT IS THE COMBINED AVERAGE? • ((30*50)+(20*60))/ (30+20) • =2700/50 =54 ANSWER.
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
Average salary of workers is 10000 and that of managers is 15000. Their combined average is 12000. What is the ratio of these two?
• We can calculate it as follows: • The ratio is 3:2. workers are 60% and managers are 40% in total numbers.
10
15
12
3 www.afterschoool.tk
2
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
Calculate correlation in the following series? X
Y
2 5 6
12 7 4
7 11
11 12
www.afterschoool.tk
X^2
Y^2
XY
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
Solution
X 2. 00 5. 00 6. 00 7. 00 11 6.20 .0 0
Y 12. 00 7.0 0 4.0 0 11. 00 9.2 12. 0 00
www.afterschoool.tk
DX DY DX^2 DY^2 DXDY (4.2 2.8 17. 7.8 (11. 0) 0 64 4 76) (1.2 (2.2 1.4 4.8 2.6 0) 0) 4 4 4 (0.2 (5.2 0.0 27. 1.0 0) 0) 4 04 4 0.8 1.8 0.6 3.2 1.4 0 0 4 4 4 4.8 2.8 23. 7.8 13. $ $ 0 0 04 4 44 (0.0 0.0 8.5 10. 1.3 0) 0 6 16 6 2.9 3.1 0.1 3 9 5 AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
Steps . . . 1. Calculate DX and DY (deviations from averages of X and Y) 2. Calculate DX^2 and DY^2 & their averages 3. Calculate square roots of averages of DX^2 and DY^2, these are standard deviations 4. Calculate DXDY and its average – this is covariance. 5. Divide covariance by product of standard deviation of X and Y. Answer. www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
What is standard deviation of the following series? • 10,10,10,10,16,16,16,16
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
Solution x frequency 10 4 16 4 8
www.afterschoool.tk
fx dx 40 -3 64 3 104 Avg: 13
d x^ fdx^ 2 2 9 36 9 36 72
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
9 3
Solution . . 1. Calculate FX (multiply X to F) 2. Calculate DX (take difference of X from mean) 3. Calculate DX^2 4. Calculate FDX^2 5. Divide sum of FDX^2 by sum of frequency 6. Take square root of FDX^2 / total F = 3. www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
Calculate both regression from following data X
Y
2
12
5
7
6
4
7
11
11
12
www.afterschoool.tk
X^2
Y^2
XY
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
SOLUTION
X 2.00
5.00 6.00 7.00 11.0 0 6.20
Y 12.00
7.0 0 4.0 0 11. 00 12. 00 9.20 B=
www.afterschoool.tk
DX (4.20) (1.2 0) (0.2 0) 0.80 $ 4.80 (0.0 0) $ 0.16
DY 2.80 (2.2 0) (5.2 0)
DX^2
17.64 1.4 4 0.0 4 0.6 1.80 4 23. 2.80 $ 04 $ 8.5 0.00 6 $ 0.13
DY^2 7.84 4.8 4 27. 04 3.2 4 7.8 4 $10 .16
DXDY (11.76) 2.64 1.04 1.44 13.44 1.36
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
SOLUTION • • • • • • • • •
Y = a +Bx B= covariance / variance of X B = 1.36/8.56 = .16 9.2 = A +.16*6.2 A = 8.2 answer. X = A +BY B = covariance / variance of Y =1.36/10.16 =.13 thus 6.2 = A +.13*9.2 A =5 answer.
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
Solution 1. 2. 3. 4.
First calculate covariance Divide covariance by variances Find B Find A by putting the formula Y = a+bx or x = a+by
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
ABOUT AFTERSCHO☺OL Afterschoool conducts three year integrated PGPSE (after class 12th along with IAS / CA / CS) and 18 month PGPSE (Post Graduate Programme in Social Entrepreneurship) along with preparation for CS / CFP / CFA /CMA / FRM. This course is also available online also. It also conducts workshops on social entrepreneurship in schools and colleges all over India – start social entrepreneurship club in your institution today with the help from afterschoool and help us in developing society.
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
Why such a programme? • To promote people to take up entrepreneurship and help develop the society • To enable people to take up franchising and other such options to start a business / social development project • To enable people to take up social development as their mission • To enable people to promote spirituality and positive thinking in the world www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
Who are our supporters? • Afterschoolians, our past beneficiaries, entrepreneurs and social entrepreneurs are supporting us. • You can also support us – not necessarily by money – but by being promotor of our concept and our ideas.
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
About AFTERSCHO☺OL PGPSE – the best programme for developing great entrepreneurs • • • • •
Most flexible, adaptive but rigorous programme Available in distance learning mode Case study focused- latest cases Industry oriented practical curriculum Designed to make you entrepreneurs – not just an employee • Option to take up part time job – so earn while you learn • The only absolutely free course on internet www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
Workshops from AFTERSCHO☺OL • • • • • • • • •
IIF, Delhi CIPS, Jaipur ICSI Hyderabad Branch Gyan Vihar, Jaipur Apex Institute of Management, Jaipur Aravali Institute of Management, Jodhpur Xavier Institute of Management, Bhubaneshwar Pacific Institute, Udaipur Engineering College, Hyderabad
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
Flexible Specialisations: • • • • • • • • • •
Spiritualising business and society Rural development and transformation HRD and Education, Social Development NGO and voluntary work Investment analysis,microfinance and inclusion Retail sector, BPO, KPO Accounting & Information system (with CA / CS /CMA) Hospital management and Health care Hospitality sector and culture and heritage Other sectors of high growth, high technology and social relevance
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
Salient features: • The only programme of its kind (in the whole world) • No publicity and low profile course • For those who want to achieve success in life – not just a degree • Flexible – you may stay for a month and continue the rest of the education by distance mode. / you may attend weekend classes • Scholarships for those from poor economic background • Latest and constantly changing curriculum – keeping pace with the time • Placement for those who are interested • Admissions open throughout the year • Latest and most advanced technologies, books and study material www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
Components • • • • • • • • • • • • • •
Pedagogy curriculum and approach based on IIM Ahmedabad and ISB Hyderabad (the founder is alumnus from IIMA & ISB Hyderabad) Meditation, spiritualisation, and self development Essential softwares for business Business plan, Research projects Participation in conferences / seminars Workshops on leadership, team building etc. Written submissions of research projects/articles / papers Interview of entrepreneurs, writing biographies of entrepreneurs Editing of journals / newsletters Consultancy / research projects Assignments, communication skill workshops Participation in conferences and seminars Group discussions, mock interviews, self development diaryng Mind Power Training & writing workshop (by Dr. T.K.Jain)
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
Pedagogy • • • • • • • • •
Case analysis, Articles from Harvard Business Review Quiz, seminars, workshops, games, Visits to entrepreneurs and industrial visits Presentations, Latest audio-visuals Group discussions and group projects Periodic self assessment Mentoring and counselling Study exchange programme (with institutions out of India) • Rural development / Social welfare projects www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
Branches • AFTERSCHO☺OL will shortly open its branches in important cities in India including Delhi, Kota, Mumbai, Gurgaon and other important cities. Afterschooolians will be responsible for managing and developing these branches – and for promoting social entrepreneurs.
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
Case Studies • We want to write case studies on social entrepreneurs, first generation entrepreneurs, ethical entrepreneurs. Please help us in this process. Help us to be in touch with entrepreneurs, so that we may develop entrepreneurs.
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
Basic values at AFTERSCHO☺OL • • • • • •
Share to learn more Interact to develop yourself Fear is your worst enemy Make mistakes to learn Study & discuss in a group Criticism is the healthy route to mutual support and help • Ask fundamental questions : why, when, how & where? • Embrace change – and compete with yourself only www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
www.afterschoool.tk social entrepreneurship for better society
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
BUSINESS STATISTICS Dr. T.K. Jain.
AFTERSCHO☺OL Centre for social entrepreneurship Bikaner M: 9414430763 [email protected] www.afterschool.tk, www.afterschoool.tk www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
THERE ARE 2 GROUPS WITH AVERAGE OF 50 AND 60 AND GROUP SIZE OF 30 AND 20. WHAT IS THE COMBINED AVERAGE? • ((30*50)+(20*60))/ (30+20) • =2700/50 =54 ANSWER.
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
Average salary of workers is 10000 and that of managers is 15000. Their combined average is 12000. What is the ratio of these two?
• We can calculate it as follows: • The ratio is 3:2. workers are 60% and managers are 40% in total numbers.
10
15
12
3 www.afterschoool.tk
2
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
Calculate correlation in the following series? X
Y
2 5 6
12 7 4
7 11
11 12
www.afterschoool.tk
X^2
Y^2
XY
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
Solution
X 2. 00 5. 00 6. 00 7. 00 11 6.20 .0 0
Y 12. 00 7.0 0 4.0 0 11. 00 9.2 12. 0 00
www.afterschoool.tk
DX DY DX^2 DY^2 DXDY (4.2 2.8 17. 7.8 (11. 0) 0 64 4 76) (1.2 (2.2 1.4 4.8 2.6 0) 0) 4 4 4 (0.2 (5.2 0.0 27. 1.0 0) 0) 4 04 4 0.8 1.8 0.6 3.2 1.4 0 0 4 4 4 4.8 2.8 23. 7.8 13. $ $ 0 0 04 4 44 (0.0 0.0 8.5 10. 1.3 0) 0 6 16 6 2.9 3.1 0.1 3 9 5 AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
Steps . . . 1. Calculate DX and DY (deviations from averages of X and Y) 2. Calculate DX^2 and DY^2 & their averages 3. Calculate square roots of averages of DX^2 and DY^2, these are standard deviations 4. Calculate DXDY and its average – this is covariance. 5. Divide covariance by product of standard deviation of X and Y. Answer. www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
What is standard deviation of the following series? • 10,10,10,10,16,16,16,16
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
Solution x frequency 10 4 16 4 8
www.afterschoool.tk
fx dx 40 -3 64 3 104 Avg: 13
d x^ fdx^ 2 2 9 36 9 36 72
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
9 3
Solution . . 1. Calculate FX (multiply X to F) 2. Calculate DX (take difference of X from mean) 3. Calculate DX^2 4. Calculate FDX^2 5. Divide sum of FDX^2 by sum of frequency 6. Take square root of FDX^2 / total F = 3. www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
Calculate both regression from following data X
Y
2
12
5
7
6
4
7
11
11
12
www.afterschoool.tk
X^2
Y^2
XY
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
SOLUTION
X 2.00
5.00 6.00 7.00 11.0 0 6.20
Y 12.00
7.0 0 4.0 0 11. 00 12. 00 9.20 B=
www.afterschoool.tk
DX (4.20) (1.2 0) (0.2 0) 0.80 $ 4.80 (0.0 0) $ 0.16
DY 2.80 (2.2 0) (5.2 0)
DX^2
17.64 1.4 4 0.0 4 0.6 1.80 4 23. 2.80 $ 04 $ 8.5 0.00 6 $ 0.13
DY^2 7.84 4.8 4 27. 04 3.2 4 7.8 4 $10 .16
DXDY (11.76) 2.64 1.04 1.44 13.44 1.36
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
SOLUTION • • • • • • • • •
Y = a +Bx B= covariance / variance of X B = 1.36/8.56 = .16 9.2 = A +.16*6.2 A = 8.2 answer. X = A +BY B = covariance / variance of Y =1.36/10.16 =.13 thus 6.2 = A +.13*9.2 A =5 answer.
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
Solution 1. 2. 3. 4.
First calculate covariance Divide covariance by variances Find B Find A by putting the formula Y = a+bx or x = a+by
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
ABOUT AFTERSCHO☺OL Afterschoool conducts three year integrated PGPSE (after class 12th along with IAS / CA / CS) and 18 month PGPSE (Post Graduate Programme in Social Entrepreneurship) along with preparation for CS / CFP / CFA /CMA / FRM. This course is also available online also. It also conducts workshops on social entrepreneurship in schools and colleges all over India – start social entrepreneurship club in your institution today with the help from afterschoool and help us in developing society.
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
Why such a programme? • To promote people to take up entrepreneurship and help develop the society • To enable people to take up franchising and other such options to start a business / social development project • To enable people to take up social development as their mission • To enable people to promote spirituality and positive thinking in the world www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
Who are our supporters? • Afterschoolians, our past beneficiaries, entrepreneurs and social entrepreneurs are supporting us. • You can also support us – not necessarily by money – but by being promotor of our concept and our ideas.
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
About AFTERSCHO☺OL PGPSE – the best programme for developing great entrepreneurs • • • • •
Most flexible, adaptive but rigorous programme Available in distance learning mode Case study focused- latest cases Industry oriented practical curriculum Designed to make you entrepreneurs – not just an employee • Option to take up part time job – so earn while you learn • The only absolutely free course on internet www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
Workshops from AFTERSCHO☺OL • • • • • • • • •
IIF, Delhi CIPS, Jaipur ICSI Hyderabad Branch Gyan Vihar, Jaipur Apex Institute of Management, Jaipur Aravali Institute of Management, Jodhpur Xavier Institute of Management, Bhubaneshwar Pacific Institute, Udaipur Engineering College, Hyderabad
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
Flexible Specialisations: • • • • • • • • • •
Spiritualising business and society Rural development and transformation HRD and Education, Social Development NGO and voluntary work Investment analysis,microfinance and inclusion Retail sector, BPO, KPO Accounting & Information system (with CA / CS /CMA) Hospital management and Health care Hospitality sector and culture and heritage Other sectors of high growth, high technology and social relevance
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
Salient features: • The only programme of its kind (in the whole world) • No publicity and low profile course • For those who want to achieve success in life – not just a degree • Flexible – you may stay for a month and continue the rest of the education by distance mode. / you may attend weekend classes • Scholarships for those from poor economic background • Latest and constantly changing curriculum – keeping pace with the time • Placement for those who are interested • Admissions open throughout the year • Latest and most advanced technologies, books and study material www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
Components • • • • • • • • • • • • • •
Pedagogy curriculum and approach based on IIM Ahmedabad and ISB Hyderabad (the founder is alumnus from IIMA & ISB Hyderabad) Meditation, spiritualisation, and self development Essential softwares for business Business plan, Research projects Participation in conferences / seminars Workshops on leadership, team building etc. Written submissions of research projects/articles / papers Interview of entrepreneurs, writing biographies of entrepreneurs Editing of journals / newsletters Consultancy / research projects Assignments, communication skill workshops Participation in conferences and seminars Group discussions, mock interviews, self development diaryng Mind Power Training & writing workshop (by Dr. T.K.Jain)
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
Pedagogy • • • • • • • • •
Case analysis, Articles from Harvard Business Review Quiz, seminars, workshops, games, Visits to entrepreneurs and industrial visits Presentations, Latest audio-visuals Group discussions and group projects Periodic self assessment Mentoring and counselling Study exchange programme (with institutions out of India) • Rural development / Social welfare projects www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
Branches • AFTERSCHO☺OL will shortly open its branches in important cities in India including Delhi, Kota, Mumbai, Gurgaon and other important cities. Afterschooolians will be responsible for managing and developing these branches – and for promoting social entrepreneurs.
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
Case Studies • We want to write case studies on social entrepreneurs, first generation entrepreneurs, ethical entrepreneurs. Please help us in this process. Help us to be in touch with entrepreneurs, so that we may develop entrepreneurs.
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
Basic values at AFTERSCHO☺OL • • • • • •
Share to learn more Interact to develop yourself Fear is your worst enemy Make mistakes to learn Study & discuss in a group Criticism is the healthy route to mutual support and help • Ask fundamental questions : why, when, how & where? • Embrace change – and compete with yourself only www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
www.afterschoool.tk social entrepreneurship for better society
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
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