Quantitative Aptitude & Quantitative Techniques 24 November

QUANTITATIVE APTITUDE & QUANTITATIVE TECHNIQUES 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

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AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS

QUANTITATIVE APTITUDE & QUANTITATIVE TECHNIQUES 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

WHAT IS CORRELATION • Any association between two variables is called correlation. Correlation can be of various types: • Positive (example: income and demand) • Negative (example: Price and demand) • Linear (where the correlation moves in a linear fashion)( see the graph) • Curvilinear • Partial (when it is not complete). www.afterschoool.tk

AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS

Positive linear correlation.. INCOME V/S DEMAND MORE THE INCOME, MORE WILL BE THE DEMAND

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AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS

NEGATIVE LINEAR CORRELATION PRICE V/S DEMAND, HIGHER THE PRICE, LESS WILL BE THE DEMAND AND LOWER THE PRICE, HIGHER WILL BE THE DEMAND.

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AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS

Corvilinear correlation

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AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS

How to judge correlation ? • 1. Scatter Diagram Method (just plot the dots, find the mid line and prepare a graph, and observe the graph). • 2. Graphic Method • 3. Karl Pearson’s Coefficient of Correlation Method • 4. Spearman’s Rank Correlation Method • 5. Con-current deviation Method • 6. Method of Least-squares www.afterschoool.tk

AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS

Find correlation between the following two series: price

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demand 10

50

15

40

20

35

24

24

30

20

99

169

AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS

Write a note on scatter diagram? • It is the simplest and easiest measure to judge correlation. Here we plot the actual data (pairs of actual observations) on a graph paper and try to draw a line from the middle of these data. • This method is possible, when the relationship is very clearly visible – i.e. there is straight positive or negative relationship. www.afterschoool.tk

AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS

What is coefficient of correlation • It si a measure of relation (remember, it does not check causation). • It is independent of change of origin, even if we change the origin, it will remain the same. • It is denoted by r. r=0 means no correlation, r=1 means perfect positive correlation, r =-1 • Square of r is called coefficient of determination.

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AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS

What are the basic assumptions in Karl Pearson’s correlation ? • Both the data sets are based on ratio scale • Both the values are normally distributed. • There is some relationship between the two variables – which may be based on cause – effect relationship (correlation does not identify cause effect relationship). www.afterschoool.tk

AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS

What is probable error .. • We can draw two limits (upper and lower limits) where by we can ensure that there will be 50% probability that the values will lie in the range. The values of probable error may be added or subtracted to the average correlation values, to find the range. • PE =.6745*(1- r^2)/ sqrt(n) • N= number of values • R= correlation value. www.afterschoool.tk

AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS

What is standard error? • It is a better measure in comparison to probable error. It is the standard deviation of sampling distribution of the statistics drawn from randam sampling. It is 3/2 of the probable error. • S.E. = (1 – r^2)/ Sqrt(n) • There is 99.73% chanse that the values will fall in the range (upper and lower values) of correlation + - standard error. www.afterschoool.tk

AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS

What is coefficient of determination.. • It shows the proportion of total variability. • It is denoted by r^2. • If correlation is .6, it means it accounts for 36% variability, similarly, if correlation is .4, it accounts for only 16% variability of the values.

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AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS

Find the correlation between height and weight of any 5 friends… Name

Height

Weight

Amit

180

70

Giriraj Dushyant Nitin Jayant

170 180 166 168

58 53 51 49

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AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS

Solution . Name

Height

Weight dx

Dy

DXDY

DXSQR

DYSQR

Amit

180

70

7.2

13.8

99.36

51.84

190.44

Giriraj

170

58

-2.8

1.8

-5.04

7.84

3.24

Dushyant

180

53 7.2

-3.2

-23.04

51.84

10.24

Nitin

166

51

-6.8

-5.2

35.36

46.24

27.04

Jayant

168

49

-4.8

-7.2

34.56

23.04

51.84

864

281

141.2

180.8

282.8

172.8

56.2

covariance

28.24

36.16

56.56

correlation

0.6244

6.0133

7.5206

average

45.224

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AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS

Solution … • As we can see, the correlation is : .6244 (this shows that there is positive relation between height and weight, that means if height increases weight also increases).

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AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS

Calculate range,within which random values will fall with 99.7% certainty? • • • •

S.E. = (1- r^2) / sqrt (n) =(1-.6244^2)/sqrt(5) =.2729 Thus range is : .6244+.2729 and .6244 .2729 • Thus we will get the range:.8973 and .3515 answer. www.afterschoool.tk

AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS

Solution … • Step 1. calculate average of the two series. • Step 2. Calculate standard deviation of the two series. • Step 3: calculate covariance • Step 4. Divide covariance by the product of the two standard deviations. This is correlation. www.afterschoool.tk

AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS

Steps in standard deviation… • 1. calculate mean (sum divided by number of items) • 2. calculate Dx and Dy • 3. calculate squares of Dx and Dy. • 4. find mean of Dxsquare and Dy square • 5. calculate square roots of the above values. This is standard deviation. www.afterschoool.tk

AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS

Calculation of standard deviation price X

demand Y

Dx

Dy

Dx^2

Dy^2

10

50

-9.8

16.2

96

262

15

40

-4.8

6.2

23

38.4

20

35

0.2

1.2

0.04

1.44

24

24

4.2

-9.8

17.6

96

30

20

10.2

-14

104

190

99

169

Total

241

589

19.8

33.8

Var=

48.2

118

sqrt (std. dev.)

6.94

10.9

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AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS

How to calculate covariance… 1. You have already calculated Dx and Dy by now. 2. Get the product of Dx and Dy by multiplying them. 3. Now addup all these values 4. Get the average of sum of DxDy by dividing the above value by the number. 5. This is called covariance. www.afterschoool.tk

AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS

Final solution … • Divide covariance by the product of standard deviations. • This is correlation. • In the question, we have covariance = -.74 • Standard deviations are : 6.9 and 10.9. When we multiply these standard deviations to each other, we get 75.3 • Divide covariance by 75.3, we get -.98 • This correlation. Answer. www.afterschoool.tk

AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS

Final word… • Correlation will never be less than -1 and more than 1. it will always be between 1 to -1. • 1 = perfect positive correlation • -1 = perfect negative correlation.

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AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS

Final solution… price X

dema nd Y

Dx

Dy

Dx^2

Dy^2

DX * DY

10

50

-9.8

16.2

96

262

-158.76

15

40

-4.8

6.2

23

38.4

-29.76

20

35

0.2

1.2

0.04

1.44

0.24

24

24

4.2

-9.8

17.6

96

-41.16

30

20

10.2

-14

104

190

-140.76

99

169

Total

241

589

-370.2

19.8

33.8

Var=

48.2

118

-74.04

sqrt (std. dev.)

6.94

10.9

-0.98316

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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.

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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.

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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

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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

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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 EsGotitial 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)

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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 PreGotitations, 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.

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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.

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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

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AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS