STATISTICS PROJECT

Priya Mariam Simon

Aparna Rajeev

Sudhit Sethi

Jinto Antony Kurian

Objective

The main objective of our project is to acquire in-depth understanding of collection, organization and interpretation of numerical facts for taking managerial decisions. The data for the project has been collected from the Outlook (India) site. We have referred the link for the top 100 engineering colleges in India.

Here the variables used are Nominal variables, Ordinal variables and some other variables. Nominal variables used are Name of the Institution, City and G/P (Government/Private). The ordinal variable used is Rank. We have also used various other variables such as IC (Intellectual Capital), I&F (Infrastructure and Facilities), PS (Pedagogic Systems), II (Industry Interface) and P (Placement).

Database

RankName of the Institution city G/P IC I&F PS II P Total

1 IIT Kanpur Kanpur G 28.3 18.9 13.8 13.2 18.5 92.7

2 IIT Kharagpur Kharagpur G 27.9 18.8 13.7 13.5 18.3 92.2

3 IIT Bombay Mumbai G 27.2 18.6 13 13.7 18.7 91.2

4 IIT Madras Chennai G 26.7 18.3 13.3 12.9 17.8 89.1

5 IIT Delhi Delhi G 26.1 18.5 12.7 13.4 18.1 88.8

6 BITS Pilani Pilani P 25.8 17.8 13.5 13.5 17.3 87.9

7 IIT Roorkee Roorkee G 25.5 18.6 12.9 12.4 16.3 85.6

8 IT-BHU Varanasi G 23.9 18.2 12.7 11.9 15.9 82.6

9 IIT Guwahati Guwahati G 25.2 18.1 12.5 10.5 15.1 81.4

10College of Engg, Anna University Guindy G 25.3 16.7 12.4 12.8 14.1 81.3

11

Jadavpur University, Faculty of Engg & Tech Calcutta G 25.2 16.4 11.7 11.4 15.4 80.1

12Indian School of Mines Dhanbad G 24.7 15.5 12.2 12.2 14.7 79.3

13 NIT Warangal G 24.9 16.9 11.8 11.5 14 79.1

14 BIT, Mesra Ranchi P 23.6 13.7 12.3 12.3 14.2 76.1

15 NIT Trichy G 24 17.3 10.4 10.5 13.5 75.7

16Delhi College of Engineering New Delhi G 22.4 15.9 12.6 10.8 13.8 75.5

17Punjab Engineering College Chandigarh G 22 17.7 10.1 9.3 15.8 74.9

18 NIT Suratkal G 23.9 17.1 10.3 10.1 13.3 74.7

19

Motilal Nehru National Inst. of Technology Allahabad G 22.8 16.5 11.3 9.9 14.1 74.6

20

Thapar Inst of Engineering & Technology Patiala p 21.6 16.3 12.3 12.2 12 74.4

21

Bengal Eng and Science University, Shibpur Howrah G 23 15.7 12 10.5 12.1 73.3

22 MANIT Bhopal G 23.5 16.3 10.6 10.4 12.4 73.2

23PSG College of Technology Coimbatore G 21.8 14.9 9.8 13.6 12.8 72.9

24 IIIT Hyderabad G 21.3 16.3 10.3 10.7 13.9 72.5

25

Harcourt Butler Technological Institute Kanpur G 23 15.5 11.3 10.2 12.4 72.4

26

Malviya National Institute of Technology Jaipur G 22.5 16.5 10.4 9.2 13 71.6

27 VNIT Nagpur G 21.8 15.7 10.8 10.2 12.5 71

28 NIT Kozhikode G 21.9 16.8 9.9 10.2 11.9 70.7

29Dhirubhai Ambani IICT Gandhinagar P 22.7 16.3 10.6 9.6 11.2 70.4

30

Osmania Univ. College of Engineering Hyderabad G

22.7 14 10.3 10.9

12.4 70.3

31

College of Engineering, Andhra University

Vishakhapatnam G

22.5

12.7 10.7 10.8

13.5 70.2

32

Netaji Subhas Institute of Technology New Delhi G 22

16.5 9.3 9.7 12 69.5

33 NITKurukshetra G

21.8

15.7 9.9 9.6 12 69.1

34 NIT Rourkela G20.4

14.6 10.3 10.3

13.3 68.9

35 SVNIT Surat G20.3

14.2 10.1 10.6

13.6 68.8

36Govt. College of Engineering Pune G

21.2

12.2 11.1 11.5

12.7 68.7

37Manipal Institute of Technology Manipal p

21.7

12.8 11.2 10.4

12.5 68.6

38 JNTU Hyderabad G21.8

12.5 10.9 10.2

12.9 68.3

39R.V. College of Engineering Bangalore p

20.6

13.2 10.8 10.6 13 68.2

40 NIT Jamshedpur G 19.9 13.4 10.4 10.4 14 68.1

41

University Visvesvaraya College of Engg. Bangalore G 22 13.3 9.6 9.9

12.8 67.6

42 VJTI Mumbai G 20.3 12.6 10.7 10.513.4 67.5

43Vellore Institute of Technology Vellore P 20.3 16.9 9.8 10.1

10.3 67.4

44

Coimbatore Institute of Technology Coimbatore G 20.4 13 10.8 12.2

10.9 67.3

45SSN College of Engineering Chennai P 21.4 12.7 11.3 11.2

10.6 67.2

46 IIIT Allahabad G 19.2 13.6 12 10.511.8 67.1

47College of Engineering Trivandrum G 19.3 16.1 8.9 9.4

13.3 67

48 NIT Durgapur Durgapur G 20.5 12.4 11.3 10.7 12 66.9

49 SIT Calcutta G 22.9 13.4 10.1 8.911.5 66.8

50

Mumbai University Inst of Chemical Tech Mumbai G 20.2 12.5 11.4 10

12.6 66.7

51

Sardar Patel College of Engineering Mumbai p 20.1 12.7 10.2 10.4

13.2 66.6

52P.E.S. Institute of Technology Bangalore p 19.5 13.1 11 11.7 11 66.3

53

Maharashtra Institute of Technology Pune p 20.3 13.4 10 10.2

12.3 66.2

54

Amrita Institute of Technology & Science Coimbatore p 19.8 12.2 12.1 10.5

11.5 66.1

55National Institute of Engineering Mysore p 19.6 11.9 12 10.2

12.2 65.9

56B.M.S. College of Engineering Bangalore p 19.7 13.1 10.9 9.6

12.3 65.6

57Laxminarayan Institute Of Tech. Nagpur G 20.3 12.4 10.3 10.1

12.4 65.5

58Nirma Institute of Technology Ahmedabad p 19.3 13.9 10.2 10 12 65.4

59 IIIT Pune G 19.4 12.6 10.2 10.312.7 65.2

60Amity School of Engineering Noida p 19.7 13.5 9.3 10.1 12.5 65.1

61 JNTU Kakinada G 19.8 12.9 9.8 10.1 12.4 65.1

62S.J. College of Engineering Mysore P 19.7 12.8 10.8 9.4 11.9 64.6

63

Chaitanya Bharathi Inst. of Technology Hyderabad P 19.3 13.3 9.8 9.2 12.9 64.5

64 IIIT Bangalore G 19 11.6 12.1 10.7 10.9 64.3

65

SRM Institute of Science and Technology Chennai P 21 12.4 9.3 8.4 13.1 64.2

66 SASTRA Thanjavur P 18.5 13.2 12 10.3 10.1 64.1

67

Bangalore Institute of Technology Bangalore P 19.5 11.8 10.5 10.2 12 64

68

The Technological Inst. of Textile & Sciences Bhiwani G 19.7 12.9 11.3 9.3 10.7 63.9

69 IIIT Gwalior G 19.7 12.7 10.2 10.3 10.9 63.8

70 JNTU Anantpur G 18.9 12.4 11.3 9 11.8 63.4

71

M.S. Ramaiah Institute of Technology Bangalore P 18.7 14.2 10.1 8.7 11.5 63.2

72 GitamVishakhapatnam P 19.2 14.8 10.6 6.2 12.3 63.1

73 NIT Hamirpur G 18.3 14.8 9.7 7.9 12.2 62.9

74 NIT Jalandhar G 19.6 12.7 9.3 9.1 12.2 62.8

75

SV University Engineering College Tirupati G 19.8 11.5 10.3 10.1 10.7 62.4

76 NIT Raipur G 18.7 13.1 9.6 9.1 11.8 62.3

77Vasavi College of Engineering Hyderabad P 19.6 14.1 9.6 7.1 11.8 62.2

78

The ICFAI Inst of Science and Technology Hyderabad P 20.5 8.4 11.9 11.6 9.7 62.1

79 NIT Patna G 19.7 12.2 10.7 9.2 10.2 62

80

Cummins College of Engg for Women Pune G 20.1 8.7 11.7 11.3 10.1 61.9

81 VIT Pune P 17.9 11.2 11.7 10 10.5 61.3

82

Shri Ramdeo Baba K.N. Engineering College Nagpur P 18.7 13.3 10.4 8.2 9.7 60.3

83

Muffakham Jah Engineering College Hyderabad P 17.1 12.2 8.1 10.2 12.4 60

84Karunya Institute of Technology Coimbatore P 18.1 12.1 8.9 8.4 12.3 59.8

85 D.J. Sanghvi Mumbai P 18.2 12.9 8.1 9.5 11 59.7

86

Sathyabhama Engineering College Chennai P 17.6 12.4 9.5 8.2 11.8 59.5

87

Kongu Engineering College Erode P 17.8 12.7 9.3 8.5 11.2 59.4

88

Mepco Schlenk Engineering College Sivakasi P 17.5 13.8 8.7 8.5 10.8 59.3

89

Guru Nanak Dev Engineering College Ludhiana G 17.7 12.4 8.6 8.8 11.6 59.1

90

Hindustan Inst of Engineering Technology Chennai P 18.9 11.3 9.2 9.3 10.2 58.9

91SDM College of Engineering Dharwad P 16.5 12.7 8 9.6 11.7 58.5

92R.V.R. & J.C. College Of Engg Guntur P 16.8 12.1 9.6 8.7 11.2 58.4

93Jamia Millia Islamia, New Delhi New Delhi G 19.8 10.2 8.8 8.7 10.8 58.3

94K.L. College of Engineering Veddeswaram P 17.8 12.8 9.4 7.5 10.7 58.2

95

Dharmsinh Desai Institute of Technology Nadiad P 16.1 12.1 10.3 9.1 10.1 57.7

96

S.G.S. Institute of Technology & Science Indore G 16.1 11.3 9.8 9.5 10.3 57

97

Jabalpur Engineering College Jabalpur G 15.9 12.5 8.2 8.5 11.8 56.9

98

Sree Chitra Thirunal College of Engineering Trivandrum P 15.5 12.5 7.9 8.7 9.9 54.5

99

G.H. Patel College of Engg & Technology

Vallabh Vidyanagar G 15.1 12.8 9.5 7.4 9.6 54.4

100

Kalinga Institute of Industrial Technology Bhubaneshwar P 14.9 12.9 8.1 8.5 9.8 54.2

IC (Intellectual Capital) represents quality of students each institute possesses.

I&F (Infrastructure and Facilities) include land, building and various other facilities which an institute possesses.

PS (Pedagogic Systems) refer to instructional methods used for educational purposes.

II (Industry Interface) means corporate interaction with the college.

P (Placements) refer to campus recruitments

Frequency Distribution Table

Class interval

midpoints(x)

frequency(f) cf fx d d^2 fd^2

50-55 52.5 0 0 0 -18.05325.802

5 0

55-60 57.5 5 5 287.5 -13.05170.302

5851.512

5

60-65 62.5 21 26 1312.5 -8.05 64.80251360.85

3

65-70 67.5 33 59 2227.5 -3.05 9.3025306.982

5

70-75 72.5 18 77 1305 1.95 3.8025 68.445

75-80 77.5 10 87 775 6.95 48.3025 483.025

80-85 82.5 5 92 412.5 11.95142.802

5714.012

5

85-90 87.5 2 94 175 16.95287.302

5 574.605

90-95 92.5 5 99 462.5 21.95481.802

52409.01

3

95-100 97.5 1 100 97.5 26.95726.302

5726.302

5

    100   7055     7494.75

Mean Median Mode S.D

70.55 66.65 65.1 8.66

In the above data, all the values cluster around 70.55. Similarly one half of the observations in the above data is less than or equal to 66.65 and 65.1 is the value that occurs with the greatest frequency. 8.66 have been computed by taking the positive square root of variance.

Frequency distribution

0

5

21

33

18

10

5

2

5

1

0

5

10

15

20

25

30

35

52.5 57.5 62.5 67.5 72.5 77.5 82.5 87.5 92.5 97.5

midpoints

fre

qu

en

cy

Series1

The Histogram above shows each separate class in the distribution. It shows how the frequency is distributed among the various classes. It is also easy to compare the difference between each class. For example in the above histogram, we have 5 elements in the class between 55 to 60.

Frequency Polygon

Frequency Polygon

0

5

10

15

20

25

30

35

52.5 57.5 62.5 67.5 72.5 77.5 82.5 87.5 92.5 97.5

Total Value

Freq

uenc

y

Series1

Frequency Polygon shows the outline of the data pattern more clearly.

Less than ogive

Less than Ogive

0

20

40

60

80

100

120

52.5 57.5 62.5 67.5 72.5 77.5 82.5 87.5 92.5 97.5

Total value

Cum

ulat

ive

freq

uenc

y

Series1

The Ogive curve above is a graphical representation of the cumulative frequency distribution. The X axis here represents the TOTAL obtained from various attributes and Y axis represents the cumulative frequency. At any given point in the ogive curve, we can determine the number of values lying under it.

Pie Chart showing distribution of Engineering Institutes

Distribution of colleges

G60%

P40%

G

P

From the above pie chart, we can infer the distribution of the type to which the college belongs. Here in our data, we have two types; private colleges which constitute 40% and government colleges constitute 60% of the total

Table showing Correlation and Regression between IC & P

correlation 0.81

slope 0.57

intercept 0.71

R^2 0.649154

R 0.805701

Correlation between IC & P

y = 0.5707x + 0.7104

R2 = 0.6492

02468

101214161820

0 5 10 15 20 25 30

Intellectual Capital

Pla

cem

en

ts

Series1

Linear (Series1)

The above chart shows a high positive correlation between IC & P. This is a straight line (linear) regression model and is expressed with respect to the

parameters Intellectual Capital and Placement asy=0.5707x+0.7104

R2=0.6492 indicates the proportion of the variance in the placements which is explained by the independent variable (intellectual capital). The coefficient of correlation is found by using the above equation, and is 0.805 which shows

there’s a HIGH degree of correlation between the two parameters considered here.

Table showing Correlation and Regression between II & P

Correlation coefficient 0.630374

Slope 0.853955

Intercept 3.843427

r^2 0.397371

r 0.630374

Correlation between II & P

y = 0.854x + 3.8434

R2 = 0.3974

02468

101214161820

0 5 10 15

Industry Interface

Pla

cem

en

ts

Series1

Linear (Series1)

The above chart shows that there is substantial correlation between Industry Interface and Placement. This is also a straight line (linear) regression model and is expressed with respect to the parameters Industry Interface and Placement as:

y=0.854x+3.8434R2=0.397 indicates the proportion of variance between the Placements (dependent variable) which is explained by the independent variable (Industry Interface). ). The coefficient of correlation is found by using the above equation, and is 0.630 which shows there’s a SUBSTANTIAL degree of correlation between the two parameters considered here.

Rank Correlation

Rank name of the institutionIndustry Interface Placements rank rank

square of diff

1 IIT Kanpur 13.2 18.5 5 2 9

2 IIT Kharagpur 13.5 18.3 3 3 0

3 IIT Bombay 13.7 18.7 1 1 0

4 IIT Madras 12.9 17.8 6 5 1

5 IIT Delhi 13.4 18.1 4 4 0

6 BITS Pilani 13.5 17.3 3 6 9

7 IIT Roorkee 12.4 16.3 8 7 1

8 IT-BHU 11.9 15.9 11 8 9

9 IIT Guwahati 10.5 15.1 22 11 121

10College of Engg, Anna University 12.8 14.1 7 14 49

11Jadavpur University, Faculty of Engg & Tech 11.4 15.4 15 10 25

12 Indian School of Mines 12.2 14.7 10 12 4

13 NIT 11.5 14 14 15 1

14 BIT, Mesra 12.3 14.2 9 13 16

15 NIT 10.5 13.5 22 19 9

16Delhi College of Engineering 10.8 13.8 19 17 4

17Punjab Engineering College 9.3 15.8 33 9 576

18 NIT 10.1 13.3 26 21 25

19Motilal Nehru National Inst. of Technology 9.9 14.1 28 14 196

20

Thapar Inst of Engineering & Technology 12.2 12 10 34 576

21

Bengal Eng and Science University, Shibpur 10.5 12.1 22 33 121

22 MANIT 10.4 12.4 23 30 49

23PSG College of Technology 13.6 12.8 2 26 576

24 IIIT 10.7 13.9 20 16 16

25Harcourt Butler Technological Institute 10.2 12.4 25 30 25

26Malviya National Institute of Technology 9.2 13 34 24 100

27 VNIT 10.2 12.5 25 29 16

28 NIT 10.2 11.9 25 35 100

29 Dhirubhai Ambani IICT 9.6 11.2 30 40 100

30Osmania Univ. College of Engineering 10.9 12.4 18 30 144

31College of Engineering, Andhra University 10.8 13.5 19 19 0

32Netaji Subhas Institute of Technology 9.7 12 29 34 25

33 NIT 9.6 12 30 34 16

34 NIT 10.3 13.3 24 21 9

35 SVNIT 10.6 13.6 21 18 9

36Govt. College of Engineering 11.5 12.7 14 27 169

37Manipal Institute of Technology 10.4 12.5 23 29 36

38 JNTU 10.2 12.9 25 25 0

39R.V. College of Engineering 10.6 13 21 24 9

40 NIT 10.4 14 23 15 64

41

University Visvesvaraya College of Engg. 9.9 12.8 28 26 4

42 VJTI 10.5 13.4 22 20 4

43Vellore Institute of Technology 10.1 10.3 26 47 441

44Coimbatore Institute of Technology 12.2 10.9 10 42 1024

45SSN College of Engineering 11.2 10.6 17 45 784

46 IIIT 10.5 11.8 22 36 196

47College of Engineering 9.4 13.3 32 21 121

48 NIT Durgapur 10.7 12 20 34 196

49 SIT 8.9 11.5 37 39 4

50

Mumbai University Inst of Chemical Tech 10 12.6 27 28 1

51

Sardar Patel College of Engineering 10.4 13.2 23 22 1

52P.E.S. Institute of Technology 11.7 11 12 41 841

53

Maharashtra Institute of Technology 10.2 12.3 25 31 36

54

Amrita Institute of Technology & Science 10.5 11.5 22 39 289

55National Institute of Engineering 10.2 12.2 25 32 49

56B.M.S. College of Engineering 9.6 12.3 30 31 1

57Laxminarayan Institute Of Tech. 10.1 12.4 26 30 16

58Nirma Institute of Technology 10 12 27 34 49

59 IIIT 10.3 12.7 24 27 9

60Amity School of Engineering 10.1 12.5 26 29 9

61 JNTU 10.1 12.4 26 30 16

62S.J. College of Engineering 9.4 11.9 32 35 9

63Chaitanya Bharathi Inst. of Technology 9.2 12.9 34 25 81

64 IIIT 10.7 10.9 20 42 484

65

SRM Institute of Science and Technology 8.4 13.1 41 23 324

66 SASTRA 10.3 10.1 24 49 625

67Bangalore Institute of Technology 10.2 12 25 34 81

68

The Technological Inst. of Textile & Sciences 9.3 10.7 33 44 121

69 IIIT 10.3 10.9 24 42 324

70 JNTU 9 11.8 36 36 0

71

M.S. Ramaiah Institute of Technology 8.7 11.5 39 39 0

72 Gitam 6.2 12.3 47 31 256

73 NIT 7.9 12.2 43 32 121

74 NIT 9.1 12.2 35 32 9

75

SV University Engineering College 10.1 10.7 26 44 324

76 NIT 9.1 11.8 35 36 1

77Vasavi College of Engineering 7.1 11.8 46 36 100

78

The ICFAI Inst of Science and Technology 11.6 9.7 13 52 1521

79 NIT 9.2 10.2 34 48 196

80Cummins College of Engg for Women 11.3 10.1 16 49 1089

81 VIT 10 10.5 27 46 361

82

Shri Ramdeo Baba K.N. Engineering College 8.2 9.7 42 52 100

83

Muffakham Jah Engineering College 10.2 12.4 25 30 25

84Karunya Institute of Technology 8.4 12.3 41 31 100

85 D.J. Sanghvi 9.5 11 31 41 100

86

Sathyabhama Engineering College 8.2 11.8 42 36 36

87Kongu Engineering College 8.5 11.2 40 40 0

88

Mepco Schlenk Engineering College 8.5 10.8 40 43 9

89

Guru Nanak Dev Engineering College 8.8 11.6 38 38 0

90

Hindustan Inst of Engineering Technology 9.3 10.2 33 48 225

91SDM College of Engineering 9.6 11.7 30 37 49

92R.V.R. & J.C. College Of Engg 8.7 11.2 39 40 1

93Jamia Millia Islamia, New Delhi 8.7 10.8 39 43 16

94K.L. College of Engineering 7.5 10.7 44 44 0

95

Dharmsinh Desai Institute of Technology 9.1 10.1 35 49 196

96

S.G.S. Institute of Technology & Science 9.5 10.3 31 47 256

97Jabalpur Engineering College 8.5 11.8 40 36 16

98

Sree Chitra Thirunal College of Engineering 8.7 9.9 39 50 121

99G.H. Patel College of Engg & Technology 7.4 9.6 45 53 64

100Kalinga Institute of Industrial Technology 8.5 9.8 40 51 121

Total (D) 14768

Rank correlation

1-6∑D^2+(m^3-m/12)/n(n^2-1)

sum of squares of the differences

D 14768

no. of repetitions m** 2382

0.910192019

The rank correlation is calculated from the above procedure. Where the sum of the squares of the differences of the rank are taken. Since we have repetitive ranks, a modified formulae is used which is shown in the above tabular column.Using this approach the Rank Correlation is found to be .9101