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Class 11-commerce TR JAIN AND VK OHRI Solutions Statistics for Economics Chapter 12 - Correlation

Correlation Exercise 332

Solution SAQ 1

 

X and Y series show a perfect negative relationship between each other. 

Solution SAQ 2

Solution SAQ 3

Solution SAQ 4

Solution SAQ 5

Solution SAQ 6

Economics

(E)

Rank

R1

History

(H)

Rank

R2

D=

 R1 - R2

D2

66

3

58

3.5

-5

0.25

90

1

76

1

0

0

89

2

65

2

0

0

55

5

58

3.5

1.5

2.25

58

4

53

6

-2

4

44

6

49

7

-1

1

42

7

56

5

2

4

N = 7

 

 

 

 

𝛴 D2 = 11.50

58 is repeated two times in series 2. Thus, m1= 2 and following formula is used to calculate correlation.

Solution SAQ 7

X

R1

Y

R2

D = R1 - R2

D2

80

1

12

8

-7

49

78

2

13

7

-5

25

75

3.5

14

5

-1.5

2.25

75

3.5

14

5

-1.5

2.25

58

8

14

5

3

9

67

5

16

2

3

9

60

6

15

3

3

9

59

7

17

1

6

36

N = 8

 

 

 

 

𝛴 D2 = 141.5

75 is repeated two times in series 1 and 14 is repeated three times in series 2. Thus, m1= 2 and m2= 3 and following formula is used to calculate correlation.

 

Solution SAQ 8

Karl Pearson's Method:

Economics (X)

dx = X - 35

dx2

History (Y)

dy = Y - 50

dy2

dxdy

77

42

1764

35

-15

225

-630

54

19

361

58

8

64

152

27

-8

64

60

10

100

-80

52

17

289

46

-4

16

-68

14

-21

441

50

0

0

0

35

0

0

40

-10

100

0

90

55

3025

35

-15

225

-825

25

-10

100

56

6

36

-60

56

21

441

44

-6

36

-126

60

25

625

42

-8

64

-200

N = 10

𝛴 dx = 140

𝛴dx2 = 7110

N = 10

𝛴dy = -34

𝛴dy2 = 860

𝛴dxdy=-1837

Rank Difference Method:

Economics

R1

History

R2

D = R1 - R2

D2

77

2

35

9.5

-7.5

56.25

54

5

58

2

3

9

27

8

60

1

7

49

52

6

46

5

1

1

14

10

50

4

6

36

35

7

40

8

-1

1

90

1

35

9.5

-8.5

72.25

25

9

56

3

6

36

56

4

44

6

-2

4

60

3

42

7

-4

16

N = 10

 

 

 

 

𝛴D2 = 280.5

35 is repeated two times in series 2. Thus, m1= 2 and following formula is used to calculate correlation.

Correlation Exercise 333

Solution SAQ 9

Teaching

Method

Rank of A

RA

Rank of B

RB

D = RA - RB

D2

I

2

1

1

1

II

1

3

-2

4

III

5

2

3

9

IV

3

4

-1

1

V

4

7

-3

9

VI

7

5

2

4

VII

6

6

0

0

N=7

 

 

 

𝛴D2 = 28

Solution SAQ 10

Examples of perfect correlation:

  1. Relationship between study hours and marks
  2. Relationship between consumption and saving from fixed income
  3. Relationship between amount of loan taken from bank and interest paid

X

R1

Y

R2

D=R1- R2

D2

48

3

13

5.5

-2.5

6.25

33

5

13

5.5

-0.5

0.25

40

4

22

1

3

9

9

9

6

8.5

0.5

0.25

16

7

14

4

3

9

65

1

20

2

-1

1

26

6

9

7

-1

1

15

8

6

8.5

-0.5

0.25

57

2

15

3

0.1

1

N = 9

 

 

 

 

𝛴 D2 = 28

13 and 6 are repeated two times in series 2. Thus, m1= 2 and m2= 2 and following formula is used to calculate correlation.

Solution SAQ 11

 

X

dx = X - 10

dx2

Y

dy = Y - 11

dy2

dxdy

10

0

0

9

-2

4

0

6

-4

16

4

-7

49

28

9

-1

1

6

-5

25

5

10

0

0

9

-2

4

0

12

2

9

11

0

0

0

13

3

4

13

2

4

6

11

1

1

8

-3

9

-3

9

-1

1

4

-7

49

7

N = 8

𝛴dx = 0

𝛴dx2 = 32

N = 8

𝛴dy = -24

𝛴dy2 = 144

𝛴dxdy = 43

Solution SAQ 12

dx

dx2

dy

dy2

dxdy

5

25

5

25

25

-4

16

-12

144

48

-2

4

-7

49

14

20

400

25

625

500

-10

100

-10

100

100

0

0

-3

9

0

3

9

0

0

0

0

0

2

4

0

-15

225

-9

81

135

-5

25

-15

225

75

𝛴 dx = -8

𝛴 dx2 = 804

𝛴 dy = -24

𝛴 dy2 = 1262

𝛴 dxdy = 897

 

Solution SAQ 13

Entry

Judge X (RX)

Judge Y (RY)

D = RX - RY

D2

A

1

12

-11

121

B

2

9

-7

49

C

3

6

-3

9

D

4

10

-6

36

E

5

3

2

4

F

6

5

1

1

G

7

4

3

9

H

8

7

1

1

I

9

8

1

1

J

10

2

8

64

K

11

11

0

0

L

12

1

11

121

N = 12

 

 

 

𝛴 D2 = 416

Solution SAQ 14

RX

RY

D = RX - RY

D2

8

7

1

1

7

5

2

4

6

4

2

4

3

1

2

4

2

3

-1

1

1

2

-1

1

5

6

-1

1

4

8

-4

16

 

 

 

𝛴D2 = 32

Solution SAQ 15

R1

R2

R3

D1 =

R1- R2

D2 =

R1 - R3

D3 =

R2 - R3

D12

D22

D32

1

3

6

-2

-5

-3

4

25

9

6

5

4

1

2

1

1

4

1

5

8

9

-3

-4

-1

9

16

1

10

4

8

6

2

-4

36

4

16

3

7

1

-4

2

6

16

4

36

2

10

2

-8

0

8

64

0

64

4

2

3

2

1

-1

4

1

1

9

1

10

8

-1

-9

64

1

81

7

6

5

1

2

1

1

4

1

8

9

7

-1

1

8

1

1

64

 

 

 

 

 

 

𝛴D12= 200

𝛴D22 = 60

𝛴D32 = 214

 

Judges I and III have a common taste in respect of beauty as they have the highest positive rank correlation coefficient.

Correlation Exercise 334

Solution SAQ 16

Solution SAQ 17

 

Age Group

Mid Value (X)

Percentage of Players (%) (Y)

dX =

X-17.5

dY =

Y-40

dXdY

dX2

dY2

15-16

15.5

200/250×100 = 80

-2

40

-80

4

1600

16-17

16.5

150/2-00×100 = 75

-1

35

-35

1

1225

17-18

17.5

90/150×100 = 60

0

20

0

0

400

18-19

18.5

48/120×100 = 40

1

0

0

1

0

19-20

19.5

30/100×100 = 30

2

-10

-20

4

100

20-21

20.5

12/80×100 = 15

3

-25

-75

9

625

 

N = 6

 

𝛴dX = 3

𝛴dY = 60 

𝛴 dXdY = -210

𝛴dX2 = 19

𝛴 dY2 = 𝛴3950

Solution SAQ 18

 

Density (X)

dx =

X - 500

dx2

dy =

Y-1

dy2

dxdy

200

-300

90000

2

1

1

-300

500

0

0

1

0

0

0

700

200

40000

1.3

0.3

0.09

60

500

0

0

1.4

0.4

0.16

0

600

100

10000

1.6

0.6

0.36

60

900

400

160000

1.7

0.7

0.49

280

 

𝛴dx=400

𝛴dx2=300000

 

𝛴dy=3

𝛴dy2 = 2.1

𝛴dxdy = 100

Solution SAQ 19

Solution SAQ 20

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