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T.R. Jain and V.K. Ohri- Statistics for Economics Solution for Class 11 Commerce Statistics for Economics Chapter 12 - Correlation

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T.R. Jain and V.K. Ohri- Statistics for Economics Solution for Class 11 Commerce Statistics for Economics Chapter 12 - Correlation Page/Excercise 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.

T.R. Jain and V.K. Ohri- Statistics for Economics Solution for Class 11 Commerce Statistics for Economics Chapter 12 - Correlation Page/Excercise 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.

T.R. Jain and V.K. Ohri- Statistics for Economics Solution for Class 11 Commerce Statistics for Economics Chapter 12 - Correlation Page/Excercise 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

Text Book Solutions

CBSE XI Commerce - Statistics for Economics

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