Sandeep Garg Solutions for Class 11 Economics Chapter 8 - Measures of Correlation

Sandeep Garg Class 11 Economics Solutions Economics Chapter 8 – Measures of Correlation are illustrated by the professional economic educator from the contemporary edition of Sandeep Garg Economics Class 11 textbook solutions.

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Sandeep Garg Solutions Class 11 – Chapter 8

Question1

Evaluate the coefficient of rank correlation of ten artisans of a facility that is ranked in terms of their capability by 2 separate judges:

Artisans Name P Q R S T U V W X Y
Position given Judge P 2 9 5 5 2 2 4 7 8 10
Position given Judge R 3 8 5 7 2 3 2 5 10 9

Answer:

Artisans Name Position given Judge RP Position given Judge RR D= RP−RR D2
P

Q

R

S

T

U

V

W

X

Y

2

9

5

5

2

2

4

7

8

10

3

8

5

7

2

3

2

5

10

9

1

1

0

-2

0

-1

2

2

-2

1

1

1

0

4

0

1

4

4

4

1

ΣD2=20

N= 10

rk = 1 – 6ΣD2

Or, rk = \(\frac{6X20}{1000-10}\)

rk= 1 – 0.121

rk = 0.88

Hence, the coefficient of rank correlation is 0.88

Question 2

Evaluate the coefficient of rank correlation.

Maths Marks 50 60 65 70 75 40 80 85
Accountancy Marks 80 71 60 75 90 82 70 50

Answer:

Maths Marks Accountancy Marks R1 R2 D= R1−R2

 

D2
50

60

65

70

75

40

80

85

80

71

60

75

90

82

70

50

2

3

4

5

6

1

7

8

6

4

2

5

8

7

3

1

−4

−1

2

0

−2

−6

4

7

16

1

4

0

4

36

16

49

ΣD2=126

N= 8

rk = 1 – 6ΣD2

Or, rk = \(\frac{6X126}{512-8}\)

rk = 0.5

Hence, the coefficient of rank correlation is 0.5

Question 3

What is the coefficient of rank correlation of the following information

Subject A 3 5 8 4 7 10 2 1 6 9
Subject B 6 4 9 8 1 2 3 10 5 7

Answer:

RA RB D = RA− RB D2
3

5

8

4

7

10

2

1

6

9

6

4

9

8

1

2

3

10

5

7

−3

1

−1

−4

6

8

−1

−9

1

2

9

1

1

16

36

64

1

81

1

4

ΣD2=214

N= 10

rk = 1 – \(\frac{6\sum D^{2}}{N^{3}-N}\)

Or, rk = \(\frac{6X214}{1000-10}\)

rk = 0.2969

Hence, the coefficient of rank correlation is -0.297

Question 4

Evaluate rank correlation between advertisement sales and cost according to the following information

Cost 78 36 98 25 75 82 90 62 65 39
Sales (in lakh ) 84 51 91 60 68 62 86 58 53 47

Answer:

Advertising Cost

(X)

Sales

(Y)

R1 R2 D= R1−R2

 

D2
78

36

98

25

75

82

90

62

65

39

84

51

91

60

68

62

86

58

53

47

7

2

10

1

6

8

9

4

5

3

8

2

10

5

7

6

9

4

3

1

−1

0

0

−4

−1

2

0

0

2

2

1

0

0

16

1

4

0

0

4

4

ΣD2=30

N= 10

rk = 1 – \(\frac{6\sum D^{2}}{N^{3}-N}\)

Or, rk = 1- \(\frac{6X3}{1000-10}\)

rk = 1 – 0.1818 = – 0.818

Hence, the coefficient of rank correlation is -0.82

Question 5

Evaluate rank coefficient of correlation.

X 1 2 3 4 5 6 7 8 9 10 11 12
Y 12 9 6 10 3 5 4 7 8 2 11 1

Answer:

X Y R1 R2 D=R1−R2

 

D2
1

2

3

4

5

6

7

8

9

10

11

12

12

9

6

10

3

5

4

7

8

2

11

1

1

2

3

4

5

6

7

8

9

10

11

12

12

9

6

10

3

5

4

7

8

2

11

1

−11

−7

−3

−6

2

1

3

1

1

8

0

11

121

49

9

36

4

1

9

1

1

64

0

121

N = 12 ΣD2=416

Here, m= 0

rk = 1 – \(\frac{6\sum D^{2}}{N^{3}-N}\)

rk = 1- \(\frac{6X416}{1728-12}\)

Or, rk = 1 – \(\frac{2946}{1716}\)

rk = – 0.454

Hence, the coefficient of rank correlation is – 0.454

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