Sandeep Garg Solutions Class 11 Economics Chapter 8 – Measures of Correlation


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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 NamePQRSTUVWXY
Position given Judge P29552247810
Position given Judge R38572325109

Answer:

Artisans NamePosition given Judge RPPosition given Judge RR D= RP−RRD2
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

Spearmans Rank Correlation

Or, ρ = 1- (frac{6X20}{1000-10})

ρ= 1 – 0.121

ρ = 0.88

Hence, the coefficient of rank correlation is 0.88

Question 2

The following are marks of 8 students in Maths and Accountancy. Evaluate the coefficient of rank correlation.

Maths Marks5060657075408085
Accountancy Marks 8071607590827050

Answer:

Maths MarksAccountancy Marks R1R2D= 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

Spearmans Rank Correlation

Or, ρ = 1- (frac{6X126}{512-8})

ρ = 1- 1.5

ρ = 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 A35847102169
Subject B64981231057

Answer:

RARBD = 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

Spearmans Rank Correlation

ρ = 1 – (frac{6sum D^{2}}{N^{3}-N})

Or, ρ = 1- (frac{6X214}{1000-10})

ρ = 1- 1.2969

Hence, the coefficient of rank correlation is -0.2969

Question 4

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

Cost 78369825758290626539
Sales (in lakh )84519160686286585347

Answer:

Advertising Cost

(X)

Sales

(Y)

R1R2D= 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

Spearmans Rank Correlation

ρ = 1 – (frac{6sum D^{2}}{N^{3}-N})

Or, ρ = 1- (frac{6X30}{1000-10})

ρ = 1 – 0.1818

=  0.818

Hence, the coefficient of rank correlation is 0.82

Question 5

Evaluate rank coefficient of correlation.

X123456789101112
Y129610354782111

Answer:

XYR1R2D=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 = 12ΣD2=416

Here, m= 0

N= 12

Spearmans Rank Correlation

ρ = 1 – (frac{6sum D^{2}}{N^{3}-N})

ρ = 1- (frac{6X416}{1728-12})

Or, ρ = 1 – (frac{2496}{1716})

ρ = 1- 1.4545

= -0.4545

Hence, the coefficient of rank correlation is – 0.4545

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