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 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

 Artisans Name Position given Judge RP Position given Judge RR D= RP−RR D2 PQRSTUVWXY 29552247810 38572325109 -110-20-122-21 1104014441 ΣD2=20

N= 10

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

 Maths Marks Accountancy Marks R1 R2 D= R1−R2 D2 5060657075408085 8071607590827050 23456178 64258731 −4−120−2−647 161404361649 ΣD2=126

N= 8

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

 RA RB D = RA− RB D2 35847102169 64981231057 −31−1−468−1−912 91116366418114 ΣD2=214

N= 10

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

 Advertising Cost(X) Sales(Y) R1 R2 D= R1−R2 D2 78369825758290626539 84519160686286585347 72101689453 82105769431 −100−4−120022 10016140044 ΣD2=30

N= 10

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.

 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

 X Y R1 R2 D=R1−R2 D2 123456789101112 129610354782111 123456789101112 129610354782111 −11−7−3−6213118011 1214993641911640121 N = 12 ΣD2=416

Here, m= 0

N= 12

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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