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 by Judge P | 2 | 9 | 5 | 5 | 2 | 2 | 4 | 7 | 8 | 10 |
| Position given by Judge R | 3 | 8 | 5 | 7 | 2 | 3 | 2 | 5 | 10 | 9 |
Answer:
| Artisans Name | Position given by Judge RP | Position given by 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
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 |
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
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 |
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
ρ = 1 – \(\frac{6\sum D^{2}}{N^{3}-N}\)
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 |
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
ρ = 1 – \(\frac{6\sum D^{2}}{N^{3}-N}\)
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 |
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
N= 12
ρ = 1 – \(\frac{6\sum D^{2}}{N^{3}-N}\)
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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