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 | D^{2} |

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 |

ΣD^{2}=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
| D^{2} |

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 |

ΣD^{2}=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 | D^{2} |

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 |

ΣD^{2}=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 |

**Answer:**

Advertising Cost
| Sales
| R1 | R2 | D= R1−R2
| D^{2} |

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 |

ΣD^{2}=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 |

**Answer:**

X | Y | R1 | R2 | D=R1−R2
| D^{2} |

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 | ΣD^{2}=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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