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4th Edition

HEALEY + 1 other

Publisher: Cengage Learning,

ISBN: 9781305093836

Chapter 11, Problem 11.11P

Textbook Problem

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Nation |
Diversity |
Inequality |

India | 91 | 29.7 |

South Africa | 87 | 58.4 |

Kenya | 83 | 57.5 |

Canada | 75 | 31.5 |

Malaysia | 72 | 48.4 |

Kazakhstan | 69 | 32.7 |

Egypt | 65 | 32.0 |

United States | 63 | 41.0 |

Sri Lanka | 57 | 30.1 |

Mexico | 50 | 50.3 |

Spain | 44 | 32.5 |

Australia | 31 | 33.7 |

Finland | 16 | 25.6 |

Ireland | 4 | 35.9 |

Poland | 3 | 27.2 |

To determine

**To find:**

The spearman’s rho correlation.

**Given:**

The table of 15 nations on a measure of ethnic diversity and economic inequality is given below,

Nation | Diversity | Inequality |

India | 91 | 29.7 |

South Africa | 87 | 58.4 |

Kenya | 83 | 57.5 |

Canada | 75 | 31.5 |

Malaysia | 72 | 48.4 |

Kazakhstan | 69 | 32.7 |

Egypt | 65 | 32.0 |

United States | 63 | 41.0 |

Sri Lanka | 57 | 30.1 |

Mexico | 50 | 50.3 |

Spain | 44 | 32.5 |

Australia | 31 | 33.7 |

Finland | 16 | 25.6 |

Ireland | 4 | 35.9 |

Poland | 3 | 27.2 |

**Formula used:**

The formula to calculate the Spearman’s rho is given by,

Where,

The formula to calculate the difference in ranks is calculated as,

**Calculation:**

Let the Quality of life be

Consider the following table of differences in ranks,

Diversity |
Inequality |
Rank |
Rank |
||

91 | 29.7 | 1 | 13 | 144 | |

87 | 58.4 | 2 | 1 | 1 | 1 |

83 | 57.5 | 3 | 2 | 1 | 1 |

75 | 31.5 | 4 | 11 | 49 | |

72 | 48.4 | 5 | 4 | 1 | 1 |

69 | 32.7 | 6 | 8 | 4 | |

65 | 32.0 | 7 | 10 | 9 | |

63 | 41.0 | 8 | 5 | 3 | 9 |

57 | 30.1 | 9 | 12 | 9 | |

50 | 50.3 | 10 | 3 | 7 | 49 |

44 | 32.5 | 11 | 9 | 2 | 4 |

31 | 33.7 | 12 | 7 | 5 | 25 |

16 | 25.6 | 13 | 15 | 4 | |

4 | 35.9 | 14 | 6 | 8 | 64 |

3 | 27.2 | 15 | 14 | 1 | 1 |

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