The Gini coefficient is a measure of income inequality that ranges from 0 to 100% (or 0 to 1 in decimal form), where 0% indicates perfect equality (everyone has the same income) and 100% indicates maximum inequality (one person has all the income, while everyone else has none). Therefore, any Gini coefficient outside this range is invalid.
Analyzing the provided options:
- Country A has a Gini coefficient of 82% and Country B has a Gini coefficient of 38%. (Valid)
- Country A has a Gini coefficient of 25% and Country B has a Gini coefficient of 74%. (Valid)
- Country A has a Gini coefficient of 122% and Country B has a Gini coefficient of 93%. (Invalid, as Gini cannot exceed 100%)
- Country A has a Gini coefficient of 93% and Country B has a Gini coefficient of -12%. (Invalid, as Gini cannot be negative)
Since Country A is stated to have greater income inequality than Country B, the Gini coefficients must reflect that relationship.
- In the first option, Country A (82%) is greater than Country B (38%): Valid
- In the second option, Country A (25%) is less than Country B (74%): Invalid
- The third and fourth options include invalid Gini coefficients.
Thus, the only valid option that meets all criteria is:
Country A has a Gini coefficient of 82% and Country B has a Gini coefficient of 38%.