To determine the relationship between education and life expectancy, we can analyze the data using statistical measures, notably correlation.
### Step-by-Step Solution
1. List the Given Data:
- Norway:
- Life Expectancy: 81.3 years
- Years of Education: 12.6 years
- Greece:
- Life Expectancy: 80 years
- Years of Education: 10.1 years
- Colombia:
- Life Expectancy: 73.9 years
- Years of Education: 7.3 years
- Mali:
- Life Expectancy: 51.9 years
- Years of Education: 2 years
2. Calculate Sums and Means:
- Sum of Life Expectancies: 81.3 + 80 + 73.9 + 51.9 = 287.1
- Sum of Years of Education: 12.6 + 10.1 + 7.3 + 2 = 32
- Number of Countries (n): 4
- Mean Life Expectancy: \( \frac{287.1}{4} = 71.775 \)
- Mean Years of Education: \( \frac{32}{4} = 8 \)
3. Variance Calculations:
- Variance of Life Expectancy:
\( \frac{(81.3 - 71.775)^2 + (80 - 71.775)^2 + (73.9 - 71.775)^2 + (51.9 - 71.775)^2}{4} = 137.39 \)
- Variance of Years of Education:
\( \frac{(12.6 - 8)^2 + (10.1 - 8)^2 + (7.3 - 8)^2 + (2 - 8)^2}{4} = 16.31 \)
4. Covariance Calculation:
- Covariance:
\( \frac{(81.3 - 71.775)(12.6 - 8) + (80 - 71.775)(10.1 - 8) + (73.9 - 71.775)(7.3 - 8) + (51.9 - 71.775)(2 - 8)}{4} = 43.68 \)
5. Correlation Calculation:
- Correlation:
\( \frac{43.68}{\sqrt{137.39 \times 16.31}} = 0.92 \)
### Conclusion
Based on the correlation value of 0.92, which is greater than 0.7, we can infer a strong positive relationship between the two variables.
Therefore, the best description of the relationship between education and life expectancy based on the given data is:
- More education can help increase life expectancy.
