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The table shows human development indicators from 2013.

\begin{tabular}{|l|l|l|}
\hline \begin{tabular}{c}
Country and \\
rank
\end{tabular} & \multicolumn{1}{|c|}{\begin{tabular}{c}
Life \\
expectancy
\end{tabular}} & \multicolumn{1}{|c|}{\begin{tabular}{c}
Years of \\
education
\end{tabular}} \\
\hline 1. Norway & 81.3 & 12.6 \\
\hline 29. Greece & 80 & 10.1 \\
\hline 91. Colombia & 73.9 & 7.3 \\
\hline 182. Mali & 51.9 & 2 \\
\hline
\end{tabular}

Which best describes the relationship between education and life expectancy?

A. More education can help increase life expectancy.
B. Higher life expectancy can lead to more education.
C. Education and life expectancy have no relationship.
D. Education and life expectancy influence each other.



Answer :

GinnyAnswer
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.

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