1. The problem asks us to evaluate the appropriateness of a polynomial trend line fitted to data points representing average access to basic water services (%) versus ARC (%). 2. A polynomial trend line is used to model non-linear relationships by fitting a curve that can pass close to or through many data points. 3. Under-fitting occurs when the model is too simple to capture the data pattern, often missing key trends. 4. Over-fitting happens when the model is too complex, fitting noise or random fluctuations rather than the underlying trend. 5. The statement "It is under-fitted because the line doesn’t pass through all of the data points" is incorrect because a trend line rarely passes through all points; it aims to capture the overall pattern. 6. The statement "It is over-fitted but a linear line will also not be able to describe the relationship because the data are non-linear" suggests the polynomial may be too complex, but linear models are insufficient due to non-linearity. 7. The statement "It is over-fitted but a linear line will be able to describe the relationship better" contradicts the non-linear nature of the data. 8. The statement "It is under-fitted but a linear line will also not be able to describe the relationship because the data are non-linear" implies the polynomial is too simple and linear models are inadequate. 9. Given the data's non-linear pattern and the polynomial trend line fluctuating smoothly through the data, the best description is that the polynomial trend line captures the non-linear relationship better than a linear line, and it is not under-fitted. 10. Therefore, the correct statement is: "It is over-fitted but a linear line will also not be able to describe the relationship because the data are non-linear."