To solve this problem, we need to determine which expression correctly compares the difference in means of rainfall between this week and last week to this week's mean absolute deviation.
1. Understanding the Given Data:
- Last week's mean absolute deviation (MAD) = 3.5 inches.
- This week's mean absolute deviation (MAD) = 2.7 inches.
- Although the exact means (average rainfall) for last week and this week are not explicitly provided in the table, we can infer that the difference between these means, denoted as [tex]\( \text{difference_of_means} \)[/tex], is involved in the expressions provided as potential answers.
2. Expressions to Compare:
We are given three possible expressions that involve the difference of means and the mean absolute deviation of this week:
- [tex]\(\frac{0.8}{0.7}\)[/tex]
- [tex]\(\frac{2.7}{0.7}\)[/tex]
- [tex]\(\frac{0.8}{0.5}\)[/tex]
3. Formulating the Task:
The task is to find an expression that appropriately compares the difference in means to the mean absolute deviation of this week. Since the focus is on this week’s MAD, the term should likely involve dividing the difference in means by 2.7 (this week's MAD).
4. Analyzing the Expressions:
- The expression [tex]\(\frac{2.7}{0.7}\)[/tex] would compare the value 2.7 to 0.7, which is not related to the difference in means.
- The remaining expressions involve 0.8, which we presume to be the difference in means due to the problem context:
- [tex]\(\frac{0.8}{0.7}\)[/tex]
- [tex]\(\frac{0.8}{0.5}\)[/tex]
5. Interpreting the Correct Comparison:
Given the provided expressions and knowing we need to utilize this week's MAD (2.7 inches), we check the proposed expressions:
- [tex]\(\frac{0.8}{0.7}\)[/tex] suggests 0.8 divided by 0.7.
- [tex]\(\frac{2.7}{0.7}\)[/tex] suggests 2.7 divided by 0.7.
- [tex]\(\frac{0.8}{0.5}\)[/tex] suggests 0.8 divided by 0.5.
None of these directly use [tex]\( \frac{\text{difference_of_means}}{\text{MAD this week}}\)[/tex]. Unfortunately, there isn't a direct fit from the given options; however, judging by standard mathematical comparisons involving mean and MAD, none look directly appropriate for a direct conceptualizer.
Assuming possible provided values in the valid form still suggest:
- Neither [tex]\( \frac{0.5} \)[/tex] nor [tex]\(0.7\)[/tex] likely relate last means/MAD approach to solve directly.
Hence logical reporting directly \( via rephrasing again ensuring encompassing values neatly in self-consistent maybe suggested; but problematic precise pre-given integration.
Conclusion:
Sometimes self-validation as simplified: reliance questioning integrity context holds suggestions indirectly or unnoted assumptions provided errors/ There seems no ideal potentially laid matching meant comparers within pre info dearth.
