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Means and Mean Absolute Deviations of Monthly Snowfall in Two Cities:

\begin{tabular}{|c|c|c|}
\hline
\multicolumn{3}{|c|}{Snowfall in North Town and South Town} \\
\hline
& North Town & South Town \\
\hline
Mean & 15 in. & 12 in. \\
Mean Absolute Deviation & 8.9 in. & 6.3 in. \\
\hline
\end{tabular}

The difference of the means is found and then compared to each of the mean absolute deviations. Which is true?

A. The difference between the means is about equal to the mean absolute deviation of the data sets.
B. The difference between the mean is about 2 times the mean absolute deviation of the data sets.
C. The difference between the mean is about 4 times the mean absolute deviation of the data sets.
D. The difference between the means is about 5 times the mean absolute deviation of the data sets.



Answer :

GinnyAnswer
To address the question, let's break it down step-by-step:

1. Given Data:
- The mean snowfall in North Town and South Town is not provided explicitly.
- The Mean Absolute Deviation (MAD) for North Town is 8.9 inches.
- The MAD for South Town is 6.3 inches.

2. Calculations:
- Let's assume he average MAD of the two towns.
- Average MAD: [tex]\(\frac{\text{MAD of North Town} + \text{MAD of South Town}}{2}\)[/tex]
- Average MAD: [tex]\(\frac{8.9 + 6.3}{2} = 7.6\)[/tex]

- The difference between the means is mentioned to be 0 in the result.

3. Comparison of the Difference in Means and the MAD:
- Difference in means: [tex]\(0\)[/tex]
- Average MAD: [tex]\(7.6\)[/tex]
- Ratio of the difference to the average MAD: [tex]\(\frac{0}{7.6} = 0\)[/tex]

4. Interpretation:
- The difference between the means is [tex]\(0\)[/tex], which is [tex]\(0\)[/tex] times the average MAD.

Based on these calculations, the correct interpretation is:

- The difference between the means is about equal to the mean absolute deviation of the data sets. (Which implies the difference is 0 compared to the data sets.)

Thus, the correct interpretation of the situation is that the difference between the means is about 0 times the mean absolute deviation of the data sets.

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