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The table records the rainfall in two cities during a particular week. Which statements about the data are true?

\begin{tabular}{|c|c|}
\hline Rainfall in McKesson (inches) & Rainfall in Sansome (inches) \\
\hline 3.76 & 3.14 \\
\hline 2.45 & 3.01 \\
\hline 3.01 & 2.36 \\
\hline 3.82 & 2.26 \\
\hline 2.32 & 2.12 \\
\hline 3.97 & 2.71 \\
\hline 1.74 & 1.97 \\
\hline
\end{tabular}

A. Their means cannot be compared based on their mean absolute deviations because the mean absolute deviation for McKesson's rainfall is nearly twice that of Sansome's.

B. Their means cannot be compared based on their mean absolute deviations because the mean absolute deviation for Sansome's rainfall is nearly twice that of McKesson's.

C. The difference of the means of the two cities is 0.5.

D. The difference of the means of the two cities is 1.

Sagot :

GinnyAnswer
Sure! Let's analyze the given statements about the rainfall data in McKesson and Sansome for a particular week.

1. First, let's determine the mean rainfall for both cities:
- The mean rainfall in McKesson is approximately [tex]\(3.01\)[/tex] inches.
- The mean rainfall in Sansome is approximately [tex]\(2.51\)[/tex] inches.

2. Next, let's determine the mean absolute deviation (MAD) for both cities:
- The MAD for McKesson's rainfall is [tex]\(0.72\)[/tex] inches.
- The MAD for Sansome's rainfall is [tex]\(0.38\)[/tex] inches.

3. Now let's compute the difference of the means of the two cities:
- The difference in the means is [tex]\(3.01 - 2.51 = 0.5\)[/tex] inches.

4. Finally, let's analyze the given statements one by one:

- Statement 1: Their means cannot be compared based on their mean absolute deviations because the mean absolute deviation for McKesson's rainfall is nearly twice that of Sansome's.
- This statement is not true. Even though the MAD for McKesson's rainfall is nearly twice that of Sansome's, it does not imply that their means cannot be compared. Hence, this statement is false.

- Statement 2: Their means cannot be compared based on their mean absolute deviations because the mean absolute deviation for Sansome's rainfall is nearly twice that of McKesson's.
- This statement is not true. The MAD for Sansome's rainfall is not nearly twice that of McKesson's. Hence, this statement is also false.

- Statement 3: The difference of the means of the two cities is 0.5.
- This statement is true because the difference in the means is indeed [tex]\(0.5\)[/tex] inches.

- Statement 4: The difference of the means of the two cities is 1.
- This statement is not true. The difference in the means is [tex]\(0.5\)[/tex] inches, not [tex]\(1\)[/tex] inch.

Based on this analysis, the only correct statement from the given options is:

- The difference of the means of the two cities is [tex]\(0.5\)[/tex].
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