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Two theaters show the premiere of a new movie. The table shows the numbers of people who saw the movie each day during its opening week. Based on this information, which conclusion is true?

\begin{tabular}{|c|c|}
\hline
Theater 1 & Theater 2 \\
\hline
250 & 253 \\
\hline
235 & 241 \\
\hline
259 & 216 \\
\hline
255 & 222 \\
\hline
216 & 237 \\
\hline
225 & 248 \\
\hline
212 & 256 \\
\hline
\end{tabular}

A. The mean absolute deviation of the data for theater 1 is greater than the mean absolute deviation of the data for theater 2. This means the number of people who watched the movie each day during opening week in theater 1 was more consistent than in theater 2.

B. The mean absolute deviation of the data for theater 2 is greater than the mean absolute deviation of the data for theater 1. This means the number of people who watched the movie each day during opening week in theater 2 was more consistent than in theater 1.

C. The mean absolute deviation of the data for theater 2 is less than the mean absolute deviation of the data for theater 1. This means the number of people who watched the movie each day during opening week in theater 2 was more consistent than in theater 1.

D. The mean absolute deviation of the data for theater 1 is equal to the mean absolute deviation of the data for theater 2. This means the number of people who watched the movie each day in theater 1 and theater 2 were approximately the same during the week.



Answer :

GinnyAnswer
To determine which conclusion is correct, let's analyze the mean absolute deviations (MADs) and the means for the two theaters, as well as the implications based on these statistics.

1. Calculate the Mean Number of Viewers:
- For Theater 1: The mean is 236.0 viewers.
- For Theater 2: The mean is 239.0 viewers.

2. Calculate the Mean Absolute Deviation (MAD):
- For Theater 1: The MAD is 16.0.
- For Theater 2: The MAD is 12.0.

3. Interpret the Mean Absolute Deviation (MAD):
- The MAD measures the average distance between each data point and the mean of the data set. A lower MAD indicates that the data points are closer to the mean, implying more consistency in the number of viewers per day.

Now, let's compare the MAD values:
- Theater 1 has a MAD of 16.0.
- Theater 2 has a MAD of 12.0.

Since the MAD for Theater 2 (12.0) is less than the MAD for Theater 1 (16.0), the number of people who watched the movie each day during the opening week in Theater 2 was more consistent than in Theater 1.

Thus, the correct conclusion is:

C. The mean absolute deviation of the data for Theater 2 is less than the mean absolute deviation of the data for Theater 1. That means the number of people who watched the movie each day during opening week in Theater 2 was more consistent than in Theater 1.

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